Author name code: low ADS astronomy entries on 2022-09-14 =author:"Low, B.C." OR =author:"Low, Boon Chye" ------------------------------------------------------------------------ Title: Chapter 6 - Coronal Magnetism as a Universal Phenomenon Authors: Low, B. C. Bibcode: 2019sgsp.book..207L Altcode: In the 60 years after E. N. Parker's prediction of the existence of the solar wind and the magnetic origin of coronal heating, space-borne and ground-based observations have built a conceptually complete phenomenology of the corona as a fully ionized hydromagnetic atmosphere responding in step to the global magnetic reversals of the Sun in 11-year cycles. This phenomenology is reviewed with the theoretical ideas it motivated, describing the photospheric emergence of new-cycle magnetic fluxes of a reversed polarity into the corona, ubiquitous coronal heating, hydromagnetic self-organization, explosive energy release, and the breaking of self-confinement into flows of expansion winds and episodic ejections of magnetic structures. High electrical and thermal conductivities at coronal million-degree temperatures have central roles. The corona obeys a hemispherical rule independent of magnetic cycle, that self-organized structures have a statistical preference for left- and right-handed magnetic twists, respectively, in the northern and southern hemispheres relative to the rotational axis. It is pointed out, perhaps for the first time, that this hemispherical rule is a hydromagnetic implication of the Parker (1955a,b) dynamo, straightforward to deduce graphically from his book Cosmical Magnetic Fields (1979). Solar physics has reached a broad-brush physical understanding of the corona solar-wind system as the prototype of a universal astrophysical phenomenon. Title: Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics Authors: Low, B. C. Bibcode: 2015SCPMA..58.5626L Altcode: 2015SCPMA..58a5626L; 2014arXiv1412.6158L Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics: Eulerian and Lagrangian descriptions of three dimensional (3D) MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clarifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low- β limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results in sheet dissipation, resistive heating and topological changes in the field notwithstanding the small resistivity. Strong Faraday induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun's corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented. Title: The Rayleigh-Taylor Instability and the role of Prominences in the Chromosphere-Corona Mass Cycle Authors: Berger, Thomas; Liu, Wei; Hillier, Andrew; Scullion, Eamon; Low, Boon Chye Bibcode: 2014AAS...22421201B Altcode: We review recent results in the study of so-called "prominence bubbles", a buoyant instability discovered in quiescent solar prominences by the Hinode/SOT instrument in 2007. Analysis of the plasma flows along the boundary of the bubbles indicates that shear flows leading to Kelvin-Helmholtz instability waves can develop into the seed perturbations triggering the Rayleigh-Taylor instability. The non-linear phase of the RT instability leads to the formation of large turbulent plumes that transport the bubble plasma (and presumably magnetic flux) into the overlying coronal flux rope. We propose that the upward turbulent transport of hot bubble plasma and the downflows of cooler chromospheric plasma in the prominence are related aspects of a large-scale "chromosphere-corona mass cycle" in which hot plasma and magnetic flux and helicity from the chromosphere are transported upwards while the cooler prominence plasma downflows, which decouple from the magnetic field they are originally frozen-into, represent the condensation return flows of the cycle. This cycling enables a mechanism by which magnetic flux and helicity build up in the coronal flux rope while mass drains out of the flux rope, eventually triggering a "loss of confinement" eruption in the form of a CME. Title: A solar tornado caused by flares Authors: Panesar, N. K.; Innes, D. E.; Tiwari, S. K.; Low, B. C. Bibcode: 2014IAUS..300..235P Altcode: An enormous solar tornado was observed by SDO/AIA on 25 September 2011. It was mainly associated with a quiescent prominence with an overlying coronal cavity. We investigate the triggering mechanism of the solar tornado by using the data from two instruments: SDO/AIA and STEREO-A/EUVI, covering the Sun from two directions. The tornado appeared near to the active region NOAA 11303 that produced three flares. The flares directly influenced the prominence-cavity system. The release of free magnetic energy from the active region by flares resulted in the contraction of the active region field. The cavity, owing to its superior magnetic pressure, expanded to fill this vacated space in the corona. We propose that the tornado developed on the top of the prominence due to the expansion of the prominence-cavity system. Title: Coronal Condensation in Funnel Prominences as Return Flows of the Chromosphere-Corona Mass Cycle Authors: Liu, Wei; Berger, Thomas E.; Low, B. C. Bibcode: 2014IAUS..300..441L Altcode: We present SDO/AIA observations of a potentially novel type of prominence, called ``funnel prominence'', that forms out of coronal condensation at magnetic dips.

They can drain a large amount of mass (up to ~1015 g day-1) and may play an important role as return flows of the chromosphere-corona mass cycle. Title: Funnel Prominences as Return Flows of the Chromosphere-Corona Mass Cycle: SDO/AIA Observations of Coronal Condensation Authors: Liu, Wei; Berger, T.; Low, B. C. Bibcode: 2013SPD....44...42L Altcode: It has recently been proposed that prominences play an important role as return flows of the chromosphere-corona mass cycle, in which hot plasma is transported upward in forms of spicules and prominence bubbles (likely due to flux emergence), while cool plasma drains downward in forms of vertical prominence threads (Berger et al. 2011 Nature). A critical step in this cycle is the condensation of the million-degree coronal plasma into T<10,000 K prominence material by a radiative cooling instability (i.e., thermal non-equilibrium), as numerically simulated (Karpen & Antiochos 2008; Xia et al. 2012) and first evidenced in recent SDO/AIA observations (Liu et al. 2012; Berger et al. 2012 ApJL). Such a runaway cooling process occurs in coronal loops of various sizes and generally leads to condensation at magnetic dips and formation of funnel-shaped prominences. A moderate-sized prominence can drain a significant mass of typically 10^15 gram/day, which is comparable to the mass of a CME or a fraction of the entire corona. Here we present a survey of funnel prominences that appear to be common in AIA observations at various locations and times. We find longer cooling times in longer/taller coronal loops whose densities are lower, consistent with the expected quadratic dependence on density of the optically-thin radiative loss. We propose that such funnel prominences, usually small in size, can constitute a new type of prominences, and similar processes can produce elementary building blocks of large-scale quiescent prominences in filament channels. This picture is supported by the recent theoretical development on spontaneous formation of current sheets and condensations manifested as prominence threads (Low et al. 2012a, b, ApJ).Abstract (2,250 Maximum Characters): It has recently been proposed that prominences play an important role as return flows of the chromosphere-corona mass cycle, in which hot plasma is transported upward in forms of spicules and prominence bubbles (likely due to flux emergence), while cool plasma drains downward in forms of vertical prominence threads (Berger et al. 2011 Nature). A critical step in this cycle is the condensation of the million-degree coronal plasma into T<10,000 K prominence material by a radiative cooling instability (i.e., thermal non-equilibrium), as numerically simulated (Karpen & Antiochos 2008; Xia et al. 2012) and first evidenced in recent SDO/AIA observations (Liu et al. 2012; Berger et al. 2012 ApJL). Such a runaway cooling process occurs in coronal loops of various sizes and generally leads to condensation at magnetic dips and formation of funnel-shaped prominences. A moderate-sized prominence can drain a significant mass of typically 10^15 gram/day, which is comparable to the mass of a CME or a fraction of the entire corona. Here we present a survey of funnel prominences that appear to be common in AIA observations at various locations and times. We find longer cooling times in longer/taller coronal loops whose densities are lower, consistent with the expected quadratic dependence on density of the optically-thin radiative loss. We propose that such funnel prominences, usually small in size, can constitute a new type of prominences, and similar processes can produce elementary building blocks of large-scale quiescent prominences in filament channels. This picture is supported by the recent theoretical development on spontaneous formation of current sheets and condensations manifested as prominence threads (Low et al. 2012a, b, ApJ). Title: Newtonian and Non-Newtonian Magnetic-field Relaxations in Solar-coronal MHD Authors: Low, B. C. Bibcode: 2013ApJ...768....7L Altcode: This paper treats the relaxation of a magnetic field into a minimum-energy force-free state in a cold (pressure-less) viscous fluid, under the frozen-in condition of perfect electrical conductivity and letting the viscosity-dissipated energy be completely lost. A non-Newtonian fluid in popular use is studied in relation to the Newtonian viscous fluid, as two alternative numerical means to (1) construct force-free fields representing solar coronal structures in realistic geometry and (2) investigate the Parker theory of spontaneous formation of electric current sheets as a basic MHD process. Faraday's induction equation imposes an independent condition on the fluid velocity at rigid, perfectly conducting boundaries. This boundary condition is quite compatible with Newtonian mechanics but not with the non-Newtonian fluid model where velocity is equated to the Lorentz force with a free, positive multiplicative-factor. This defining property gives rise to unphysical or artificial singularities not previously known that are completely distinct from the physically admissible singularities representing the current sheets of the Parker theory. In particular, the non-Newtonian fluid takes a magnetic field with neutral points from any one of a continuum of initial states into an unphysical state instead of the proper force-free end-state accessible by Newtonian relaxation. The validity of previously published MHD results based on this non-Newtonian fluid, including some counterclaims against the Parker theory, is dubious. Investigating the Parker theory requires numerical relaxation models capable of anticipating and accurately describing inevitable current-sheet singularities. By including a weak resistivity to dissipate the inevitable current sheets as they form, the field can change topology intermittently to seek a terminal force-free state free of singularities. The minimum-energy state of this more complete model corresponds to the long-lived relaxed structures in the corona. Title: A solar tornado triggered by flares? Authors: Panesar, N. K.; Innes, D. E.; Tiwari, S. K.; Low, B. C. Bibcode: 2013A&A...549A.105P Altcode: 2012arXiv1211.6569P Context. Solar tornados are dynamical, conspicuously helical magnetic structures that are mainly observed as a prominence activity.
Aims: We investigate and propose a triggering mechanism for the solar tornado observed in a prominence cavity by SDO/AIA on September 25, 2011.
Methods: High-cadence EUV images from the SDO/AIA and the Ahead spacecraft of STEREO/EUVI are used to correlate three flares in the neighbouring active-region (NOAA 11303) and their EUV waves with the dynamical developments of the tornado. The timings of the flares and EUV waves observed on-disk in 195 Å are analysed in relation to the tornado activities observed at the limb in 171 Å.
Results: Each of the three flares and its related EUV wave occurred within ten hours of the onset of the tornado. They have an observed causal relationship with the commencement of activity in the prominence where the tornado develops. Tornado-like rotations along the side of the prominence start after the second flare. The prominence cavity expands with the accelerating tornado motion after the third flare.
Conclusions: Flares in the neighbouring active region may have affected the cavity prominence system and triggered the solar tornado. A plausible mechanism is that the active-region coronal field contracted by the "Hudson effect" through the loss of magnetic energy as flares. Subsequently, the cavity expanded by its magnetic pressure to fill the surrounding low corona. We suggest that the tornado is the dynamical response of the helical prominence field to the cavity expansion.

Movies are available in electronic form at http://www.aanda.org Title: SDO/AIA Detection of Solar Prominence Formation within a Coronal Cavity Authors: Berger, Thomas E.; Liu, Wei; Low, B. C. Bibcode: 2012ApJ...758L..37B Altcode: 2012arXiv1208.3431B We report the first analyses of SDO/AIA observations of the formation of a quiescent polar crown prominence in a coronal cavity. The He II 304 Å (log T max ~ 4.8 K) data show both the gradual disappearance of the prominence due to vertical drainage and lateral transport of plasma followed by the formation of a new prominence 12 hr later. The formation is preceded by the appearance of a bright emission "cloud" in the central region of the coronal cavity. The peak brightness of the cloud progressively shifts in time from the Fe XIV 211 Å channel, through the Fe XII 193 Å channel, to the Fe IX 171 Å channel (log T max ~ 6.2, 6.1, 5.8 K, respectively) while simultaneously decreasing in altitude. Filter ratio analysis estimates the initial temperature of the cloud to be approximately log T ~ 6.25 K with evidence of cooling over time. The subsequent growth of the prominence is accompanied by darkening of the cavity in the 211 Å channel. The observations imply prominence formation via in situ condensation of hot plasma from the coronal cavity, in support of our previously proposed process of magnetothermal convection in coronal magnetic flux ropes. Title: The Hydromagnetic Interior of a Solar Quiescent Prominence. II. Magnetic Discontinuities and Cross-field Mass Transport Authors: Low, B. C.; Liu, W.; Berger, T.; Casini, R. Bibcode: 2012ApJ...757...21L Altcode: This second paper of the series investigates the transverse response of a magnetic field to the independent relaxation of its flux tubes of fluid seeking hydrostatic and energy balance, under the frozen-in condition and suppression of cross-field thermal conduction. The temperature, density, and pressure naturally develop discontinuities across the magnetic flux surfaces separating the tubes, requiring the finite pressure jumps to be compensated by magnetic-pressure jumps in cross-field force balance. The tangentially discontinuous fields are due to discrete currents in these surfaces, δ-function singularities in the current density that are fully admissible under the rigorous frozen-in condition but must dissipate resistively if the electrical conductivity is high but finite. The magnetic field and fluid must thus endlessly evolve by this spontaneous formation and resistive dissipation of discrete currents taking place intermittently in spacetime, even in a low-β environment. This is a multi-dimensional effect in which the field plays a central role suppressed in the one-dimensional (1D) slab model of the first paper. The study begins with an order-of-magnitude demonstration that of the weak resistive and cross-field thermal diffusivities in the corona, the latter is significantly weaker for small β. This case for spontaneous discrete currents, as an important example of the general theory of Parker, is illustrated with an analysis of singularity formation in three families of two-dimensional generalizations of the 1D slab model. The physical picture emerging completes the hypothesis formulated in Paper I that this intermittent process is the origin of the dynamic interiors of a class of quiescent prominences revealed by recent Hinode/SOT and SDO/AIA high-resolution observations. Title: Granular-Scale Magnetic Flux Cancellations in the Photosphere Authors: Kubo, M.; Low, B. C.; Lites, B. W. Bibcode: 2012ASPC..454...41K Altcode: We find the unresolved flux removal process at the polarity inversion line formed by canceling opposite-polarity magnetic elements. Further details and results of this work can be seen in Kubo et al. (2010). Title: The Hydromagnetic Interior of a Solar Quiescent Prominence. I. Coupling between Force Balance and Steady Energy Transport Authors: Low, B. C.; Berger, T.; Casini, R.; Liu, W. Bibcode: 2012ApJ...755...34L Altcode: 2012arXiv1203.1056L This series of papers investigates the dynamic interiors of quiescent prominences revealed by recent Hinode and SDO/AIA high-resolution observations. This first paper is a study of the static equilibrium of the Kippenhahn-Schlüter diffuse plasma slab, suspended vertically in a bowed magnetic field, under the frozen-in condition and subject to a theoretical thermal balance among an optically thin radiation, heating, and field-aligned thermal conduction. The everywhere-analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system. For most values of the total mass frozen into a given bowed field, force balance and steady energy transport cannot both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness, within which the frozen-in condition must break down. An exact, resistive hydromagnetic extension of the Kippenhahn-Schlüter slab is also presented, resolving the mass-sheet singularity into a finite-thickness layer of steadily falling dense fluid. Our hydromagnetic result suggests that the narrow, vertical prominence Hα threads may be falling across magnetic fields, with optically thick cores much denser and ionized to much lower degrees than conventionally considered. This implication is discussed in relation to (1) the recent SDO/AIA observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors, (2) the canonical range of 5-60 G determined from spectral polarimetric observations of prominence magnetic fields over the years, and (3) the need for a more realistic multi-fluid treatment. Title: SDO/AIA Observations of Sustained Coronal Condensation in Prominences as Return Flows of the Chromosphere-Corona Mass Cycle Authors: Liu, Wei; Berger, T.; Low, B. C. Bibcode: 2012AAS...22020708L Altcode: It has recently been proposed that prominences are manifestations of a magneto-thermal convection process that involves ever-present dynamic descents of cool material threads and upflows of hot bubbles (Berger et al. 2011 Nature). On global scales, prominences may play an important role as the return flows of the chromosphere-corona mass cycle, in which hot mass is originally transported upward through spicules. A critical step in this cycle is the condensation of million-degree coronal plasma into T<10,000 K prominence material by radiative cooling instability. However, direct observation of coronal condensation has been difficult in the past, a situation recently changed. We present here the first example observed with SDO/AIA, in which hours of gradual cooling through multiple EUV channels (from 2 MK to 80,000 K) in large-scale loops leads to eventual condensation at magnetic dips, where we find evidence of magnetic reconnection and subsequent outflows. A moderate-size prominence of 10^14 gram is then formed. Its mass is not static but maintained by a continual supply through condensation at a high rate of 10^10 gram/s against a comparable drainage through numerous vertical threads at less than free-fall speeds. Most of the total condensation of 10^15 gram, comparable to a CME mass and an order of magnitude more than the instantaneous mass of the prominence itself, is drained in merely one day. These new observations show that a macroscopically quiescent prominence is microscopically dynamic (Liu, Berger, Low 2012 ApJL), involving the passage of a significant mass that bears important implications for the chromosphere-corona mass cycle. This interpretation is further supported by the recent theoretical development on spontaneous formation of current sheets and cool condensations (Low, Berger, Casini, & Liu, 2012 submitted to ApJ). Title: The Hydromagnetic Nature of Quiescent Prominences Authors: Low, B. C.; Berger, T.; Casini, R.; Liu, W. Bibcode: 2012decs.confE..84L Altcode: High-resolution observations of quiescent prominences with Hinode and SDO have revealed within their interiors the ever-¬present descent at less than free-fall speeds of cool, vertical dense filaments interspersed among upward, narrow streams at comparable speeds of heated, low-density plasma. We address the physical nature of this dynamical state. Despite the high magnetic Reynolds numbers characterizing this hydromagnetic environment, magnetic reconnection takes place via spontaneous formation and dissipation of current sheets by the coupled effects of highly-anisotropic thermal conduction, gravity, optically-thin radiation, heating, and high electrical conductivity. In this interesting new version of the theory of Parker (1994, Spontaneous current sheets in magnetic fields, Cambridge U Press), pervasive reconnections produce a perennial local descent of dense condensations under gravity along newly reconnected magnetic field lines and a concurrent turbulent rise of buoyant pockets of heated magnetized plasma through the large-scale magnetic structure. This mechanism may explain the massive downward drainage through a quiescent prominence observed recently (Liu et al. 2012 ApJ 745, L21) and, in the broader context, relate the quiescent prominence to the surrounding chromosphere/corona as a novel, large-scale, magneto-thermal convective phenomenon (Berger et al. 2011, Nature 472, 197). Title: SDO/AIA Observations of Sustained Coronal Condensation and Mass Drainage in Prominences as Return Flows of the Chromosphere-Corona Mass Cycle Authors: Liu, Wei; Berger, Thomas; Low, B. C. Bibcode: 2012decs.confE..90L Altcode: It has recently been proposed that prominences are manifestations of a magneto-thermal convection process that involves ever-present dynamic descents of cool material threads and upflows of hot bubbles (Berger et al. 2011 Nature). On global scales, prominences may play an important role as the return flows of the chromosphere-corona mass cycle, in which hot mass is originally transported upward through spicules. A critical step in this cycle is the condensation of million-degree coronal plasma into T<10,000 K prominence material by radiative cooling instability. However, direct observation of coronal condensation has been difficult in the past, a situation recently changed with the launch of the Hinode/SOT and SDO/AIA. We present here the first example observed with SDO/AIA, in which hours of gradual cooling through multiple EUV channels (from 2 MK to 80,000 K) in large-scale loops leads to eventual condensation at magnetic dips, forming a moderate-size prominence of 10^14 gram. The prominence mass is not static but maintained by a continual supply through condensation at a high rate of 10^10 gram/s against a comparable drainage through numerous vertical threads at less than free-fall speeds. Most of the total condensation of 10^15 gram, comparable to a CME mass and an order of magnitude more than the instantaneous mass of the prominence itself, is drained in merely one day. These new observations show that a macroscopically quiescent prominence is microscopically dynamic, involving the passage of a significant mass that bears important implications for the chromosphere-corona mass cycle. This interpretation is further supported by the recent theoretical development on spontaneous formation of current sheets and cool condensations (Low, Berger, Casini, & Liu, this meeting). Title: First SDO/AIA Observation of Solar Prominence Formation Following an Eruption: Magnetic Dips and Sustained Condensation and Drainage Authors: Liu, Wei; Berger, Thomas E.; Low, B. C. Bibcode: 2012ApJ...745L..21L Altcode: Imaging solar coronal condensation forming prominences was difficult in the past, a situation recently changed by Hinode and the Solar Dynamics Observatory (SDO). We present the first example observed with the SDO/Atmospheric Imaging Assembly, in which material gradually cools through multiple EUV channels in a transequatorial loop system that confines an earlier eruption. Nine hours later, this leads to eventual condensation at the dips of these loops, forming a moderate-size prominence of ~1014 g, to be compared to the characteristic 1015 g mass of a coronal mass ejection (CME). The prominence mass is not static but maintained by condensation at a high estimated rate of 1010 g s-1 against a comparable, sustained drainage through numerous vertical downflow threads, such that 96% of the total condensation (~1015 g) is drained in approximately one day. The mass condensation and drainage rates temporally correlate with the total prominence mass. The downflow velocity has a narrow Gaussian distribution with a mean of 30 km s-1, while the downward acceleration distribution has an exponential drop with a mean of ~1/6 g , indicating a significant canceling of gravity, possibly by the Lorentz force. Our observations show that a macroscopically quiescent prominence is microscopically dynamic, involving the passage of a significant mass through it, maintained by a continual mass supply against a comparable mass drainage, which bears important implications for CME initiation mechanisms in which mass unloading is important. Title: SDO/AIA Observations of Coronal Condensation Leading to Prominence Formation Authors: Liu, Wei; Berger, T.; Low, B. C.; Casini, R. Bibcode: 2011SPD....42.2119L Altcode: 2011BAAS..43S.2119L Coronal condensation takes place when million degree coronal plasma undergoes radiative cooling instability. Direct observation of coronal condensation in prominences has been difficult in the past, but with the launch of the Hinode/SOT and SDO/AIA instruments, numerous observations of plasma condensing "out of nowhere" high up in quiescent prominences have been captured. We present here one such event seen with SDO/AIA. On 25-Nov-2010, a prominence above the southwest limb is swept away by a nearby eruption, and for next a few hours there is no visible 304 A material in the local corona. Then, a portion of the coronal loops at the same location progressively sags and forms a local dip, where the first sign of new, cool material appears, 7.5 hours after the eruption. This is a clear indication of coronal condensation, and the gradual sag of the loops is likely a result of increasing weight of the condensed material that has been accumulated at the dip. Similar condensation occurs nearby at a larger rate and leads to the formation of a moderate-size prominence. The estimated prominence mass increases linearly for about 7 hours at a rate of 2.6e10 grams/sec and reaches approximately 6e14 grams. Simultaneously, the prominence drains through vertical flows of approximately 32 km/s, bringing the mass back to the chromosphere. We estimate the mass drain rate to be 2.7e10 grams/sec, which, together with the estimated mass accumulation rate, implies a coronal condensation rate of approximately 5.3e10 grams/sec. This study can provide critical information about the coupling between condensation energetics and MHD, prominence mass cycles, and coronal mass ejections initiated by loss of anchoring prominence mass (e.g., Low 2001). Title: Magneto-thermal convection in solar prominences Authors: Berger, Thomas; Testa, Paola; Hillier, Andrew; Boerner, Paul; Low, Boon Chye; Shibata, Kazunari; Schrijver, Carolus; Tarbell, Ted; Title, Alan Bibcode: 2011Natur.472..197B Altcode: Coronal cavities are large low-density regions formed by hemispheric-scale magnetic flux ropes suspended in the Sun's outer atmosphere. They evolve over time, eventually erupting as the dark cores of coronal mass ejections. Although coronal mass ejections are common and can significantly affect planetary magnetospheres, the mechanisms by which cavities evolve to an eruptive state remain poorly understood. Recent optical observations of high-latitude `polar crown' prominences within coronal cavities reveal dark, low-density `bubbles' that undergo Rayleigh-Taylor instabilities to form dark plumes rising into overlying coronal cavities. These observations offered a possible mechanism for coronal cavity evolution, although the nature of the bubbles, particularly their buoyancy, was hitherto unclear. Here we report simultaneous optical and extreme-ultraviolet observations of polar crown prominences that show that these bubbles contain plasma at temperatures in the range (2.5-12)×105 kelvin, which is 25-120 times hotter than the overlying prominence. This identifies a source of the buoyancy, and suggests that the coronal cavity-prominence system supports a novel form of magneto-thermal convection in the solar atmosphere, challenging current hydromagnetic concepts of prominences and their relation to coronal cavities. Title: Chromospheric Jet and Growing "Loop" Observed by Hinode: New Evidence of Fan-spine Magnetic Topology Resulting from Flux Emergence Authors: Liu, Wei; Berger, Thomas E.; Title, Alan M.; Tarbell, Theodore D.; Low, B. C. Bibcode: 2011ApJ...728..103L Altcode: 2010arXiv1012.1897L We present observations of a chromospheric jet and growing "loop" system that show new evidence of a fan-spine topology resulting from magnetic flux emergence. This event, occurring in an equatorial coronal hole on 2007 February 9, was observed by the Hinode Solar Optical Telescope in the Ca II H line in unprecedented detail. The predecessor of the jet is a bundle of fine material threads that extend above the chromosphere and appear to rotate about the bundle axis at ~50 km s-1 (period lsim200 s). These rotations or transverse oscillations propagate upward at velocities up to 786 km s-1. The bundle first slowly and then rapidly swings up, with the transition occurring at the onset of an A4.9 flare. A loop expands simultaneously in these two phases (velocity: 16-135 km s-1). Near the peak of the flare, the loop appears to rupture; simultaneous upward ejecta and mass downflows faster than free-fall appear in one of the loop legs. The material bundle then swings back in a whip-like manner and develops into a collimated jet, which is orientated along the inferred open-field lines with transverse oscillations continuing at slower rates. Some material falls back along smooth streamlines, showing no more oscillations. At low altitudes, the streamlines bifurcate at presumably a magnetic null point and bypass an inferred dome, depicting an inverted-Y geometry. These streamlines closely match in space the late Ca II H loop and X-ray flare loop. These observations are consistent with the model that flux emergence in an open-field region leads to magnetic reconnection, forming a jet and fan-spine topology. We propose that the material bundle and collimated jet represent the outer spine in quasi-static and eruptive stages, respectively, and the growing loop is a two-dimensional projection of the three-dimensional fan surface. Title: The Craig - Sneyd Analytic Solutions to the Parker Problem Authors: Low, B. C. Bibcode: 2010SoPh..266..277L Altcode: 2010SoPh..tmp..159L This paper follows up on the conclusion by Craig and Sneyd (2005) that the solutions to a linearized magnetostatic problem are counterexamples to the magnetostatic model of Parker (1972), demonstrating a general absence of continuous equilibrium for a magnetic field with an arbitrarily prescribed topology. The analysis presented here shows that Craig and Sneyd had incorrectly rejected an important subset of those solutions in a misunderstanding of the Parker model. The complete set of solutions when correctly interpreted is, in fact, physically consistent with the Parker model. A general discussion of the Parker theory of spontaneous current sheets is given. Title: The Topological Changes of Solar Coronal Magnetic Fields. III. Reconnected Field Topology Produced by Current-sheet Dissipation Authors: Janse, Å. M.; Low, B. C. Bibcode: 2010ApJ...722.1844J Altcode: In this paper, the third in a series of papers on topological changes of magnetic fields, we study how the dissipation of an initial current sheet (CS) in a closed three-dimensional (3D) field affects the field topology. The initial field is everywhere potential except at the location of the CS which is in macroscopic equilibrium under the condition of perfect conductivity. In the physical world of extremely high, but finite, conductivity, the CS dissipates and the field seeks a new equilibrium state in the form of an everywhere potential field since the initial field is everywhere untwisted. Our semi-analytical study indicates that the dissipation of the single initial CS must induce formation of additional CSs in extensive parts of the magnetic volume. The subsequent dissipation of these other sheets brings about topological changes by magnetic reconnection in order for the global field to become potential. In 2D fields, the magnetic reconnection due to the dissipation of a CS is limited to the magnetic vicinity of the dissipating sheet. Thus, the consequence of CS dissipation is physically and topologically quite different in 2D and 3D fields. A discussion of this result is given in general relation to the Parker theory of spontaneous CSs and heating in the solar corona and solar flares. Title: The Parker Magnetostatic Theorem Authors: Low, B. C. Bibcode: 2010ApJ...718..717L Altcode: 2010arXiv1002.4399L We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities. Title: Granular-scale Magnetic Flux Cancellations in the Photosphere Authors: Kubo, M.; Low, B. C.; Lites, B. W. Bibcode: 2010ApJ...712.1321K Altcode: 2010arXiv1003.2863K We investigate the evolution of five granular-scale magnetic flux cancellations just outside the moat region of a sunspot by using accurate spectropolarimetric measurements and G-band images with the Solar Optical Telescope (SOT) aboard Hinode. The opposite-polarity magnetic elements approach a junction of the intergranular lanes and then collide with each other there. The intergranular junction has strong redshifts, darker intensities than the regular intergranular lanes, and surface converging flows. This clearly confirms that the converging and downward convective motions are essential for the approaching process of the opposite-polarity magnetic elements. However, the motion of the approaching magnetic elements does not always match with their surrounding surface flow patterns in our observations. This suggests that, in addition to the surface flows, subsurface downward convective motions and subsurface magnetic connectivities are important for understanding the approach and collision of the opposite-polarity elements observed in the photosphere. We find that the horizontal magnetic field appears between the canceling opposite-polarity elements in only one event. The horizontal fields are observed along the intergranular lanes with Doppler redshifts. This cancellation is most probably a result of the submergence (retraction) of low-lying photospheric magnetic flux. In the other four events, the horizontal field is not observed between the opposite-polarity elements at any time when they approach and cancel each other. These approaching magnetic elements are more concentrated rather than gradually diffused, and they have nearly vertical fields even while they are in contact each other. We thus infer that the actual flux cancellations are highly time-dependent events at scales less than a pixel of Hinode SOT (about 200 km) near the solar surface. Title: Granular scale magnetic flux cancellations . Authors: Kubo, M.; Low, B. C.; Lites, B. W. Bibcode: 2010MmSAI..81..790K Altcode: We summarize the evolution of granular-scale ``magnetic-flux cancellation'' as observed with Hinode/SOT. Further details and results of this work are given in \citet{Kubo2009}. Title: Observations of Large-Scale Dynamic Bubbles in Prominences Authors: de Toma, G.; Casini, R.; Berger, T. E.; Low, B. C.; de Wijn, A. G.; Burkepile, J. T.; Balasubramaniam, K. S. Bibcode: 2009ASPC..415..163D Altcode: Solar prominences are very dynamic objects, showing continuous motions down to their smallest resolvable spatial and temporal scales. However, as macroscopic magnetic structures, they are remarkably stable during their quiescent phase. We present recent ground-based and Hinode observations of large-scale bubble-like, dynamic sub-structures that form within and rise through quiescent prominences without disrupting them. We investigate the similarities and differences of the Hinode and ground-based observations and discuss their implications for models of prominences. Title: Spontaneous Current Sheet Formation and Break-Up of Magnetic Flux Surfaces Authors: Bhattacharyya, R.; Low, B. C.; Smolarkiewicz, P. K. Bibcode: 2009ASPC..415..451B Altcode: The dynamics of spontaneous current sheet formation is demonstrated in a viscous, perfectly conducting, incompressible magnetofluid through numerical simulations. The magnetic field is represented in terms of evolving flux surfaces which are the possible sites of current sheet formation. The computation follows global magnetic flux surfaces of simple initial geometry as they deform into more complex forms creating current sheets in the process. Ultimately, the flux surfaces break their initial topology, as the spatial scale of surface folds decreases below the model resolution. This breaking is used to identify the sites of the current sheets formation. Title: Polarimetric Diagnostics of Unresolved Chromospheric Magnetic Fields Authors: Casini, R.; Manso Sainz, R.; Low, B. C. Bibcode: 2009ApJ...701L..43C Altcode: 2008arXiv0811.0512C For about a decade, spectropolarimetry of He I λ10830 has been applied to the magnetic diagnostics of the solar chromosphere. This resonance line is very versatile as it is visible both on disk and in off-limb structures, and it has a good sensitivity to both the weak-field Hanle effect and the strong-field Zeeman effect. Recent observations of an active-region filament showed that the linear polarization was dominated by the transverse Zeeman effect, with very little or no hint of scattering polarization. This is surprising, since the He I levels should be significantly polarized in a conventional scattering scenario. To explain the observed level of atomic depolarization by collisional or radiative processes, one must invoke plasma densities larger by several orders of magnitude than currently known values for prominences. We show that such depolarization can be explained quite naturally by the presence of an unresolved, highly entangled magnetic field, which averages to give the ordered field inferred from spectropolarimetric data, over the typical temporal and spatial scales of the observations. We present a modeling of the polarized He I λ10830 in this scenario, and discuss its implications for the magnetic diagnostics of prominences and spicules, and for the general study of unresolved magnetic field distributions in the solar atmosphere. Title: The Topological Changes of Solar Coronal Magnetic Fields. II. The Reclosing of an Opened Field Authors: Low, B. C.; Janse, Å. M. Bibcode: 2009ApJ...696..821L Altcode: This is a study of the spontaneous formation of current sheets responding to the closing of an opened magnetic field by resistive reconnection in an electrically, highly conducting atmosphere outside a unit sphere. Pairs of initial-final equilibrium states are calculated explicitly, taking the field to be composed of three systems of untwisted flux in both states. In the initial state, two of the three flux systems are closed potential fields whereas the third system contains an equilibrium current sheet that keeps the potential fields on its two sides globally open. The final state is an everywhere potential field, with all three flux systems closed, produced by the resistive dissipation of the current sheet in the initial state. The unit sphere is taken to be a rigid, perfectly conducting wall during reconnection, so that the normal flux distribution is unchanged on the unit sphere. Field solutions subject to this unchanging boundary condition are obtained with and without the assumption of axisymmetry. The mathematical model has been designed to show that the topological changes produced by the current-sheet dissipation are simple under axisymmetry but radically different in the absence of axisymmetry, a fundamental point established in the first paper of this series. In the general case, the topological changes imply that other current sheets must have formed. Some of these current sheets form on the separatrix flux surfaces of the multipolar field. Others form throughout the closed-flux systems induced by volumetric changes. The opening and reclosing of magnetic fields during a solar coronal mass ejection may produce a multitude of current sheets not previously anticipated in the current understanding of this phenomenon. Basic to this study is a general topological property of magnetic flux tubes treated separately in the Appendix. Title: The Topological Changes of Solar Coronal Magnetic Fields. I. Spontaneous Current Sheets in Three-Dimensional Fields Authors: Janse, Å. M.; Low, B. C. Bibcode: 2009ApJ...690.1089J Altcode: We present mathematical models to demonstrate the inevitability of current-sheet formation in a cylindrical magnetic field governed by the ideal hydromagnetic induction equation, as described by the Parker theory. This process, central to the heating of the solar corona, is radically different in fully three-dimensional fields as compared with two-dimensional fields. Magnetic neutral points or separatrix flux surfaces are necessary for sheet formation in two-dimensional fields. In fully three-dimensional fields, current sheets form readily even in the complete absence of neutral points and separatrix surfaces, and these sheets can form densely throughout the field in response to changes in the magnetic volume. This general result is established for cylindrical fields that are topologically untwisted, including the first direct demonstration of sheet formation in the absence of any magnetic neutral point. We discuss simple implications of this basic result for solar flares and coronal heating. In subsequent papers, we apply our result to coronal mass ejections and solar flares. Title: Magnetic Relaxation in the Solar Corona Authors: Miller, Kenneth; Fornberg, Bengt; Flyer, Natasha; Low, B. C. Bibcode: 2009ApJ...690..720M Altcode: This is a mathematical study of the long-lived hydromagnetic structures produced in the tenuous solar corona by the turbulent, resistive relaxation of a magnetic field under the condition of extremely high electrical conductivity. The relaxation theory of Taylor, originally developed for a laboratory device, is extended to treat the open atmosphere where the relaxing field must interact with its surrounding fields. A boundary-value problem is posed for a two-dimensional model that idealizes the corona as the half Cartesian plane filled with a potential field (1) that is anchored to a rigid, perfectly conducting base and (2) that embeds a force-free magnetic field in the form of a flux-rope oriented horizontally and perpendicular to the Cartesian plane. The flux-rope has a free boundary, which is an unknown in the construction of a solution for this atmosphere. Pairs of magnetostatic solutions are constructed to represent the initial and final states of a flux-rope relaxation that conserve both the total magnetic helicity and total axial magnetic flux, using a numerical iterative method specially developed for this study. The collection of numerical solutions found provides an insight into the interplay among several hydromagnetic properties in the formation of long-lived coronal structures. In particular, the study shows (1) that the outward spread of reconnection between a relaxing flux-rope and its external field may be arrested at some outer magnetic flux surface within which a constant-α force-free field emerges as the minimum-energy state and (2) that this outward spread is complicated by an inward, partial collapse of the relaxing flux-rope produced by a loss of internal magnetic pressure. Title: Magnetically driven activity in the solar corona: a path to understanding the energetics of astrophysical plasmas Authors: Gibson, Sarah; Bastian, Tim; Lin, Haoscheng; Low, B. C.; Tomczyk Bibcode: 2009astro2010S..94G Altcode: No abstract at ADS Title: Rise of a Dark Bubble through a Quiescent Prominence Authors: de Toma, G.; Casini, R.; Burkepile, J. T.; Low, B. C. Bibcode: 2008ApJ...687L.123D Altcode: We report on a dynamical event observed in a quiescent prominence on 2007 November 8: a well-formed dark "bubble" with a bright core rose vertically through the prominence without causing it to erupt. This event was observed in Hα and He I 1083 nm with the instruments of the Mauna Loa Solar Observatory. The dark bubble had a size of over 40'' and rose from the prominence base, at an average speed of ~12 km s-1, forming a bright compression front as it traversed the prominence. It finally assumed a "keyhole" shape before fading. The bright core embedded in the dark bubble was observed to rise from the solar limb, accelerating from ~12 to ~20 km s-1, leaving a thin trail of material behind. Subsequent observations indicate that this was not an exceptional event, but rather that similar disturbances do occur occasionally in prominences without disrupting them. In this Letter we present the November 8 observations, and propose a possible interpretation of the physical mechanism behind these dynamic events. Title: Parker spontaneous current-sheets in topologically untwisted magnetic fields Authors: Low, B. C. Bibcode: 2008iac..talk..202L Altcode: 2008iac..talk....5L No abstract at ADS Title: The Solar Interior-Atmospheric System Authors: Athay, R. G.; Low, B. C.; White, O. R. Bibcode: 2008ASPC..383..315A Altcode: This article discusses an unpublished paradigm by Athay that relates the general properties of the solar photosphere, chromosphere, and corona to the stream of photons, kinetic energy, and magnetic fields flowing from the solar interior. Using the Athay paradigm, we discuss the physics of the solar atmosphere and its coupling to the solar dynamo to clarify the connection of observed structures and variations in the three layers to their hydromagnetic interpretation. The details of the eleven-year cycles of solar activity are quite different, but each cycle exhibits two invariant features. First, the chromosphere and corona are always present above the photosphere in its turbulent state maintained by the radiative flux escaping at the surface as the solar luminosity. Second, the solar magnetic field is globally reversed early in each cycle, accompanied by systematic drifts in magnetic activity shown in the sunspot butterfly diagram of each cycle. We describe a scenario for the corresponding systematic changes in the upper solar atmosphere that recover the minimum-activity corona from one cycle to the next. We discuss in some detail the mechanisms that heat the atmosphere and process the magnetic flux continually emerging from the interior, providing a unified view of the interior-atmospheric system. Title: The Topological Nature of Boundary Value Problems for Force-Free Magnetic Fields Authors: Low, B. C.; Flyer, N. Bibcode: 2007ApJ...668..557L Altcode: The difficulties of constructing a three-dimensional, continuous force-free magnetic field in the solar corona are investigated through a boundary value problem posed for the unbounded domain external to a unit sphere. The normal field component Bn and the boundary value αb of the twist function α on the unit sphere, combined with the demand for a vanishing field at infinity, do constitute sufficient conditions for determining a solution if it exists, but Bn and αb cannot be prescribed independently. An exhaustive classification of the admissible (Bnb)-pairs is developed, using the topological properties of the α flux surfaces implied by their footprints described by the constant-αb curves on the unit sphere. The incompatibilities arising from boundary conditions contradicting the field equations are distinguished from the interesting one of (Bnb) being, in principle, admissible but requiring a weak solution describing a force-free field containing inevitable magnetic tangential discontinuities. This particular incompatibility relates the boundary value problem to the Parker theory of spontaneous current sheets in magnetic fields embedded in electrically perfectly conducting fluids. Our investigation strategically skirts around some important but formidable mathematical problems to arrive at physically definite conclusions and insights on the construction of force-free fields, both in the practical task of modeling coronal magnetic fields with magnetopolarimetric data and in the basic understanding of the Parker theory. Two specific demonstrations of (Bnb) are given to illustrate circumstances under which a continuous solution to the boundary value may or may not exist. Title: Coronal hydromagnetic implosions Authors: Janse, Å. M.; Low, B. C. Bibcode: 2007A&A...472..957J Altcode: Aims:The released magnetic energy in coronal events, i.e. in flares and coronal mass ejections (CMEs), is believed to have been stored locally in the coronal magnetic field. The energy in a magnetic field B is distributed in space with density {B2 over 8 π} that is also the isotropic magnetic pressure at each point in space. A localized release of magnetic energy would therefore imply a localized reduction of magnetic pressure. Hence, such a release could lead to an implosion of the magnetic structure as its atmospheric surrounding pushes inward. Whether an implosion would take place immediately depends on how fast the released energy can escape, through optically-thin radiation, thermal conduction, hydromagnetic waves, and, the magnetic channeling of high-energy particles.
Methods: We determined whether an expansion or an implosion would occur when cylindrical tubes of twisted flux relaxed to lower energy states. Depending on the dynamical nature of the relaxation we assumed, relevant dynamical invariants were invoked to relate a particular end state to the given initial state.
Results: Comparing the initial and the end state, we found that when most of the liberated energy escaped the cylinder imploded. The results suggest that implosions may take place simultaneously with flares and CMEs. Title: Spectral Lines for Polarization Measurements of the Coronal Magnetic Field. IV. Stokes Signals in Current-carrying Fields Authors: Judge, P. G.; Low, B. C.; Casini, R. Bibcode: 2006ApJ...651.1229J Altcode: We present the first theoretical, forward calculations of the Stokes profiles of several magnetic dipole (``M1'') coronal emission lines produced in current-carrying magnetic structures. An idealized coronal model of Low, Fong, and Fan is used, which describes a spherically symmetric, hydrostatic background atmosphere, isothermal at a coronal temperature of 1.6×106 K. Embedded is a global, axisymmetric magnetic field that is everywhere potential except at a quiescent prominence, consisting of an infinitesimally thin, equatorial current sheet whose weight is supported by the outward discrete Lorentz force in the sheet. This model contains a physically nontrivial, localized magnetic structure, although the atmospheric plasma is thermally of the simplest stratification possible. The calculated M1 coronal lines show clear and distinct signatures of the presence and magnitude of this localized magnetic structure, in both linear and circular polarizations, even though the thermal structure is almost homogeneous. The morphology of maps of linear polarization is particularly sensitive to the existence and strength of the current sheets, as field lines wrap around them according to the Biot-Savart law, and the linear polarization responds to different projections of field line directions onto local radius vectors. Of the M1 lines studied, those of Fe XIII (1074.7 nm) and Si X (1430.1 nm) are especially promising because of their relatively strong linear polarization. These forward calculations provide a basis for optimism that emission-line measurements may reveal the presence and nature of current systems in the corona, and provide motivation for developing instruments capable of routinely measuring polarized light in forbidden coronal lines. Title: Spontaneous Current Sheets in an Ideal Hydromagnetic Fluid Authors: Low, B. C. Bibcode: 2006ApJ...649.1064L Altcode: Parker's theory of spontaneous current sheets, or magnetic tangential discontinuities, in electrically perfectly conducting fluids is demonstrated for globally untwisted magnetic fields in the Chandrasekhar-Kendall representation. All the three-dimensional, globally untwisted fields sharing the same flux distribution, fixed at the rigid boundary of the domain, span an infinity of different field topologies, each preserved in a field under the frozen-in condition. The general result is obtained and illustrated that only one of these topologies allows a field to relax into an everywhere continuous force-free state, namely, the potential field uniquely determined by the boundary flux distribution. All other topologies require the field to find a force-free state containing inevitable tangential magnetic discontinuities. This result extends a class of two-dimensional demonstrations of the Parker theory to three dimensions. A field of a fixed topology and boundary flux distribution can be in a continuous state in one equilibrium but may have to contain inevitable tangential discontinuities on transition to another equilibrium. This property, demonstrated here with untwisted fields, is probably the hydromagnetic origin of flares occurring in the course of slow evolution in the solar corona. Title: Magnetic Helicity in a Two-Flux Partitioning of an Ideal Hydromagnetic Fluid Authors: Low, B. C. Bibcode: 2006ApJ...646.1288L Altcode: A primitive form of magnetic helicity is constructed that (1) recovers the classical helicity of a wholly contained magnetic field, as well as the Berger-Field relative helicity of a partially contained magnetic field, and (2) generalizes the infinity of global, helicity-like invariants derived by Bhattacharjee & Dewar for a plasma approaching toroidal magnetostatic equilibrium. This construction is based on a general partitioning of an ideal hydromagnetic fluid into disjoint, infinitesimally thin, toroidal subvolumes using a two-flux description of the embedded magnetic field. Each of these toroidal subvolumes of fluid is endowed with a gauge-independent magnetic helicity conserved during its ideal Lagrangian evolution. This conservation law constitutes an equivalent statement of the frozen-in condition. The Chandrasekhar-Kendall solenoidal representation of a magnetic field is conceptually related to the two-flux description in the basic theory developed. Magnetic helicity-related phenomena in the solar corona are briefly discussed to provide an astrophysical context for this basic development, postponing proper applications to the papers to follow. Title: Magnetic Field Confinement in the Corona: The Role of Magnetic Helicity Accumulation Authors: Zhang, Mei; Flyer, Natasha; Low, Boon Chye Bibcode: 2006ApJ...644..575Z Altcode: 2006astro.ph..3011Z A loss of magnetic field confinement is believed to be the cause of coronal mass ejections (CMEs), a major form of solar activity in the corona. The mechanisms for magnetic energy storage are crucial in understanding how a field may possess enough free energy to overcome the Aly limit and open up. Previously, we have pointed out that the accumulation of magnetic helicity in the corona plays a significant role in storing magnetic energy. In this paper, we investigate another hydromagnetic consequence of magnetic-helicity accumulation. We propose a conjecture that there is an upper bound on the total magnetic helicity that a force-free field can contain. This is directly related to the hydromagnetic property that force-free fields in unbounded space have to be self-confining. Although a mathematical proof of this conjecture for any field configuration is formidable, its plausibility can be demonstrated with the properties of several families of power-law, axisymmetric force-free fields. We put forth mathematical evidence, as well as numerical, indicating that an upper bound on the magnetic helicity may exist for such fields. Thus, the accumulation of magnetic helicity in excess of this upper bound would initiate a nonequilibrium situation, resulting in a CME expulsion as a natural product of coronal evolution. Title: The Internal Structures and Dynamics of Solar Quiescent Prominences Authors: Petrie, G. J. D.; Low, B. C. Bibcode: 2005ASPC..346..211P Altcode: We present generalized Kippenhahn-Schlüter (KS) equilibrium solutions of the magnetohydrodynamic (MHD) equations, constructed of arrays of laminated isothermal (KS) prominence sheets whose temperatures, sag angles and dip positions may vary arbitrarily from sheet to sheet. This great versatility allows us to model the filamentary structure of prominences and illustrate why their observed dimensions differ from their characteristic hydrostatic scale lengths. We also apply these equilibria to investigate the role of internal prominence motions in solar magnetism. The solar corona is continually being injected with magnetic flux from the solar interior, flux that cannot be annihilated in bulk by the electrically highly conducting corona. Ascending small-scale structures as well as large-scale eruptions of prominences may both serve to carry excess magnetic flux out of the corona. This process is investigated with an interest in the dissipation of tangential discontinuities forming spontaneously in the supporting magnetic field of a prominence. The net effect of the magnetic reconnection is a downflow of mass accompanied by an upward transport of magnetic flux. This effect may play an important, direct and indirect, role in ejecting magnetic flux from the corona into interplanetary space. Thin counter-streaming layers of prominence plasma predicted by this work have already been observed. Title: Magnetic Field Confinement in the Solar Corona. II. Field-Plasma Interaction Authors: Flyer, N.; Fornberg, B.; Thomas, S.; Low, B. C. Bibcode: 2005ApJ...631.1239F Altcode: The numerical study of axisymmetric force-free magnetic fields in the unbounded space outside a unit sphere, presented in the first paper of this series, is extended to treat twisted fields in static equilibrium with plasma pressure and weight in a polytropic atmosphere. The study considers dipolar magnetic fields all sharing the same boundary flux distribution on the unit sphere and characterized with (1) a nonlinear distribution of its azimuthal field component expressed as a power of the poloidal flux function and (2) a plasma distribution varying linearly with the poloidal flux function. Nonlinear boundary value problems are solved numerically to generate a continuum of solutions with two parameters to control the total azimuthal flux and the strength of field-plasma interaction. The study includes the force-free fields of the first paper as a special case. Models with polytropic indices Γ=7/6, 14/11 are treated to show the interplay between the degree of magnetic twist and hydrostatic stratification in determining atmospheric structures, with particular interests in magnetic flux ropes and their storage of magnetic energy and azimuthal flux at levels above those bounds applicable to force-free fields. The concluding discussion relates physical insights from the study to the solar corona and the energetics of coronal mass ejections and flares. Title: The Hydromagnetic Nature of Solar Coronal Mass Ejections Authors: Zhang, Mei; Low, Boon Chye Bibcode: 2005ARA&A..43..103Z Altcode: Solar coronal mass ejections (CMEs) are a major form of activity on the Sun. A CME takes 1015-16 g of plasma from the low corona into the solar wind, to disturb the near-Earth space if the CME direction is favorable. We summarize current observations and ideas of CME physics to provide a hydromagnetic view of the CMEs as the products of continual magnetic flux emergence and an interplay between magnetic reconnection and approximate magnetic-helicity conservation in the corona. Each flux emergence brings helicity to accumulate additively in a coronal structure while excess magnetic energy is flared away by reconnection. Self-confinement eventually fails with a CME shedding the accumulated helicity out of the low corona to enable the field to reach the minimum-energy state. Similar evolutionary processes may occur in other magnetic stars and galaxies. Title: The Dynamical Consequences of Spontaneous Current Sheets in Quiescent Prominences Authors: Petrie, G. J. D.; Low, B. C. Bibcode: 2005ApJS..159..288P Altcode: The solar corona is continually being injected with magnetic flux from the solar interior, flux that cannot be annihilated in bulk by the electrically highly conducting corona. Observations have shown that mass loss through downflows within solar prominences may be responsible for the ascent and eventual eruption of these prominences. Ascending small-scale structures as well as large-scale eruptions of prominences may both serve to carry excess magnetic flux out of the corona. We investigate the dissipation and field reconnection across the tangential discontinuities that form spontaneously in the supporting magnetic field of a prominence. Our analysis of a variety of postdissipation, nonequilibrium states provides instructive insights into the observable motions in prominences. The net effect of the magnetic reconnection is a downflow of mass accompanied by an upward transport of magnetic flux. This effect may play an important, direct and indirect, role in ejecting magnetic flux from the corona into interplanetary space. Shock waves are a natural consequence of this dissipative process, and their detection may serve as a diagnostic observational tool. Thin counterstreaming layers of prominence plasma predicted by this work have already been observed. Title: The Internal Structures and Dynamics of Solar Quiescent Prominences Authors: Low, B. C.; Petrie, G. J. D. Bibcode: 2005ApJ...626..551L Altcode: We present generalized Kippenhahn-Schlüter (KS) equilibrium and steady-flow solutions of the magnetohydrodynamic (MHD) equations. These solutions are constructed of arrays of laminated isothermal KS prominence sheets whose temperatures, sag angles, and dip positions may vary arbitrarily from sheet to sheet. Moreover, the sheets can move at arbitrary constant uniform velocities relative to each other within their planes. This great versatility allows us to model the filamentary structure of prominences and illustrate why their observed dimensions differ from their characteristic hydrostatic scale lengths. We are also able to explain observed vertical and horizontal velocities as naturally arising steady rigid motions of plasma sheets in local force equilibrium but global nonequilibrium. Title: Three-dimensional Structures of Magnetostatic Atmospheres. VII. Magnetic Flux Surfaces and Boundary Conditions Authors: Low, B. C. Bibcode: 2005ApJ...625..451L Altcode: We treat a long-standing difficulty with the boundary conditions for the governing equations derived in the third paper of this series describing magnetic fields in equilibrium in a three-dimensional atmosphere. The force-free magnetic fields are special cases of this magnetostatic model. Among the flux surfaces of these magnetic fields, those of constant twist parameter, the so-called α-surfaces, have a basic topological property previously pointed out by Aly for force-free fields. This property dictates a natural set of boundary conditions for the field equations and can be used to reduce the vector field equations to a novel form, illustrated here with analytical examples of three-dimensional force-free fields. The physical implications of this theoretical development for solar coronal magnetic fields are discussed. Title: Magnetostatic Structures of the Solar Corona. III. Normal and Inverse Quiescent Prominences Authors: Low, B. C.; Zhang, M. Bibcode: 2004ApJ...609.1098L Altcode: Analytical solutions describing equilibrium magnetic fields in the solar corona, deformed by prominence-like plasma condensations in the Cartesian plane, are treated in this paper. The equilibrium equations for this class of problems usually take different forms in distinct subdomains, separated by free boundaries to be solved as one of the unknowns, across which solutions on the two sides are matched by suitable jump conditions. By idealizing the plasma condensations as a horizontal, circular cylinder whose weight in a uniform gravitational field is supported by an external magnetic field, we avoid solving free-boundary problems and present a method to directly construct solutions presenting prominence magnetic fields in the so-called normal and inverse configurations. The solutions illustrate the morphologies of plasma and vector magnetic field distributions in the cylindrical condensations in relation to the magnetic fields beneath the condensations. These solutions provide theoretical magnetic field properties that may be relevant to the current renewed interest in observing solar prominence magnetic fields by polarimetric spectroscopy. Title: Magnetic Field Confinement in the Solar Corona. I. Force-free Magnetic Fields Authors: Flyer, N.; Fornberg, B.; Thomas, S.; Low, B. C. Bibcode: 2004ApJ...606.1210F Altcode: Axisymmetric force-free magnetic fields external to a unit sphere are studied as solutions to boundary value problems in an unbounded domain posed by the equilibrium equations. It is well known from virial considerations that stringent global constraints apply for a force-free field to be confined in equilibrium against expansion into the unbounded space. This property as a basic mechanism for solar coronal mass ejections is explored by examining several sequences of axisymmetric force-free fields of an increasing total azimuthal flux with a power-law distribution over the poloidal field. Particular attention is paid to the formation of an azimuthal rope of twisted magnetic field embedded within the global field, and to the energy storage properties associated with such a structure. These sequences of solutions demonstrate (1) the formation of self-similar regions in the far global field where details of the inner boundary conditions are mathematically irrelevant, and (2) the possibility that there is a maximum to the amount of azimuthal magnetic flux confined by a poloidal field of a fixed flux anchored rigidly to the inner boundary. The nonlinear elliptic boundary value problems we treat are mathematically interesting and challenging, requiring a specially designed solver, which is described in the Appendix. Title: The Filamentary Structures of Quiescent Prominences Authors: Low, B. C.; Petrie, G. J. D. Bibcode: 2004AAS...204.5503L Altcode: 2004BAAS...36Q.761L We present examples from a rich family of magnetostatic solutions describing sheets of vertical filamentary plasmas suspended in a bow-shaped magnetic field. These solutions are characterized with the realism of uneven loadings of mass on the field lines which produces a sheared field topology associated with a coupling between the field-aligned and cross-field current densities. These analytical models are useful for forward calculations of prominence emission and absorption, as well as the polarimetric signatures of prominence magnetic fields.

The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Magnetic Energy Storage in the Two Hydromagnetic Types of Solar Prominences Authors: Zhang, M.; Low, B. C. Bibcode: 2004ApJ...600.1043Z Altcode: We present analytical solutions that describe the hydromagnetic support of solar prominences in two characteristic configurations, called normal and inverse. We model the corona as axisymmetric outside a unit sphere and treat the prominence as a distributed cold plasma inside a purely azimuthal magnetic flux rope, held in equilibrium by the prominence weight and by an external poloidal magnetic field rigidly anchored to the base of the modeled corona. We focus on the storage of magnetic energy, in particular its potential for driving solar coronal mass ejections (CMEs). Our calculations indicate that both characteristic magnetic configurations are capable of storing enough magnetic energy to overcome the Aly limit for opening up an initially closed magnetic field. These calculations also indicate that magnetic topology is an important influence in magnetic energy storage. Fields with a normal configuration are more likely to attain energetic states leading to CME-type expulsions than those with an inverse configuration, a property we use to explain Leroy's observations of the height distributions of the two types of solar prominences. Title: Coronal mass ejections and solar magnetism Authors: Low, B. C. Bibcode: 2004cosp...35..496L Altcode: 2004cosp.meet..496L The ultimate cause of activity in the solar corona is magnetic-flux emergence culminating in the reversal of the solar global magnetic field in the early part of each eleven-year cycle. The million-degree corona is effectively a perfect electrical conductor and yet is resistively dissipative through the Parker process of spontaneous current sheets. It is in such a hydromagnetic atmosphere where the magnetic flux of a new cycle must mix with the opposite flux of the old cycle. Although the corona is structurally complex and rapidly evolving during a field reversal, its characteristic activity-minimum form is faithfully recovered in each cycle. Coronal mass ejections play a central role in this remarkable phenomenon. I will describe this view of the corona to point out its implication that magnetic flux systems may be bodily transported from the solar interior first into the corona and then out as coronal mass ejections into the solar wind. This global process couples the corona to the solar dynamo. Title: The Mass of a Solar Quiescent Prominence Authors: Low, B. C.; Fong, B.; Fan, Y. Bibcode: 2003ApJ...594.1060L Altcode: This paper follows up on our recent paper on the role of prominence mass in the storage of magnetic energy for driving a coronal mass ejection (CME). The previous paper erroneously rejected a set of sheet-prominence solutions, the recovery of which allows for a simple theoretical estimate of the mass of a quiescent prominence. For coronal fields of 5-10 G, these hydromagnetic solutions suggest that a prominence mass of (1-26)×1016 g is needed to hold detached magnetic fields of intensity comparable to the coronal fields in an unbounded atmosphere such that the global magnetic field is energetically able to spontaneously open up and still have enough energy to account for the kinetic and gravitational potential energies carried away in a CME. This simple result is discussed in relation to observed prominence magnetic field intensities, densities, and masses, pointing to the relevance of such observations to the question of magnetic energy storage in the solar corona. Title: A Morphological Study of Helical Coronal Magnetic Structures Authors: Low, B. C.; Berger, M. A. Bibcode: 2003ApJ...589..644L Altcode: Magnetostatic solutions describing magnetic flux ropes in realistic geometry are used to study solar coronal structures observed to have sigmoidal forms in soft X-rays. These solutions are constructed by embedding a rope of helically symmetric force-free magnetic fields in an external field such that force balance is assured everywhere. The two observed sigmoidal shapes, the S shapes and the mirror-reflected S shapes referred to as Z shapes in this paper, are found in both hemispheres of the solar corona, but observations made over the last two solar cycles suggest that the Z and S shapes occur preferentially in the northern and southern solar hemispheres, respectively. Our study makes an identification of the sigmoidal high-temperature coronal plasmas with heating by the spontaneous formation of current sheets described by the theory of Parker. This process involves a tangential discontinuity developing across a ribbon-like, twisted flux surface through an interaction between a magnetic flux rope and the photosphere, under conditions of high electrical conductivity. In this identification, Z- and S-shaped sigmoids are associated with flux ropes with negative and positive magnetic helicities, respectively. This association is physically consistent with the conclusion, based independently on measurements of prominence magnetic fields, that magnetic flux ropes occur preferentially with negative and positive helicities in the northern and southern solar hemispheres, respectively. Title: Magnetic Flux Emergence into the Solar Corona. III. The Role of Magnetic Helicity Conservation Authors: Zhang, M.; Low, B. C. Bibcode: 2003ApJ...584..479Z Altcode: This paper treats the reconfiguration of a twisted magnetic field, from an initial two-flux system containing a current sheet to a minimum-energy state, under the conservation of total relative magnetic helicity. In the specific model presented, we assume that a fresh magnetic field of the opposite polarity has emerged into a corona containing a preexisting magnetic field, both represented by constant-α force-free fields with the same constant α. The magnetic reconnection that takes place between the two twisted magnetic flux systems during a relaxation is assumed to take the field to a minimum-energy state that keeps the total relative magnetic helicity conserved. Our calculations suggest that this kind of relaxation may result in the formation of magnetic flux ropes and may change the twist directions in flux ropes in situations where flux ropes exist in the emerging or preexisting fields. These effects are all due to the interplays between the internal magnetic helicities of the two flux systems and their mutual magnetic helicity, with redistribution of these helicities through magnetic reconnection. In the absence of an interior current sheet, the lowest α force-free field always has the minimum magnetic energy for a given magnetic helicity, as Berger has shown. When an interior current sheet is present, this result breaks down. The lowest α force-free magnetic field with an interior equilibrium current sheet does not always have the minimum magnetic energy for a given total magnetic helicity. Implications of our results for flux emergence in the solar corona are also addressed. Title: Magnetic Reconnection and the Solar Corona (Invited review) Authors: Low, B. C. Bibcode: 2003ASPC..286..335L Altcode: 2003ctmf.conf..335L No abstract at ADS Title: Dynamics of CME Driven by a Buoyant Prominence Flux Tube Authors: Fan, Y.; Low, B. C. Bibcode: 2003ASPC..286..347F Altcode: 2003ctmf.conf..347F No abstract at ADS Title: Magnetic flux ropes: Would we know one if we saw one? Authors: Gibson, S. E.; Low, B. C.; Leka, K. D.; Fan, Y.; Fletcher, L. Bibcode: 2002ESASP.505..265G Altcode: 2002IAUCo.188..265G; 2002solm.conf..265G There has been much debate lately about whether twisted magnetic flux ropes exist in the corona. When asked for observational evidence of them, the temptation is to show images of apparently twisted structures. However, we must be very careful of projection effects in interpreting these observations. Two critical aspects of understanding how we might observe flux ropes are 1) the 3D nature of the flux rope, and 2) physically, which bits are visible and for what reasons? In this paper we will use a simple but physically reasonable 3D analytic model to address these two issues, and develop techniques that can in future be used on more general models, both analytic and numerical. Title: Magnetic coupling between the corona and the solar dynamo Authors: Low, B. C. Bibcode: 2002ESASP.505...35L Altcode: 2002solm.conf...35L; 2002IAUCo.188...35L We summarize published works describing the behavior of the large-scale solar corona over an 11-year solar cycle. This hydromagnetic description goes beyond magnetic flux emergence, flares, coronal mass ejections, prominences and their related structures as individual events to see their collective role in the coronal reversal of the global magnetic field in response to the solar dynamo. Central to this process is an implied transport of systems of twisted magnetic flux from the solar dynamo, first into the corona and then out as coronal mass ejections into the heliosphere. This transport combined with the observed hemispherical distribution of magnetic twists in the solar atmosphere suggests an active coupling in which the corona serves as a magnetic sink for the dynamo. Title: Magnetic Flux Emergence into the Solar Corona. II. Global Magnetic Fields with Current Sheets Authors: Zhang, M.; Low, B. C. Bibcode: 2002ApJ...576.1005Z Altcode: Hydromagnetic structural and stability properties of global magnetic fields with current sheets are discussed in this paper. These fields describe solar coronal magnetic structures that form when a fresh magnetic field of opposite polarity has emerged into the corona containing a preexisting magnetic field. Three classes of axisymmetric fields are treated. The first is characterized by a continuous normal field distribution at the boundary and an infinitesimally thin current sheet in the field. As ideal hydromagnetic equilibria, these fields are globally stable, but they are resistively unstable within the current sheet. Magnetic reconnection is unavoidable no matter how large the electrical conductivity is. The other two classes of fields may be stable without this kind of resistive nonequilibrium. Of particular interest among them are equilibrium fields with finite-thickness current sheets in force balance with pressure gradients and gravity. These fields are shown to have enough free magnetic energy to let some parts of its field to become open during magnetic reconnection, an effect important for the dynamics of coronal mass ejections. Title: Quiescent Solar Prominences and Magnetic-Energy Storage Authors: Fong, B.; Low, B. C.; Fan, Y. Bibcode: 2002ApJ...571..987F Altcode: Analytical solutions are presented to describe the hydromagnetic support of quiescent solar prominences treated as cold plasma sheets in the characteristic normal and inverse configurations. The solar corona is modeled to be axisymmetric outside a unit sphere, with the prominence sheet lying in the equatorial plane extending from the sphere out to a finite radial distance subject to an inverse-square Newtonian gravity. The relationship between prominence support and the global topology of the surrounding poloidal magnetic field is discussed, with a particular interest in the role of magnetic flux ropes in the support of inverse prominences. A novel solution is also studied describing a rope of purely azimuthal magnetic flux held in equilibrium by the weight of an internal distribution of cold mass and by an external poloidal magnetic field rigidly anchored to the base of the model corona. This solution illustrates the role that prominence weight may play in storing magnetic energy for driving coronal mass ejections. Title: Emergence of twisted magnetic flux into the corona Authors: Gibson, S.; Low, B. C.; Fan, Y.; Fletcher, L. Bibcode: 2002AAS...200.3603G Altcode: 2002BAAS...34..693G The interaction between emerging magnetic structures and preexisting overlying coronal structures will be addressed using a combination of observations and physical models that incorporate a range of twisted magnetic topologies. Solar explosive events such as coronal mass ejections (CMEs) and flares are commonly considered to be driven by the free magnetic energy stored in twisted (current carrying) coronal magnetic fields. Understanding the origin and the three-dimensional nature of these twisted coronal magnetic structures is a crucial step towards explaining and predicting CMEs and flares. One possible and appealing picture is that the twisted coronal magnetic structures form as a result of the emergence of twisted magnetic flux tubes from the solar interior. We might imagine a scenario where a flux rope forms sub-photospherically, emerges through the photosphere, exists in the corona until it loses its stability and erupts in a CME which moves out through interplanetary space until ultimately impacting on the Earth's magnetosphere. Attractively simple as this picture is, reality is likely to be more complicated since the various regimes are physically very different and pre-existing structures would get in the way of our traveling flux rope. We will concentrate on joining up two of these regimes, by considering how a flux rope could rise from beneath the photosphere and emerge into the corona, interacting with pre-existing coronal structures. We will approach this problem by using a combination of numerical models of the flux rope emergence from beneath the photosphere, analytic models of coronal dynamic and equilibrium magnetic structures, and photospheric and coronal observations of the 3-d structure and evolution of a so-called "sigmoidal", or S-shaped active region. In so doing we hope to gain essential insight into how twisted magnetic fields are formed and how they could be ultimately removed from the solar corona. Title: Towards an Operational Sun-to-Earth Model for Space Weather Forecasting Authors: Gombosi, T. I.; Clauer, C. R.; De Zeeuw, D. L.; Hansen, K. C.; Manchester, W. B.; Powell, K. G.; Ridley, A. J.; Roussev, I.; Sokolov, I. V.; Toth, G.; Wolf, R. A.; Sazykin, S.; Holzer, T. E.; Low, B. C.; Richmond, A. D.; Roble, R. G. Bibcode: 2002AGUSMSH51B..06G Altcode: We are presently developing a physics based, modular, large-scale model of the solar-terrestrial environment simulating space weather phenomena and providing a framework to test theories and explore the possibility of operational use in space weather forecasting. This talk will describe the main components of the model (a global MHD code, an upper atmosphere and ionosphere model, and the inner magnetosphere drift physics model). We will also discuss the testing and transitioning the model through CCMC to operational use by NOAA SEC and the Air Force. Particular attention will be paid to the need of validation and metrics studies. Title: The Hydromagnetic Origin of the Two Dynamical Types of Solar Coronal Mass Ejections Authors: Low, B. C.; Zhang, M. Bibcode: 2002ApJ...564L..53L Altcode: We propose a qualitative theory relating flux rope coronal mass ejections (CMEs) to initial states, represented by inverse or normal quiescent prominences corresponding to whether the flux rope magnetic field circulates in the same or opposite sense relative to the surrounding coronal magnetic field. Our theory explains the observed dual character of CME speed-height profiles in terms of the interplays between flux rope expulsion and magnetic reconnection in topologically different magnetic environments and relates CMEs, prominences, and flares to coronal magnetic field reversal during activity maximum. Title: Magnetic Flux Emergence into the Solar Corona. I. Its Role for the Reversal of Global Coronal Magnetic Fields Authors: Zhang, M.; Low, B. C. Bibcode: 2001ApJ...561..406Z Altcode: Some physical insights into how the corona reverses its global magnetic field are described in this paper based on a set of elementary hydromagnetic calculations. We assume that a fresh magnetic field of opposite polarity has emerged into a corona containing a preexisting magnetic field. The inevitable magnetic reconnection that takes place between the two magnetic flux systems may result in an expulsion of magnetic flux to infinity. Our calculations suggest the following physical story of the coronal reversal process: When the emerged flux exceeds the preexisting flux by a critical amount, the corona will reverse its polarity. Before this critical ratio is attained, the field with the emerged flux may have enough energy to let only one or two bipolar parts of the multipolar field open up. This opening-up process, taking place as a coronal mass ejection (CME), may take some of the preexisting flux out of the corona and thus increase the emerged-to-preexisting flux ratio and bring the corona closer to the critical value for its global magnetic reversal. Our calculations also indicate that it is possible that the position where the field opens up may be different from that where the new flux emerges. This may help explain the difference in the latitude distribution of active regions and CMEs during a solar cycle as observed by Hundhausen. Title: Coronal mass ejections, magnetic flux ropes, and solar magnetism Authors: Low, B. C. Bibcode: 2001JGR...10625141L Altcode: This review on coronal mass ejections (CMEs) treats hydromagnetic issues posed by observations, in order to relate CMEs to flares and prominence eruptions and to consider the roles these processes play in the evolution of the solar corona in the course of an 11-year cycle. This global view of the corona, proposed in varying degrees of completeness by the author, physically connects the corona to the photosphere and the dynamo in the solar interior. This view is synthesized afresh starting with CME phenomenology, in order to include some new insights and to arrive at definite statements on the hydromagnetic nature of CMEs. The synthesis shows that each CME culminates a long, coherent physical process involving magnetic-flux emergence; flares and magnetic reconnection; creation of long-lived, large-scale coronal structures; conservation of magnetic helicity; and failure of confinement of magnetic flux ropes in the open atmosphere. Each CME contributes a systematic permanent change to the coronal magnetic field. In this view the cumulative changes brought by all the CMEs in the course of a solar cycle have fundamental implications for the magnetic-flux budgets of the photosphere and the corona. Title: Three-dimensional and twisted: An MHD interpretation of on-disk observational characteristics of coronal mass ejections Authors: Gibson, S. E.; Low, B. C. Bibcode: 2000JGR...10518187G Altcode: A physical interpretation of observed coronal ``on-disk'' manifestations of an Earth-directed coronal mass ejection (CME) is presented. The fundamental question of how the CME's magnetic field and its plasma distribution are related is largely unanswered, because a crucial piece of the puzzle, that is the three-dimensional (3-D) morphology of the CME, remains difficult to ascertain so long as coronal observations are limited to projections onto a single plane of the sky. In order to understand the relationship between observations of CMEs projected at the solar limb and those projected on the solar disk, some sort of model of the 3-D CME is required. In this paper we address both the question of the 3-D morphology of the CME and the more fundamental question of the nature of the plasma-magnetic field relationship, by comparing the limb and on-disk CME representations of an analytic 3-D MHD model based on a spheromak-type flux rope magnetic field configuration. In particular, we show that the morphology of twin dimmings (also referred to as transient coronal holes) observed in X ray and EUV can be reproduced by the CME model as the on-disk projection of the prominence cavity modeled for limb CMEs. Moreover, the bright core of a limb CME, generally corresponding to the material in an erupting prominence, may be interpreted to be the S-shaped central core of the modeled on-disk CME, splitting the cavity into twin dimmings when observed head-on without obstruction. The magnetic field structure of this central core exhibits many of a filament's magnetic field features required to match observations. Finally, we consider the nature of S-shaped filaments and X-ray ``sigmoids'' in the context of the model, in terms of localized heating and cooling acting on the modeled CME magnetic field structure. Title: Magnetostatic atmospheres possessing identical invariants of ideal magnetohydrodynamics Authors: Manchester, Ward; Low, B. C. Bibcode: 2000PhPl....7.1263M Altcode: A physical analysis is presented of two distinct families of two-dimensional (2D) analytical solutions for isothermal periodic magnetostatic atmospheres in uniform gravity, one arrived at by Dungey and the other arrived at by Low and Manchester. It is demonstrated that particular members of the two families of 2D equilibria may be generated from the same planar state by plasma displacements which move the system through continuous sequences of equilibria while ensuring flux freezing. The two families of solutions both possess undulating magnetic field lines but geometrically different flux surfaces. The Dungey solutions can be created from a planar state by an undulating deformation whose spatial variation is along the field lines. By contrast, the 2D plane of variation of the Low-Manchester solutions lies at an angle to the field lines of the planar state. As a result, a mixed mode of undulating, interchange and shearing displacements must be made to the planar state to produce the more complex 2D state. Finally, the physical properties of these topologically equivalent states, including the magnetic and electrical helicities and the hydromagnetic potential energy, as introduced by Mouschovias, are discussed in terms of the variational principles of Kruskal and Kulsrud. Title: Equilibrium and Stability of Magnetostatic Atmospheres. I. Dungey-Type Isothermal States Authors: Low, B. C.; Manchester, Ward, IV Bibcode: 2000ApJ...528.1026L Altcode: Two families of analytical solutions are presented that describe isothermal magnetostatic atmospheres in uniform gravity and varying in two Cartesian dimensions. The solutions in each family share a common set of magnetic flux surfaces but have different profiles of field intensity, magnetic shear, and plasma distribution across these flux surfaces such that force balance is satisfied. A family of solutions with this mathematical degree of freedom had previously been found by Dungey. The construction and properties of the new solutions are described. The hydromagnetic stability of these solutions is discussed by using the sufficiency criteria of Hu to determine those profiles of magnetic field and plasma that assure stability for the whole system. Among the stable equilibria found are examples of sheared magnetic structures intruding into a uniformly magnetized, isothermal atmosphere. One of the two families of solutions is extended to equilibrium states that vary fully with all three Cartesian coordinates. These extended solutions allow the possibility of constructing complex structures by juxtapositioning discrete three-dimensional magnetic structures built separately. These two-dimensional and three-dimensional magnetostatic states may be useful as initial states for numerical simulation of time-dependent magnetohydrodynamic processes in the solar atmosphere. Title: Coronal Mass Ejections, flares and prominences Authors: Low, B. C. Bibcode: 1999AIPC..471..109L Altcode: 1999sowi.conf..109L This article describes the hydromagnetic relationships among Coronal Mass Ejections, flares and prominences to put these phenomena in the context of the solar corona evolving in response to the solar dynamo. Title: Topologically Equivalent Magnetostatic Atmospheres and Numerical MHD Simulations of Buoyancy Instabilities Authors: Manchester, W.; Low, B. C. Bibcode: 1999AAS...194.5508M Altcode: 1999BAAS...31..911M We present a physical application of two distinct families of two-dimensional analytical solutions which describe isothermal periodic magnetostatic atmospheres in uniform gravity. We demonstrate that members of both families of 2D solutions can be arrived at from the same planar atmosphere by finite plasma displacements which ensures the conservation of mass and magnetic flux. The fist family of solutions is characterized by undulating field lines which are confined to the plane of variation. By contrast, the second family of solutions has the plane of variation rotated away from the field lines. As a result, this family possesses a sheared field geometry with a field component out of the plane of variation. A striking feature of this 2D configuration is the way in which the field lines becomes highly sheared as the undulations increase in height. Both families of solutions are used as initial states for two-dimensional, time-dependent magnetohydrodynamic numerical simulations of buoyancy instabilities. The simulations demonstrate how the magnetic field component out of the plane of variation propagates into rising loops by the action of shear Alfven waves. We show that this has a profound effect on the buoyancy instability and that the resulting velocity field resembles the photospheric shear flow observed across the polarity inversion line of flux emerging regions. Title: Partially Open Solar Coronal Magnetic Field in 3D Magnetostatic Atmosphere Authors: Low, B. C.; Dikpati, M. Bibcode: 1999AAS...194.9408L Altcode: 1999BAAS...31..992L We present a family of analytic solutions describing the quiescent solar corona as magnetostatic equilibrium states in the presence of a 1/r(2) gravity. These solutions assume no symmetry so that large-scale coronal magnetic structures may be modeled in realistic geometry. In particular, these solutions are capable of modeling multiple helmet-streamer belts associated with several magnetic polarity inversion lines at the base of the corona, with each streamer-belt sandwiched between coronal regions of open magnetic fields. The neglect of the solar wind limits the applicability of such models to the low solar corona. These solutions are useful as illustrative examples of the global magnetic field topologies expected in the solar corona, and, as initial states for three-dimensional, time-dependent magnetohydrodynamic numerical simulations as a means of developing coronal models that include the effect of the solar wind. *The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Complex magnetohydrodynamic bow shock topology in field-aligned low-β flow around a perfectly conducting cylinder Authors: de Sterck, H.; Low, B. C.; Poedts, S. Bibcode: 1998PhPl....5.4015D Altcode: Two-dimensional ideal magnetohydrodynamic (MHD) simulations are presented that demonstrate several novel phenomena in MHD shock formation. The stationary symmetrical flow of a uniform, planar, field-aligned, low-β and superfast magnetized plasma around a perfectly conducting cylinder is calculated. The velocity of the incoming flow is chosen such that the formation of fast switch-on shocks is possible. Using a time marching procedure, a stationary bow shock is obtained, composed of two consecutive interacting shock fronts. The leading shock front has a dimpled shape and is composed of fast, intermediate and hydrodynamic shock parts. A second shock front follows the leading front. Additional intermediate shocks and tangential discontinuities are present in the downstream part of the flow. The intermediate shocks are of the 1-3, 1-4, 2-4 and 1=2-3=4 types. This is a confirmation in two dimensions of recent results on the admissibility of these types of shocks. Recently it has also been shown that the 1=2-3=4 shock, embedded in a double compound wave, is present in the analytical solution of some planar one-dimensional MHD Riemann problems. This MHD flow with interacting shocks may have applications for some observed features of fast solar Coronal Mass Ejections and other phenomena in low-β space plasmas. Title: A Time-Dependent Three-Dimensional Magnetohydrodynamic Model of the Coronal Mass Ejection Authors: Gibson, S. E.; Low, B. C. Bibcode: 1998ApJ...493..460G Altcode: We present a theoretical magnetohydrodynamic (MHD) model describing the time-dependent expulsion of a three-dimensional coronal mass ejection (CME) out of the solar corona. The model relates the white-light appearance of the CME to its internal magnetic field, which takes the form of a closed bubble, filled with a partly anchored, twisted magnetic flux rope, and embedded in an otherwise open background field. The model is constructed by solving in closed form the time-dependent ideal MHD equations for a γ = 4/3 polytrope making use of a similarity assumption and the application of a mathematical stretching transformation in order to treat a complex field geometry with three-dimensional variations. The density distribution frozen into the expanding CME magnetic field is obtained. The scattered white light integrated along the line of sight shows the conspicuous three features often associated with CMEs as observed with white-light coronagraphs: a surrounding high-density region, an internal low-density cavity, and a high-density core. We also show how the orientation of this three-dimensional structure relative to the line of sight can give rise to a variety of different geometric appearances in white light. These images generated from a CME model in a realistic geometry offer an opportunity to directly compare theoretical predictions on CME shapes with observations of CMEs in white light. The mathematical methods used in the model construction have general application and are described in the Appendices. Title: Self-similar Time-dependent MHD in Three-dimensional Space Authors: Low, B. C.; Gibson, S. E. Bibcode: 1997AAS...19112006L Altcode: 1997BAAS...29.1403L A general class of self-similar exact solutions to the time-dependent ideal MHD equations was discovered in the early eighties (Low 1982 ApJ 254, 796; Low 1984 ApJ 281, 392). These solutions describe exploding or imploding atmospheres in the polytropic approximation with a 4/3 index and in the presence of Newtonian gravity. A full range of accelerating, decelerating, or inertial explosions or implosions are possible. A novel feature of these solutions is that they allow for full variation in three dimensional space unstricted by any spatial symmetry, presenting an opportunity for generating models of exploding or imploding atmospheres in realistic geometry. The reduction of the problem from four dimensional space-time to the three-dimensional similarity space leads to governing equations which are still highly non-trivial to solve. This paper presents the results of a method of solution which yields a three-dimensional, analytic model of a coronal mass ejection carrying a ball of twisted magnetic fields pushing its way through surrounding open magnetic fields in a time-dependent expulsion out of the solar corona (Gibson and Low 1998 ApJ, in press). This method may be useful in other astrophysical applications. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Flux Emergence and Prominences: a New Scenario for 3-DIMENSIONAL Field Geometry Based on Observations with the Advanced Stokes Polarimeter Authors: Lites, B. W.; Low, B. C. Bibcode: 1997SoPh..174...91L Altcode: This paper presents an interpretation of the evolution of the vector magnetic field at the photosphere based on measurements of the advanced Stokes polarimeter, along with chromospheric Hα from the Lockheed instrument operating on La Palma and X-ray images of the corona from Yohkoh. These measurements are consistent with the emergence of a nearly closed magnetic structure from the solar interior into the corona. The highly non-potential field topology inferred from the data suggests that strong field-aligned currents exist in the emergent magnetic structure as it buoyantly rises through the photosphere. Material trapped in this closed structure is pulled upward to later condense into a prominence. By analogy of this small active region evolution with the observed properties of large quiescent prominences, we speculate that this process might also be operative on a much larger scale. A 3-dimensional magnetostatic model is presented which has many topological features in common with the observations. Title: Solar activity from the coronal perspective. Authors: Low, B. C. Bibcode: 1997smf..conf....1L Altcode: No abstract at ADS Title: Solar Activity and the Corona Authors: Low, B. C. Bibcode: 1996SoPh..167..217L Altcode: This review puts together what we have learned about coronal structures and phenomenology to synthesize a physical picture of the corona as a voluminous, thermally and electrically highly-conducting atmosphere responding dynamically to the injection of magnetic flux from below. The synthesis describes complementary roles played by the magnetic heating of the corona, the different types of flares, and the coronal mass ejections as physical processes by which magnetic flux and helicity make their way from below the photosphere into the corona, and, ultimately, into interplanetary space. In these processes, a physically meaningful interplay among dissipative magnetohydrodynamic turbulence, ideal ordered flows, and magnetic helicity determines how and when the rich variety of relatively long-lived coronal structures, spawned by the emerged magnetic flux, will evolve quasi-steadily or erupt with the impressive energies characteristic of flares and coronal mass ejections. Central to this picture is the suggestion, based on recent theoretical and observational works, that the the emerged flux may take the form of a twisted flux rope residing principally in the corona. Such a flux rope is identified with the low-density cavity at the base of a coronal helmet, often but not always encasing a quiescent prominence. The flux rope may either be bodily transported into the corona from below the photosphere, or reform out of a state of flaring turbulence under some suitable constraint of magnetic-helicity conservation. The appeal of this synthesis is its physical simplicity and the manner it relates a large set of diverse phenomena into a self-consistent whole. The implications of this view point are discussed. Title: Current sheets in the solar minimum corona Authors: Gibson, S. E.; Bagenal, F.; Low, B. C. Bibcode: 1996JGR...101.4813G Altcode: We analytically combine stress-free current sheets with a coronal magnetostatic bulk current model. We begin by imposing a current sheet at the equator as an upper boundary condition on the modeled coronal field. We find that in order to reproduce the sharp gradients across the boundaries of helmet streamers, we also have to add current sheets along the interface between open and closed field lines. We find a description of coronal magnetic field and density in the presence of both bulk and sheet currents that matches both white light and photospheric magnetic flux observations. Title: The Role of Coronal Mass Ejections in Solar Activity Authors: Low, B. C. Bibcode: 1996ASPC...95..148L Altcode: 1996sdit.conf..148L No abstract at ADS Title: Magnetohydrodynamic processes in the solar corona: flares, coronal mass ejections and magnetic helicity. Authors: Low, B. C. Bibcode: 1996ASIC..481..133L Altcode: The magnetized, million-degree solar corona evolves in cycles of about eleven years, in dynamical response to newly generated magnetic fluxes emerging from below to eventually reverse the global magnetic polarity. Over the larger scales, the corona does not erupt violently all the time. Violent events like the flares and episodic ejections of material into interplanetary space occur frequently, several times a day, but they often originate in long-lived magnetic structures which form continually throughout the solar cycle. In this paper, the creation, stability, and eventual eruption of these structures are discussed from basic principles, drawing on recent advances in observation and theory. A global view is offered in which different pieces of observation relate physically, with distinct roles for the conservation of magnetic helicity and the releases of magnetic energy in dissipated and ordered forms. Title: The spontaneous formation of current-sheets in astrophysical magnetic fields. Authors: Low, B. C. Bibcode: 1996ASIC..481..109L Altcode: This article is an introduction to Parker's idea that electric current sheets form spontaneously in astrophysical magnetic fields under the condition of high electrical conductivity. Upon formation, the current sheets will collapse to such small widths as to result in resistive reconnection of magnetic fields and heating, despite the very large but finite electrical conductivity. This mechanism is an attractive explanation of the ubiquitous association between magnetic fields and heated plasmas in many astrophysical situations. The hydromagnetic process of this mechanism is illustrated, using a well-studied two-dimensional Cartesian model involving a quadrupolar magnetic field with or without a magnetic null point. Title: The Possible Ascent of a Closed Magnetic System through the Photosphere Authors: Lites, B. W.; Low, B. C.; Martinez Pillet, V.; Seagraves, P.; Skumanich, A.; Frank, Z. A.; Shine, R. A.; Tsuneta, S. Bibcode: 1995ApJ...446..877L Altcode: We present a comprehensive interpretation of the evolution of a small magnetic region observed during its entire disk passage. The vector magnetic field measurements from the Advanced Stokes Polarimeter, along with Hα and magnetogram measurements from the Lockheed SOUP instrument operating at the Swedish Solar Observatory on La Palma, and soft X-ray images from the Yohkoh satellite support the hypothesis that we have observed the passage of a nearly closed magnetic system through the photosphere into the corona. The observations suggest that as the magnetic flux begins to emerge into the photosphere it shows a rather simple geometry, but it subsequently develops a small δ-sunspot configuration with a highly sheared vector field along the polarity inversion line running through it. At that stage, the vector field is consistent with a concave upward magnetic topology, indicative of strong electric currents above the photosphere. An Hα prominence is found above this inversion line when the δ-sunspot is fully formed. These observed features and the sequence of events are interpreted in terms of a nearly closed magnetic system that rises through the photosphere into the corona as a result of magnetic buoyancy. The magnetic system persists in the corona well after the dark δ-sunspot has disappeared in the photosphere We suggest that this coronal structure is in quasi-static equilibrium with its buoyancy partially countered by the weight of the plasma trapped at the bottom of closed magnetic loops. The plausibility of such a scenario is demonstrated by a three-dimensional magnetostatic model of the emergence of a closed, spheroidal magnetic system in the corona, in which the Lorentz force arising from cross-field currents is balanced by the gravitational and pressure forces. This theoretical model carries many features in common with the observed morphology of our active region. Title: Magnetostatic Structures of the Solar Corona. II. The Magnetic Topology of Quiescent Prominences Authors: Low, B. C.; Hundhausen, J. R. Bibcode: 1995ApJ...443..818L Altcode: This paper treats the magnetic properties of the quiescent prominence as a part of the larger coronal structure made up of the prominence, cavity, and helmet dome. A rigorous analysis of the mechanical support of a vertical prominence sheet suspended in equilibrium by magnetic fields in uniform gravity shows that the finite vertical extension of the prominence sheet has an important dynamic constraint. For the inverse topology with the prominence magnetic field pointing opposite to the field implied by the bipolar photospheric region below, this constraint requries the prominence sheet to be embedded in a horizontal, nearly force-free, magnetic flux rope which crucially supports a part of the prominence weight by current attraction from above. A similar analysis of the support problem is carried out for the prominence in the normal topology in which both prominence and photospheric magnetic fields point in the same sense. Starting with the observation that most prominences are of the inverse topology, a recent model is extended to show that this topology implies that the prominence sits in a two-flux magnetic system, one flux connecting the bipolar magnetic sources in the photosphere below and the other forming a rope which embeds the prominence and runs above and parallel to the photospheric polarity-inversion line. This model physically relates several pieces of well-known but hitherto disjoint observations. The prominence flux rope manifests itself as the cavity in the corona and as the filament channel in the chromosphere. The chromospheric fibril patterns associated with prominences and filament channels can, for the first time, be modeled faithfully. Several physical implications on the origin of the prominence and questions deriving from the results are discussed. Title: Coronal mass ejections and magnetic helicity Authors: Low, B. C. Bibcode: 1994ESASP.373..123L Altcode: 1994soho....3..123L No abstract at ADS Title: A Class of Force-Free Magnetic Fields for Modeling Pre-Flare Coronal Magnetic Configurations Authors: Chou, Y. P.; Low, B. C. Bibcode: 1994SoPh..153..255C Altcode: Three-dimensional, quasi-static evolutions of coronal magnetic fields driven by photospheric flux emergence are modeled by a class of analytic force-free magnetic fields. Our models relate commonly observed photospheric magnetic phenomena, such as the formation and growth of sunspots, the emergence of an X-type separator, and the collision and merging of sunspots, to the three-dimensional magnetic fields in the corona above. By tracking the evolution in terms of a continuous sequence of force-free states, we show that flux emergence and submergence along magnetic neutral lines in the photosphere are essential processes in all these photospheric phenomena. The analytic solutions we present have a parametric regime within which the magnetic energy attained by an evolving force-free field may be of the order of 1030 ergs to several 1031 ergs, depending on the magnetic environment into which an emerging flux intrudes. The commonly used indicators of magnetic shear in magnetogram interpretation are discussed in terms of field connectivity in our models. It is demonstrated that the crossing angle of the photospheric transverse magnetic field with the neutral line may not be a reliable indicator of the magnetic shear in the coronal field above, due to the complexity of three-dimensionality. The poorly understood constraint of magnetic-helicity conservation on the availability of magnetic free energy for a flare is briefly discussed. Title: Magnetostatic Structures of the Solar Corona. I. A Model Based on the Cauchy Boundary Value Problem Authors: Hundhausen, J. R.; Low, B. C. Bibcode: 1994ApJ...429..876H Altcode: A model is presented for the static equilibrium of a magnetized, polytropic atmosphere stratified by uniform gravity and invariant in a Cartesian direction. The profiles of plasma pressure and magnetic shear as functions of the magnetic stream function, which render the governing equation linear, lead to unphysical features if these profiles are applied to the infinite half-space bounded below by a plane. These undesirable features are shown to be removed when these special profiles are localized to a region bounded by a magnetic flux surface, outside of which is an atmosphere in plane-parallel hydrostatic equilibrium with a potential magnetic field. Two families of solutions are constructed by direct solution of the Cauchy boundary value problem for the Laplace equation, one with continuous and the other with discontinuous pressures across this magnetic boundary. Illustrative solutions are analyzed, with applications to long-lived density enhancements and depletions in the solar corona. In particular, the hydromagnetic stability of pressure discontinuities is studied as an example of a general result due to Hu (1988). It is pointed out that the stability of the sharp interface between the prominence cavity and the high-density coronal helmet may be understood in terms of competing effects arising from density stratification and magnetic curvature. The model presented lays the mathematical groundwork for the other papers of the series. Title: Magnetohydrodynamic processes in the solar corona: Flares, coronal mass ejections, and magnetic helicity Authors: Low, B. C. Bibcode: 1994PhPl....1.1684L Altcode: The magnetized, million-degree solar corona evolves in cycles of about 11 years, in dynamical response to newly generated magnetic fluxes emerging from below to eventually reverse the global magnetic polarity. Over the larger scales, the corona does not erupt violently all the time. Violent events like the flares and episodic ejections of material into interplanetary space occur frequently, several times a day, but they often originate in long-lived magnetic structures that form continually throughout the solar cycle. In this paper, the creation, stability, and eventual eruption of these structures are discussed from basic principles, drawing on recent advances in observation and theory. A global view is offered in which different pieces of observation relate physically, with distinct roles for the conservation of magnetic helicity and the release of magnetic energy in dissipated and ordered forms. Title: The Free Energies of Partially Open Magnetic Fields and Coronal Mass Ejections Authors: Smith, D. F.; Low, B. C. Bibcode: 1994scs..conf...97S Altcode: 1994IAUCo.144...97S The results of Low and Smith (1993) on how to circumvent Aly's limitation on the energy of force-free magnetic fields are briefly reviewed. Two non-force-free configurations with energies in excess of the energy of the corresponding completely open field are discussed: 1. A magnetic bubble configuration with completely detached field lines. 2. A combined configuration consisting of closed field lines with plasma compressed against the star and a superimposed helmet streamer with all field lines tied to the surface. It is shown that the bubble configuration is unstable. Title: A Class of Three-dimensional Isothermal Laminated Equilibria and Their Stability Authors: Chou, Y. P.; Low, B. C.; Bhattacharjee, A. Bibcode: 1993ApJ...416..379C Altcode: Three-dimensional ideal magnetostatic equilibria with laminated magnetic field in which one component of the magnetic field vanishes, are constructed for isothermal coronal plasmas in the presence of uniform gravity. Three subsets of the general solution are found to be absolutely stable, when subject to rigid anchoring of the magnetic field lines at the base of the atmosphere. The magnetic fields in these cases carry currents. For equilibria with general magnetic strength variations, the criteria for stability are obtained by minimizing the energy integral. Numerical solutions for the Euler-Lagrange equations that result from the minimization procedure are given, and are used to determine critical equilibrium parameters that give a bound for the marginal stability. For low values of plasma β(≡ 8πp/B2), the scale length of the plasma density variation can be small and the magnetic shear can be large, suggestive of the observed fine plasma loops and the rapid fluctuation of the inclination angle of the field lines in the sunspot penumbra. Title: Mass acceleration processes: The case of the coronal mass ejection Authors: Low, B. C. Bibcode: 1993AdSpR..13i..63L Altcode: 1993AdSpR..13...63L A theoretical review is given on what drives the coronal mass ejection, centering on the question of the origin of its total energy, typically of the order of a few 1031 erg. This energy accounts for the work of lifting and accelerating the ejected mass as well as a significant amount left in the open magnetic field created by the ejection. It is pointed out that the total energy cannot be stored in the pre-eruption corona entirely in the form of force-free electric currents, based on a plausible magnetohydrodynamic conjecture of Aly. Storage in the form of cross-field electric currents held in equilibrium by pressure and gravitational forces seems possible, in particular if these currents are associated with closed magnetic fluxes entirely detached from the atmospheric base. The implications and physical issues of these results for the mass ejection are discussed, leading to several suggestions for future study.

The National Center for Atmospheric Research is sponsored by the National Science Foundation of the United States Title: The Free Energies of Partially Open Coronal Magnetic Fields Authors: Low, B. C.; Smith, D. F. Bibcode: 1993ApJ...410..412L Altcode: A simple model of the low corona is examined in terms of a static polytropic atmosphere in equilibrium with a global magnetic field. The question posed is whether magnetostatic states with partially open magnetic fields may contain magnetic energies in excess of those in fully open magnetic fields. Based on the analysis presented here, it is concluded that the cross-field electric currents in the pre-eruption corona are a viable source of the bulk of the energies in a mass ejection and its associated flare. Title: The Nature of the Quiescent Prominence Cavity Authors: Low, B. C. Bibcode: 1993BAAS...25.1218L Altcode: No abstract at ADS Title: A Class of Three-Dimensional Isothermal Laminated Equilibria and Their Stability Authors: Chou, Y. P.; Low, B. C.; Bhattacharjee, A. Bibcode: 1993BAAS...25Q1208C Altcode: No abstract at ADS Title: Force-free Magnetic Fields with Singular Current-Density Surfaces Authors: Low, B. C. Bibcode: 1993ApJ...409..798L Altcode: This paper is a study of a family of nonlinear force-free magnetic fields, in Cartesian geometry and invariant in a given direction, as simple models of the magnetic fields in the solar corona. Posed as a problem in the infinite half-space bounded below by the photosphere taken as a rigid plane, the solution is constructed with the field-aligned currents confined within a cylindrical plasma surface outside of which the magnetic field is potential. An infinity of solutions are shown to be tractable by the method of images of potential theory. Among the results presented is the demonstration of a magnetic flux surface in the plasma interior, which is ideally stable, where the electric current density becomes an integrable infinity, created quasi-statically by continuous boundary displacement of the magnetic footpoints. This result is discussed in connection with Parker's theory of coronal heating by the dissipation of electric current sheets. Simple modifications of the force-free solutions are also carried out to demonstrate (1) the formation of a magnetic cusp point in a bipolar magnetic field in equilibrium with an isotropic pressure, and (2) the possibility of a Kuperus-Raadu type prominence embedded in a horizontal, helical magnetic flux rope. Title: Three-dimensional Structures of Magnetostatic Atmospheres. V. Coupled Electric Current Systems Authors: Low, B. C. Bibcode: 1993ApJ...408..689L Altcode: The magnetostatic equations describing equilibrium among the Lorentz, pressure, and gravitational forces are transformed to a statement of Ampere's law incorporating the condition of equilibrium. The pressure as a function of space is expressed in terms of the gravitational potential, a component of the magnetic field, and an arbitrary third variable to complete a set of local curvilinear coordinates. The coupling of the two current systems is shown to be manifest in the need for the third variable to describe the pressure structure. A discussion relating the derived equations to other known forms of the magnetostatic equations is presented. Title: Three-dimensional Structures of Magnetostatic Atmospheres. VI. Examples of Coupled Electric Current Systems Authors: Low, B. C. Bibcode: 1993ApJ...408..693L Altcode: Attention is given to exact solutions which describe the static equilibrium of atmospheres stratified by a uniform gravity, in the presence of magnetic fields lying in parallel vertical planes. These equilibrium states consist of different, highly varied structures in these planes stacked together in global equilibrium. A subset of the solutions presented describe a magnetostatic system closed by a simple equation of state, namely, an atmosphere which conducts heat perfectly along the magnetic field but no heat across it. It is found that periodic structures in adjacent magnetic flux planes can march out of step as a result of an irrational ratio between their periods, leading to extreme electric current densities despite the boundedness of the magnetic intensity and plasma pressure. Title: Three-dimensional Structures of Magnetostatic Atmospheres. IV. Magnetic Structures over a Solar Active Region Authors: Low, B. C. Bibcode: 1992ApJ...399..300L Altcode: A static model is presented for the long-lived structures over a solar active region dominated by a pair of sunspots of opposite magnetic polarities. The magnetic field is approximately force-free high in the atmosphere but interacts strongly with the plasma and gravity in the lower region through cross-field electric currents. Basic atmospheric features long discussed in the literature can be reproduced in realistic geometry, such as the density depletion over a sunspot, magnetic shear, and levitated magnetic flux ropes interpretable as chromospheric filaments. Explicit solutions showing these features are described and compared, with a discussion of the implications for the interpretation of vector-magnetograph data. These solutions are illustrative examples taken from a large set obtainable by transforming the magnetostatic equations to solvable, linear differential equations given in the preceding paper in this series. Title: Self-similar Magnetohydrodynamics. V. Gravitating Spheres and Spheroids Authors: Low, B. C. Bibcode: 1992ApJ...390..567L Altcode: This paper presents a family of explicit, time-dependent magnetohydrodynamic solutions describing gravitating, magnetized, gamma = 4/3 polytropes in the shape of a spheroid undergoing self-similar expansion or contraction in vacuum. Included in this family are the solutions for a gravitating, magnetized sphere, which are mathematically akin to Prendergast's (1956) equilibrium solutions for a static magnetic star. The solutions presented here are of basic physical interest and may be useful for the testing of multidimensional, numerical magnetohydrodynamic codes which include self-gravity as an important effect. Title: A Numerical Scheme for the Modeling of Electric Current Sheet Formation in the Solar Atmosphere Authors: Charbonneau, P.; Low, B. C. Bibcode: 1992ASPC...26..531C Altcode: 1992csss....7..531C No abstract at ADS Title: Formation of electric-current sheets in the magnetostatic atmosphere Authors: Low, B. C. Bibcode: 1992A&A...253..311L Altcode: An analytical illustration is presented of the theorem by Parker (1989, 1990), which states that a magnetic field with an arbitrarily prescribed topology in an electrically perfectly conducting medium tends toward equilibrium states with either embedded electric current sheets or magnetic tangential discontinuities. The illustration concerns an isothermal atmosphere in which the Lorentz force does not vanish, but rather balances pressure and gravitational forces in static equilibrium. It is shown that the quasi-static evolution of the atmosphere in response to a continuously changing plasma pressure distribution at the atmospheric base can bring an initially smooth state to one in which an electric current sheet forms. Title: On the Spontaneous Formation of Electric Current Sheets above a Flexible Solar Photosphere Authors: Low, B. C. Bibcode: 1991ApJ...381..295L Altcode: This paper treats the general tendency for a magnetic field in an electrically perfectly conducting plasma to seek an equilibrium state with embedded electric current sheets or magnetic tangential discontinuities. This property is simplest to demonstrate theoretically with two-dimensional force-free magnetic fields in the infinite half-space above a plane boundary where magnetic footpoints are rigidly anchored. The principal results of recent treatments of this simple model are summarized and extended to clarify their basic physics in order to answer the criticism of this model by Karpen et al. (1990). These authors have concluded that the formation of current sheets in this model depended on the use of rigid boundary conditions to the extent that current sheets would not form if the boundary is not rigid but is replaced by a gravitationally stratified photosphere of finite thickness. It is shown that the conclusion of these authors is not valid, based on a physical analysis and an explicit magnetostatic construction of a possible equilibrium state in which a current sheet has formed in the presence of a flexible photosphere. Title: Three-Dimensional Magnetostatic Equilibrium Authors: Low, B. C. Bibcode: 1991BAAS...23..967L Altcode: No abstract at ADS Title: Three-dimensional Structures of Magnetostatic Atmospheres. III. A General Formulation Authors: Low, B. C. Bibcode: 1991ApJ...370..427L Altcode: This paper presents a mathematical description of the three-dimensional structures of static, magnetized atmospheres in terms of the electric-current flux surfaces. In the first paper of this series, a class of three-dimensional magnetostatic states was presented. These states are characterized by electric currents flowing perpendicular to gravity which was taken to be either uniform in space or spherically symmetric about a point mass. A limitation of these solutions is that the magnetic field in general cannot have a net twist. The new formulation generalizes these solutions in two significant ways, namely, to allow for other general potential body forces than the special gravitational forces assumed in the first paper and to include the presence of a net magnetic twist. This theoretical development opens up opportunities in modeling realistic solar magnetic fields as well as other astrophysical magnetic fields. The obliquely rotating magnetosphere and self-gravitating magnetized plasma clouds are two astrophysical examples for which the governing equations are derived. The complete analytic solution to a specific problem is presented, which illustrates the anchoring of a fully three-dimensional force-free magnetic field in the solar atmosphere to the base of the atmosphere through a non-force-free boundary layer where the magnetic field interacts strongly with the plasma. This and a rich variety of other three-dimensional magnetic fields will be studied in the subsequent papers of this series. Title: Modeling Solar Force-free Magnetic Fields Authors: Low, B. C.; Lou, Y. Q. Bibcode: 1990ApJ...352..343L Altcode: A class of nonlinear force-free magnetic fields is presented, described in terms of the solutions to a second-order, nonlinear ordinary differential equation. These magnetic fields are three-dimensional, filling the infinite half-space above a plane where the lines of force are anchored. They model the magnetic fields of the sun over active regions with a striking geometric realism. The total energy and the free energy associated with the electric current are finite and can be calculated directly from the magnetic field at the plane boundary using the virial theorem. In the study of solar magnetic fields with data from vector magnetographs, there is a long-standing interest in devising algorithms to extrapolate for the force-free magnetic field in a given domain from prescribed field values at the boundary. The closed-form magnetic fields of this paper open up an opportunity for testing the reliability and accuracy of algorithms that claim the capability of performing this extrapolation. The extrapolation procedure as an ill-posed mathematical problem is discussed. Title: Slow shocks in an open magnetic field near the sun Authors: Hu, You-Qiu; Zhu, Zhong-Wei; Hundhausen, A. J.; Holzer, T. E.; Low, B. C. Bibcode: 1990SCSMP..33..332H Altcode: A numerical study on the formation of the slow shock in an open magnetic field due to the motion of a coronal mass ejection driven by a magnetic flux eruption from below the corona is presented. The slow shock obtained in the numerical model is characterized by a limited latitudinal extent and a slightly flattened shape. It is determined that a fast-mode wave always coexists and interacts with the medium ahead of the slow shock and deflects the background magnetic field to create a rarefaction ahead of the slow shock and a compression in the flank. Thus, these effects have a significant influence on the geometry and features of the slow shock. Title: Solar Coronal Mass Ejections Authors: Hundhausen, A. J.; Sime, D. G.; Low, B. C. Bibcode: 1990IAUS..140...16H Altcode: No abstract at ADS Title: Equilibrium and dynamics of coronal magnetic fields. Authors: Low, B. C. Bibcode: 1990ARA&A..28..491L Altcode: The paper surveys various hydromagnetic processes whose study has been stimulated by the observed behavior of the magnetic field in the solar corona. Attention is given to the equilibrium and stability of magnetic fields, the onset mechanics of the eruption, and the large-scale organization and time-dependent ordered dynamics of the corona. The aim of this survey is to achieve a qualitative physical understanding of the basic behavior of the coronal plasma. Title: The Dynamics of Solar Coronal Magnetic Fields Authors: Low, B. C. Bibcode: 1990IAUS..140...13L Altcode: Coronal mass ejection is discussed in terms of its observable hydromagnetic processes to define the dynamics of the coronal magnetic field and thereby extrapolate the findings to other hydromagnetic phenomena. The three important observations in terms of hydromagnetism include the broad range of speeds of the mass ejections, the timing of the eruption of the prominence filaments, and the possibility of slow shocks based on the slow mass ejections. The observation of coronal mass ejection suggests that other hydromagnetic phenomena can be observed and studied using similar techniques. Title: Steady Hydromagnetic Flows in Open Magnetic Fields. II. Global Flows with Static Zones Authors: Tsinganos, K.; Low, B. C. Bibcode: 1989ApJ...342.1028T Altcode: A theoretical study of an axisymmetric steady stellar wind with a static zone is presented, with emphasis on the situation where the global magnetic field is symmetrical about the stellar equator and is partially open. In this scenario, the wind escapes in open magnetic fluxes originating from a region at the star pole and a region at an equatorial belt of closed magnetic field in static equilibrium. The two-dimensional balance of the pressure gradient and the inertial, gravitational, and Lorentz forces in different parts of the flow are studied, along with the static interplay between external sources of energy (heating and/or cooling) distributed in the flow and the pressure distribution. Title: Astrophysics of the Sun Authors: Zirin, Harold; Low, Boon Chye Bibcode: 1989PhT....42g..74Z Altcode: No abstract at ADS Title: Steady Hydromagnetic Flows in Open Magnetic Fields. III. Allowing for Variations of Density with Latitude and Nonalignment of Velocity with Magnetic Field Authors: Hu, Y. Q.; Low, B. C. Bibcode: 1989ApJ...342.1049H Altcode: A steady hydromagnetic stellar wind flowing in a rotating axisymmetric partially open magnetic field is modeled under the assumptions that the density is a function of radial distance only and that the flow is everywhere aligned to the local magnetic field. The model illustrates that monotonic acceleration of the wind speed in the polar region requires a decrease of density toward the stellar pole at fixed radial distance. In the presence of rotation, a nonalignment between the flow velocity and the magnetic field is found to be necessary for the acceleration of the poloidal flow speed from below to above the Alfven speed defined in terms of the poloidal part of the magnetic field. Title: Spontaneous Formation of Electric Current Sheets by the Expulsion of Magnetic Flux Authors: Low, B. C. Bibcode: 1989ApJ...340..558L Altcode: Two theoretical examples are given to demonstrate the spontaneous formation of electric current sheets in force-free magnetic fields frozen into a medium with an infinite electrical conductivity, as a result of the continuous displacement of the magnetic footpoints at the boundary. An initial three-lobe axisymmetric magnetic field without neutral points in the infinite medium outside a unit sphere is found to adjust to footpoint displacements by a slipping of the central lobe relative to the other two lobes. Also, a three-dimensional force-free magnetic field is studied, showing that conditions for the expulsion of flux from a local region to bring spatially separate fluxes together to form rotational discontinuities are readily obtained between ordinary magnetic surfaces. Title: Coronal mass ejections and coronal structures. Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.; Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing, R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos, P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Stewart, R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T. Bibcode: 1989epos.conf..493H Altcode: The work of this team was concerned with modelling of post-flare arches, the reconnection theory of flares, the slow variation of coronal structure, and the coronal and interplanetary detection, evolution, and consequences of mass ejections. Title: On the relationship between the topology of magnetic field lines and flux surfaces Authors: Rosner, R.; Low, B. C.; Tsinganos, K.; Berger, M. A. Bibcode: 1989GApFD..48..251R Altcode: We consider the topological relationship between magnetic field lines and magnetic flux surfaces. Magnetic helicity provides the most elementary description of the topology of magnetic field lines in terms of their linkage. In a simply-connected volume, a sufficient but not necessary condition for the total magnetic helicity to vanish is that there exist two independent families of globally-extendable flux surfaces (given by the level surfaces of Euler potentials). In contrast, the existence of two distinct global Euler potentials for multiply-connected volumes is insufficient to guarantee that the total magnetic helicity vanishes. These well-known results are discussed in the context of Frobenius' theorem as applied to the differential equations describing magnetic lines of force; and the notion of Euler potentials is extended by introducing an analogy to the Hopf map between the three-sphere and the two-sphere. Title: Magnetic free-energy in the solar atmosphere. Authors: Low, B. C. Bibcode: 1989GMS....54...21L Altcode: 1989sspp.conf...21L A program for extrapolating magnetic field in the force-free approximation has much to teach us about solar magnetic fields and this review surveys what can be done and the kind of pitfalls that beset the program. Title: Magnetic Field Configurations Associated with Polarity Intrusion in a Solar Active Region - Part Two Authors: Low, B. C. Bibcode: 1988SoPh..115..269L Altcode: The theoretical force-free magnetic fields in the first paper of this series, modeling magnetic configurations associated with polarity intrusion in active regions, are established to be all stable to linear ideal hydromagnetic perturbations under the boundary condition that anchors the lines of force rigidly to the photosphere. It is shown first that these force-free fields belong to an even larger class found by Chang and Carovillano (1981). A proof by the energy principle is then given to establish that all force-free magnetic fields in the larger class are absolutely stable. The physical implications of this result are discussed. Title: On the Hydromagnetic Stability of a Class of Laminated Force-Free Magnetic Fields Authors: Low, B. C. Bibcode: 1988ApJ...330..992L Altcode: Chang and Carovillano (1981) pointed out the existence of two classes of nonlinear force-free magnetic fields varying with three spatial dimensions which can be described analytically. In this paper, it is established by a general proof using the energy principle that one of these two classes of fields, in which all lines of force lie on parallel planes with the field pattern varying from plane to plane, are all stable to linear perturbations in the ideal hydromagnetic approximation. Laminated fields are derived which provide an excellent opportunity to study the propagation of small-amplitude hydromagnetic waves in a three-dimensional inhomogeneous magnetized medium. Title: Structure and Dynamics of Magnetic Fields in the Solar Atmosphere Authors: Low, B. C. Bibcode: 1988BAAS...20..723L Altcode: No abstract at ADS Title: Spontaneous Formation of Electric Current Sheets and the Origin of Solar Flares Authors: Low, B. C.; Wolfson, R. Bibcode: 1988ApJ...324..574L Altcode: It is demonstrated that the continuous boundary motion of a sheared magnetic field in a tenuous plasma with an infinite electrical conductivity can induce the formation of multiple electric current sheets in the interior plasma. In response to specific footpoint displacements, the quadrupolar magnetic field considered is shown to require the formation of multiple electric current sheets as it achieves a force-free state. Some of the current sheets are found to be of finite length, running along separatrix lines of force which separate lobes of magnetic flux. It is suggested that current sheets in the form of infinitely thin magnetic shear layers may be unstable to resistive tearing, a process which may have application to solar flares. Title: Electric Current Sheet Formation in a Magnetic Field Induced by Continuous Magnetic Footpoint Displacements Authors: Low, B. C. Bibcode: 1987ApJ...323..358L Altcode: Attention is given to two analytical examples illustrating the formation of an electric current sheet in a magnetic field without neutral points, as a result of a continuous boundary displacement of the magnetic footpoints. This effect can be demonstrated by resort to potential magnetic fields that are treated as special cases of the general force-free magnetic field. The problem of the force-free magnetic field is cast in terms of Euler potentials. Title: Do slow shocks precede some coronal mass ejections? Authors: Hundhausen, A. J.; Holzer, T. E.; Low, B. C. Bibcode: 1987JGR....9211173H Altcode: The observed speeds of coronal mass ejections are often below the estimated Alfvén speed but above the sound speed for the background solar corona. This suggets that slow magnetohydrodynamic shocks may form as mass ejections sweep through the corona. We argue on the basis of the Rankine-Hugoniot relations and the propagation of small-amplitude slow mode waves that the shape of a slow shock front would be flattened (with respect to a sun-centered sphere) or perhaps even concave outward (from the sun) and thus present a very different appearance from the fast coronal shock waves that have been commonly modeled as wrapping around a mass ejection. The region behind a slow shock front standing just off the top of a coronal mass ejection would extend well out beyond the visible flanks of the ejection. The deflections of coronal structures that are commonly observed well outside of these flanks (and which are inconsistent with a fast shock wrapped around the mass ejection) are consistent with the presence of the slow shock, whether they lie in the enlarged postshock region or in a region still further beyond. Although the flattering of the tops of some mass ejections suggests our proposed slow shock configuration, a true test of its existence awaits formulation of quantitative models and detailed comparison with observations. Title: Characteristics of the Expansion Associated with Eruptive Prominences Authors: Athay, R. G.; Low, B. C.; Rompolt, B. Bibcode: 1987SoPh..110..359A Altcode: Gradients of Hα and electron scattering intensities derived from instantaneous radial distributions of erupting prominence material observed at several solar radii by Illing and Athay (1986) are often markedly smaller than those inferred by comparing the intensities observed near several radii to average prominence intensities observed near the limb. In this paper, we show that gradients derived by following individual features in their outward progression with time yield values that are consistent with limb observations and that usually exceed the values obtained from instantaneous distributions. We conclude from the diversity of observed gradients that the prominence eruption cannot be described by a self-similar expansion in which the expansion velocity is a function of radius and time only. However, we cannot rule out possible self-similar solutions that allow the expansion velocity to be a function of angular direction. Title: Electric Current-Sheet Formation in a Magnetic Field Induced by Continuous Magnetic Footpoint Displacements Authors: Low, B. C. Bibcode: 1987BAAS...19..922L Altcode: No abstract at ADS Title: The velocity field of a coronal mass ejection: The event of September 1, 1980 Authors: Low, B. C.; Hundhausen, A. J. Bibcode: 1987JGR....92.2221L Altcode: A coronal mass ejection with the appearance of two sets of overlapping loops occurred at about 0600 UT on September 1, 1980, over the northwest limb of the sun. It was one of the fastest events observed by the Solar Maximum Mission coronagraph during the 1980 epoch, with apparent radial velocity components or several features approaching 1000 km s-1. A study of the slow evolution of Hα prominence filaments and coronal structures in the northwest solar sector suggests that the mass ejection resulted from the disruption of a helmet streamer in association with, possibly, two filaments to give rise to the double-loop structure. This event is well covered by 10 coronagraph images of good quality so that the complex velocity field, defined by the apparent motions of many different parts of the mass ejection, can be mapped out as a function of space and time. The results of such an analysis are presented and related to current concerns in the theoretical understanding of mass ejections. In particular, it is concluded that a self-similar description of the velocity field is a gross oversimplification and that although some evidence of wave propagation can be found, the bright features in this mass ejection are plasma structures moving (presumably) with frozen-in magnetic fields, rather than waves propagating through plasmas and magnetic fields. Title: Static Current-Sheet Models of Quiescent Prominences Authors: Wu, F.; Low, B. C. Bibcode: 1987ApJ...312..431W Altcode: A two-dimensional solar prominence model is extended to three-dimensional variations and curved current sheets. The model treats prominences as infinitely thin electric current sheets forming vertical planes supported by a magnetic potential. Equilibrium states are derived by solving Ampere's equation for a discrete current density of a surface where the Lorentz force is everywhere upward. The mass distribution is calculated to balance the Lorentz force. Linear superpositions of potential fields are employed to define three-dimensional models for periodic prominences in a given direction and for a prominence mass sheet with a finite length. Title: Modeling Two-Dimensional Solar Wind Flows (R) Authors: Low, B. C. Bibcode: 1987sowi.conf..113L Altcode: No abstract at ADS Title: Interplanetary Effects of Coronal Mass Ejections Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.; Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing, R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos, P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward, R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T. Bibcode: 1986epos.conf.6.52H Altcode: 1986epos.confF..52H No abstract at ADS Title: Initiations of Coronal Mass Ejections Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.; Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing, R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos, P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward, R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T. Bibcode: 1986epos.conf.6.27H Altcode: 1986epos.confF..27H No abstract at ADS Title: Static current-sheet models of quiescent prominences. Authors: Wu, F.; Low, B. C. Bibcode: 1986NASCP2442...69W Altcode: 1986copp.nasa...69W A particular class of theoretical models idealize the prominence to be a discrete flat electric-current sheet suspended vertically in a potential magnetic field. The weight of the prominence is supported by the Lorentz force in the current sheet. These models can be extended to have curved electric-current sheets and to vary three-dimensionally. The equation for force balance is 1 over 4 pi (del times B) times Bdel p- p9 z=zero. Using Cartesian coordinates we take, for simplicity, a uniform gravity with constant acceleration g in the direction -z. If we are interested not in the detailed internal structure of the prominence, but in the global magnetic configuration around the prominence, we may take prominence plasma to be cold. Consideration is given to how such equilibrium states can be constructed. To simplify the mathematical problem, suppose there is no electric current in the atmosphere except for the discrete currents in the cold prominence sheet. Let us take the plane z =0 to be the base of the atmosphere and restrict our attention to the domain z greater than 0. The task we have is to solve for a magnetic field which is everywhere potential except on some free surface S, subject to suit able to boundary conditions. The surface S is determined by requiring that it possesses a discrete electric current density such that the Lorentz force on it is everywhere vertically upward to balance the weight of the material m(S). Since the magnetic field is potential in the external atmosphere, the latter is decoupled from the magnetic field and its plane parallel hydrostatic pressure and density can be prescribed. Title: The Slowly Varying Corona Near Solar Activity Maximum Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.; Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing, R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos, P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward, R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T. Bibcode: 1986epos.conf.6.57H Altcode: 1986epos.confF..57H No abstract at ADS Title: Three-dimensional magnetostatic models of the large-scale corona. Authors: Bogdan, T. J.; Low, B. C. Bibcode: 1986NASCP2442..275B Altcode: 1986copp.nasa..275B A special class of magnetostatic equilibria is described, which are mathematically simple and yet sufficiently versatile so as to fit any arbitrary normal magnetic flux prescribed at the photosphere. With these solutions, the corona can be modeled with precisely the same mathematically simple procedure as has previously been done with potential fields. The magnetostatic model predicts, in addition to the coronal magnetic field, the three dimensional coronal density which can be compared with coronagraph observations. Title: Modelling of Coronal Mass Ejections and POST Flare Arches Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.; Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing, R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos, P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward, R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T. Bibcode: 1986epos.conf6.366H Altcode: 1986epos.confF.366H No abstract at ADS Title: Models of Partially Open Magnetospheres with and without Magnetodisks Authors: Low, B. C. Bibcode: 1986ApJ...310..953L Altcode: This paper presents a large class of analytic solutions describing partially open magnetic fields in static equilibrium outside a central object, which may be taken to be a planet or a star. The problem for a potential magnetic field is first treated in axisymmetric geometry, with an equatorial, stress-free electric current sheet whose presence results in part of the magnetic flux opening to infinity. The solutions can be linearly superposed to construct idealized models of the solar coronal magnetic field in a partially open configuration. These solutions are further developed to allow for stresses in the current sheet and three-dimensionality, in that order of complexity. The stresses can be balanced in equilibrium by introducing gravitational and centrifugal forces acting on dense matter confined in the electric current sheet. Explicit solutions are presented to illustrate magnetic topologies of magnetospheres having rotating and nonrotating magnetodisks. A simple physical illustration is given to estimate the total mass in the Jovian magnetodisk from the observed macroscopic parameters of the disk electric current. Title: Blowup of Force-free Magnetic Fields in the Infinite Region of Space Authors: Low, B. C. Bibcode: 1986ApJ...307..205L Altcode: The model for the quasi-static evolution of a magnetic field through force-free states in response to slow motions of its footpoints at the boundary is considered using an axisymmetric model for a bipolar magnetic field in the infinite space outside a unit sphere. It is shown that, as has been suggested, footpoint displacements exist which can take a magnetic field in further evolution beyond a critical point, through force-free states with a suitably modified form of the alpha scalar function. However, not all footpoint displacements have this property. By direct example, it is shown that other footpoint displacements exist, in response to which quasi-static evolution breaks down and the magnetic field undergoes a catastrophic opening of part of its flux. Title: The Three-dimensional Structure of Magnetostatic Atmospheres. II. Modeling the Large-Scale Corona Authors: Bogdan, T. J.; Low, B. C. Bibcode: 1986ApJ...306..271B Altcode: Employing the formalism developed in the first paper in this series, a class of magnetostatic atmospheres is constructed in a 1/r-squared gravity. These solutions possess electric current densities distributed continuously in space and directed perpendicular to the gravitational force. A self-consistent treatment of the energy balance equation is omitted, but the problem is treated in fully three-dimensional geometry, allowing for an arbitrary prescription of the normal magnetic flux at some fixed spherical surface. The prospects of modeling real coronal structures in approximate magnetostatic equilibrium with observational inputs from magnetographs and coronographs will be evident from the illustrative examples presented. Title: A Three-Dimensional Model of the Solar Coronal Helmut-Streamer Authors: Low, B. C. Bibcode: 1986BAAS...18..709L Altcode: No abstract at ADS Title: Steady Hydromagnetic Flows in Open Magnetic Fields. I. A Class of Analytic Solutions Authors: Low, B. C.; Tsinganos, K. Bibcode: 1986ApJ...302..163L Altcode: This paper introduces a class of axisymmetric steady hydromagnetic flows along open stellar magnetic fields. The full set of hydromagnetic equations that describes these flows in spherical coordinates is reduced to a set of ordinary differential equations in the radial distance from the origin. A judicious choice of free functions admits solutions for a spherically symmetric density in an otherwise nonspherically symmetric flow. In general, the flow requires a formal, steady energy addition whose amount and spatial distribution are calculated self-consistently to conserve energy everywhere. These solutions provide a rare opportunity to study the basic physics of hydromagnetic stellar winds in terms of exact relationships. The rich variety of solutions presented include flows along dipolar magnetic fields that are purely radial and those that, in addition, have θ-components. Title: Coronal mass ejections and coronal structures. Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.; Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing, R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos, P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Stewart, R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T. Bibcode: 1986NASCP2439....6H Altcode: Contents: 1. Introduction. 2. Observations. 3. Initiation of coronal mass ejections - observations. 4. Modelling of coronal mass ejections and post-flare arches. 5. Interplanetary effects of coronal mass ejections. 6. The slowly varying corona near solar activity maximum. 7. Summary. Title: Physical processes in the solar corona. Authors: Rosner, R.; Low, B. C.; Holzer, T. E. Bibcode: 1986psun....2..135R Altcode: Contents: Transport theory (fundamental parameter regimes, the "ideal" problem, viscosity, parallel thermal energy transport, perpendicular transport, some comments on model building). Magnetohydrodynamic processes in the corona (equilibrium magnetic fields, linear stability and nonequilibrium, time-dependent phenomena). Energy and momentum balance of open and closed coronal structures (coronal holes and high-speed streams, Alfvén waves in the lower solar atmosphere, energy supply to magnetically closed coronal regions). Title: Coronal mass ejections. Authors: Low, B. C. Bibcode: 1986HiA.....7..743L Altcode: The ejection of coronal mass by the sun is characterized, reviewing the results of recent observational and theoretical investigations. Topics discussed include the structure of loop-type ejections, the relatively low ejection speeds (less than the Alfven and gravitational speeds except near the solar maximum), the variation of occurrence rate with the solar cycle, and the association of ejections with prominence events, with or without flares. Consideration is given to numerical MHD simulations of ejection-initiation mechanisms (both impulsive-energy and coronal-structure-instability models), helmet structures, and the three-dimensional nature of the ejection loop. The value of coronal mass ejections as easily observable members of a larger class of astrophysical events (magnetized-plasma expulsion from gravitational wells) is indicated. Title: Some Recent Developments in the Theoretical Dynamics of Magnetic Fields Authors: Low, B. C. Bibcode: 1985SoPh..100..309L Altcode: This article describes recent developments in the theoretical investigation of magnetostatic equilibrium in the presence of gravity, nonequilibrium in hydromagnetics, and classical problems in hydromagnetic stability. The construction of magnetostatic equilibria has progressed beyond geometrically idealized systems, such as the axisymmetric system, to fully three-dimensional systems capable of modelling realistic solar structures. Nonequilibrium in a magnetic field with an arbitrary interweaving of lines of force due to random footpoint motion is a novel and subtle property with important implications for the solar atmosphere. Work begun by Parker and subsequent developments are described. To the extent quasi-static solar structures are approximated by stable equilibrium, ideal hydromagnetic stability theory provides a first insight into how stability is achieved in the solar environment. A qualitative physical picture based on recent stability analyses is given. The article places emphasis on understanding basic principles and issues rather than detailed results which can be found in the published literature. Title: Axisymmetric expansion of a rotating adiabatic gas Authors: Low, B. C. Bibcode: 1985ApJ...293...44L Altcode: A differentially rotating adiabatic gas can exhibit axisymmetric, time-dependent, self-similar expansion. Analytic hydrodynamic solutions describing such an expansion are derived. These solutions are the generalization of well known spherically symmetric self-similar solutions for which rotation is not included. Basic properties are discussed and illustrated with explicit solutions for rotating gaseous bodies expanding freely in vacuum. The existence of these self-similar solutions is due to a compatibility in the transport of the pressure, density, and angular momentum of a gamma = 5/3 adiabatic gas undergoing expansion. The distribution of pressure gradient and centrifugal force can be maintained in an invariant form so that acceleration is everywhere radial at all time. A rotating, ejected stellar envelope may evolve asymptotically into such a state of motion. The discussion relates these self-similar solutions to others found recently for time-dependent magnetohydrodynamic flows in the presence of gravity. Title: Three-dimensional structures of magnetostatic atmospheres. I - Theory Authors: Low, B. C. Bibcode: 1985ApJ...293...31L Altcode: This paper presents two families of magnetostatic equilibrium states for two atmospheres, one with a uniform gravity and the other with a gravity due to a point mass in spherical geometry. Taking the electric current to be everywhere perpendicular to the gravitational force, the fully three-dimensional problem is shown to be amenable to analytic treatment. The equilibrium equations are reducible to a single nonlinear scalar partial differential equation. The assumption on the electric-current orientation is less restrictive than those used to generate three-dimensional magnetostatic states in previous studies. Consequently, the new magnetostatic solutions reported here exhibit a rich variety of possible magnetic topologies. A subset of these solutions have magnetic topologies identical to those of the set of all potential magnetic fields. This subset of solutions are analyzed as illustrative examples, with an application to model the three-dimensional magnetic structure of cool plasma loops, often observed in the EUV corona. The prospect for modeling realistic structures in the solar atmosphere with observational inputs is pointed out. The discussion relates the theoretical development to the property of nonequilibrium discussed by Parker and others. Title: Modeling solar magnetic structures Authors: Low, B. C. Bibcode: 1985svmf.nasa...49L Altcode: Some ideas in the theoretical study of force-free magnetic fields and magnetostatic fields, which are relevant to the effort of using magnetograph data as inputs to model the quasi-static, large-scale magnetic structures in the solar atmosphere are discussed. Basic physical principles will be emphasized. An attempt will be made to assess what we may learn, physically, from the models based on these ideas. There is prospect for learning useful physics and this ought to be an incentive for intensifying the efforts to improve vector magnetograph technology and to solve the basic radiative-transfer problems encountered in the interpretation of magnetograph raw data. Title: Three-dimensional magnetostatic models of coronal structures. Authors: Bogdan, T. J.; Low, B. C. Bibcode: 1985BAAS...17Q.632B Altcode: No abstract at ADS Title: Modeling solar magnetic structures. Authors: Low, B. C. Bibcode: 1985NASCP2374...49L Altcode: The author discusses some ideas in the theoretical study of force-free magnetic fields and magnetostatic fields, which are relevant to the effort of using magnetograph data as inputs to model the quasi-static, large-scale magnetic structures in the solar atmosphere. Title: Theory of Coronal Mass Ejection Transients Authors: Low, B. C. Bibcode: 1985spit.conf..988L Altcode: No abstract at ADS Title: On the large-scale magnetostatic coronal structures and their stability Authors: Low, B. C. Bibcode: 1984ApJ...286..772L Altcode: A class of solutions to magnetostatic calculations is examined for their fruitfulness in predicting the structures of solar coronal loops and their hydromagnetic stability in the presence of linear perturbations. An ideal, one-fluid, MHD equation describes a polytropic plasma and stability is analyzed rigorously in terms of continuum mechanics. It is noted that the polytropic approximation is crude, since little is known of coronal heating processes, but that the approach is transparent to easy physical interpretation. Attention is focused on global closed magnetic fields and classical helmet-streamer structures. Two classes of magnetostatic equilibrium solutions are obtained, and the existence of an open magnetic field is shown to lead to unstable equilibrium when the base length of the closed field region reaches a critical magnitude. No conclusions could be drawn regarding stability below the critical value. Title: An Analytic Model for Hydromagnetospheres Authors: Tsinganos, K.; Low, B. C. Bibcode: 1984ESASP.207..289T Altcode: 1984plap.rept..289T Steps needed to isolate a general solution of the complete hydromagnetic equations are outlined. In this solution, the axisymmetric magnetosphere that surrounds the central object consists of two regions. The first, around the magnetic equator, is controled by closed and dipole-like magnetic field lines wherein the plasma is in static equilibrium with the magnetic and gravitational fields. The second, around the magnetic axis, is controlled by flows along the open and monopole-like magnetic field lines. The total pressure is continuous everywhere and the solution is globally consistent. In the solar wind, for example, coronal holes can be associated with the region of open field lines and helmet streamer-type structures with the static regions of closed lines. In cosmic jets the accretion disk can be associated with the region of closed lines and the jet with the outflows along the open magnetic lines. Similar considerations may apply to the pulsar magnetosphere and bipolar flows from molecular clouds. Title: Self-Similar Magnetohydrodynamics - Part Four - the Physics of Coronal Transients Authors: Low, B. C. Bibcode: 1984ApJ...281..392L Altcode: In this theoretical study, the white-light coronal transient is regarded to be a fully developed magnetohydrodynamic flow that plows into a preexisting ambient atmosphere. To keep the mathematical problem simple, a model is considered where the ambient atmosphere has no magnetic field whereas the outflow carries a substantial axisymmetric magnetic field. A contact surface forms to drive a strong gasdynamic shock that travels ahead and compresses the ambient atmosphere. Such a global flow, with the effect of gravity included, is illustrated with a set of exact, analytic, self-similar solutions of magnetohydrodynamics. The governing nonlinear equations, derived in the first paper of this series, are solved with a general technique, constructing explicitly the gasdynamic shock and the trailing contact surface. Various types of magnetic field configurations in the outflow behind the contact surface are shown to give rise to plasma structures which resemble those commonly observed in white-light transients, such as loops, voids, and blobs. It is advocated that the coronal transient is a result of a hydromagnetic system becoming gravitationally unstable in the low corona. This takes place when the magnetic tension force and solar gravity fail to counter the natural tendency of a magnetized plasma to expand. A physical picture of this dynamic process is described, and some quantitative properties to relate to observation are pointed out. The original self-similar theory requires an adiabatic index γ = 4/3. It is shown that this constraint can be relaxed to γ ≠ 4/3, raising interesting questions of heating and cooling in an expanding plasma. For future interest, an appendix is attached to extend the self-similar theory to allow for three-dimensional distributions of the magnetic field and plasma and to incorporate Newtonian self-gravity. Title: Self-similar magnetohydrodynamics. III - The subset of spherically symmetric gasdynamic flows. IV - The physics of coronal transients Authors: Low, B. C. Bibcode: 1984ApJ...281..381L Altcode: A set of spherically symmetric, time-dependent self-similar gasdynamic flows is presented. A polytropic gas with γ = 4/3 is assumed, and a 1/r2 gravity is present. Explicit analytic solutions are presented to illustrate the expansion of an atmosphere into vacuum as well as into an ambient atmosphere. In the latter example, the outflow is separated from the undisturbed ambient atmosphere by a strong gasdynamic shock. Among the nonlinear properties illustrated are the acceleration and deceleration of a shock in an extended atmosphere and the acceleration of the outer layers of the atmosphere to high speeds by the shock. Title: Three-dimensional magnetostatic atmospheres - Magnetic field with vertically oriented tension force Authors: Low, B. C. Bibcode: 1984ApJ...277..415L Altcode: Further developments in a study of three-dimensional magnetostatic equilibrium in the presence of a vertical uniform gravity are reported. In an earlier study, a set of analytic solutions for coronal structures was constructed with the constraint that the three-dimensional magnetic field lies in parallel vertical planes. This constraint is now relaxed, leading to geometrically more realistic solutions. These equilibrium states are characterized by the magnetic tension force being vertical everywhere and the total pressure being a function of height only. The nonlinear equations describing these special magnetic fields are derived with the use of Euler potentials. Two illustrative examples are given in explicit form, suggesting the quiescent prominence to be a highly inhomogeneous structure, composed of local density enhancements and depletions embedded in a three-dimensional sheared magnetic field. Title: Evolution of solar magnetic flux. Authors: Boris, J. P.; DeVore, C. R.; Golub, L.; Howard, R. F.; Low, B. C.; Sheeley, N. R., Jr.; Simon, G. W.; Tsinganos, K. C. Bibcode: 1984NASRP1120....3B Altcode: Contents: Introduction. Appearance of magnetic flux: models for flux emergence, unexplained observations. Dynamics of surface magnetic flux: magnetic flux transport, magnetic flux structure. Disappearance of magnetic flux: theoretical considerations, observations of flux disappearance. Summary. Title: Coronal transients and their interplanetary effects. Authors: Hundhausen, A. J.; Burlaga, L. F.; Feldman, W. C.; Gosling, J. T.; Hildner, E.; House, L. L.; Howard, R. A.; Krieger, A. S.; Kundu, M. R.; Low, B. C.; Sheeley, N. R., Jr.; Steinolfson, R. S.; Stewart, R. T.; Stone, R. G.; Wu, S. T. Bibcode: 1984NASRP1120....6H Altcode: Contents: 1. Introduction. 2. Background material: Ancient history - solar flares and geomagnetic storms. Modern history - interplanetary shock waves. Coronal transients or mass ejections. 3. The present: Theoretical models. New observations of coronal mass ejections. 4. The future: Solar origins. Interplanetary effects. Title: Nonlinear periodic solutions for the isothermal magnetostatic atmosphere Authors: Low, B. C.; Hundhausen, A. J.; Zweibel, E. G. Bibcode: 1983PhFl...26.2731L Altcode: Zweibel and Hundhausen (1982) have obtained analytically a family of isothermal, horizontally periodic, magnetostatic atmospheres in a uniform gravitational field. The present investigation is concerned with another set of period analytic solutions, taking into account the equilibrium configuration of plasma condensations in an otherwise everywhere uniform field. The physics of the support of the condensations by the embedded magnetic field is of interest to the study of solar prominences and interstellar clouds. Attention is given to the nonlinear problem, the general results, models for plasma condensations, and questions of stability. Title: Hydromagnetic Solar Wind in a Partially Open Magnetic Field Authors: Low, B. C.; Tsinganos, K. Bibcode: 1983BAAS...15..995L Altcode: No abstract at ADS Title: The Energy of Electric Current Sheets - Part Two - the Magnetic Free Energy and the Photospheric Magnetic Flux Authors: Low, B. C.; Hu, Y. Q. Bibcode: 1983SoPh...84...83L Altcode: The free energy associated with current sheets formed by displacing magnetic dipoles in a highly conducting medium is discussed. Specific models are illustrated, based on the idea that the free energy of a magnetic field in the solar atmosphere is the energy librated after the field has relaxed to a potential state that preserves the photospheric flux distribution. Previous calculations by other authors based on the consideration of discrete currents were incorrect because the interaction between the atmospheric currents and the highly conducting photosphere was not accounted for properly. It is shown that when this interaction is included, the consideration of discrete currents leads to the same result based on continuous magnetic field consideration. Title: Non Axisymmetric Magnetostatic Equilibrium - Part One - a Perturbation Theory Authors: Hu, W. R.; Hu, Y. Q.; Low, B. C. Bibcode: 1983SoPh...83..195H Altcode: This paper considers the structural properties of a sunspot-like magnetic flux tube which lacks perfect axisymmetry. The flux tube is taken to be in static equilibrium with an atmosphere in a uniform gravity. Assuming the departure from axisymmetry to be slight, the equations for the first order non-axisymmetric part of the equilibrium are derived in cylindrical coordinates. These first order equations reduce to a linear second order hyperbolic partial differential equation in the r-z plane. Whereas Cauchy type boundary conditions are appropriate for hyperbolic equations, physical considerations dictate the specification of boundary conditions on a closed surve for our problem of interest. The construction of solutions to this boundary value problem is illustrated with three analytically soluble cases, where the zero-order axisymmetric equilibria are chosen to have magnetic field geometry of different complexity. A physical discussion of the results is given. Title: Expulsion of magnetized plasmas from coronae Authors: Low, B. C. Bibcode: 1983IAUS..102..467L Altcode: Recent MHD analytic treatments are adduced in a physical accounting of the mechanism by which magnetized plasma is sporadically spilled out of the sun's gravitational bounds. The same physical process is suggested to occur in the white light transient phenomena of other coronae. The coronal transient is interpreted as the outflow of a gravitationally unbound, preexisting hydromagnetic structure in the corona. The observed white light density structure is a part of this moving, preexisting structure, and the ambient atmosphere is swept upward and sideways by a large scale outflow. Title: Magnetostatic atmospheres with variations in three dimensions Authors: Low, B. C. Bibcode: 1982ApJ...263..952L Altcode: The static equilibrium of a fully ionized atmosphere with an embedded magnetic field, in the presence of a uniform gravity, is considered under the assumption that the magnetic field lines lie in parallel vertical planes perpendicular to the x-axis in Cartesian coordinates. The system is allowed to vary in all three dimensions. A nonlinear, second-order hyperbolic partial differential equation having y and z as independent variables is shown to be a necessary condition on the magnetic surfaces for an equilibrium state to exist. Selected explicit solutions are presented which illustrate various structural properties of prominence-like density enhancements, coronal magnetic arcades, as well as discrete bipolar plasma loops, for which explicit equilibrium solutions with three-dimensional extensions are for the first time presented. Title: The Energy of Electric Current Sheets - Part One - Models with Moving Magnetic Dipoles Authors: Hu, Y. Q.; Low, B. C. Bibcode: 1982SoPh...81..107H Altcode: This paper treats two problems on the formation of electric current sheets in the highly electrically conducting solar atmosphere. The first problem concerns a vertical current sheet formed by decreasing the distance between a pair of parallel magnetic line-dipoles lying on the photosphere. The solution to this problem was given previously by Priest and Raadu. With an interest in the flare phenomenon, they derived a formula for the energy stored through the presence of the current sheet. We show that this formula is incorrect. Firstly, there is an error of sign in the derivation of Priest and Raadu, so that, when corrected, the formula gives a negative value for the stored energy. Secondly, the formula is shown to refer to an energy quite different from the free energy associated with the current sheet. To calculate for the current free energy, it is important to account for the `frozen-in' condition in the highly conducting photosphere. Title: Self-similar magnetohydrodynamics. II - The expansion of a stellar envelope into a surrounding vacuum Authors: Low, B. C. Bibcode: 1982ApJ...261..351L Altcode: The axisymmetric self-similar expansion of a stellar envelope into a surrounding vacuum is treated. Two exact solutions are presented to describe the time-dependent magnetohydrodynamics of the envelope, assuming a polytrope with adiabatic index gamma equals 4/3. The boundary conditions at the interface with vacuum are treated explicitly, and a matching solution of Maxwell's equations is obtained to describe the electromagnetic waves propagating into the vacuum, ahead of the expanding envelope. As the envelope disperses to infinity, out of the gravitational bound of the stellar core, the magnetic field is stretched to a radial configuration. The energy properties are discussed, showing, in particular, why the gamma equals 4/3 polytrope exhibits self-similar expansion and how the total magnetic energy in the envelope may be either decreasing or increasing with time during the expansion, depending on the distribution of the plasma. Title: Magnetic Field Configurations Associated with Polarity Intrusion in a Solar Active Region - Part One - the Force-Free Fields Authors: Low, B. C. Bibcode: 1982SoPh...77...43L Altcode: This paper presents a new class of exact solutions describing the non-linear force-free field above a spatially localized photospheric bipolar magnetic region. An essential feature is the variation in all three Cartesian directions and this could not be modelled adequately with previously known symmetric force-free fields. Sequences of force-free fields are constructed and analyzed to simulate the slow growth of a pair of spots on the photosphere. The axis connecting the spots executes rotational motion, distorting the photospheric neutral line separating fluxes of opposite signs. We show directly from the analytic solutions that the resulting reversal of the positions of the spots relative to the background field is associated with (i) the creation of magnetic free energy, (ii) the severe shearing of localized low-lying loops in the vicinity where the photospheric transverse field aligns with the photospheric neutral line, and (iii) the emergence and disappearance of flux from the photosphere at these highly stressed regions. The model relates theoretically for the first time these different magnetic field features that have been suggested by observation and theoretical considerations to be flare precursors. A general formula, based on the virial theorem, is also given for the free energy of a force-free field, strictly in terms of the field value at the photosphere. This formula has obvious practical application. Title: The initiation of a coronal transient Authors: Low, B. C.; Munro, R. H.; Fisher, R. R. Bibcode: 1982ApJ...254..335L Altcode: The coronal transient/eruptive prominence event of August 5, 1980, observed by the Mauna Loa experiment system is analysed. This event provided data on the early development of the transient in the low corona between 1.2 and 2.2 solar radii, information that was not available when earlier attempts were made to explain transient phenomena. The transient's initial appearance in the form of a rising density-depleted structure, before the eruption of the associated prominence, is explained as an effect of magnetic buoyancy. The data suggest that this transient has a density depletion of 17% to 33% relative to an undisturbed corona which is approximately isothermal with a temperature of 1.5 x 10 to the 6th K and a coronal density of 1.0 x 10 to the 9th/cu cm at the base of the corona. Title: Self-similar magnetohydrodynamics. I - The gamma = 4/3 polytrope and the coronal transient Authors: Low, B. C. Bibcode: 1982ApJ...254..796L Altcode: The full set of ideal magnetohydrodynamic (MHD) equations for a gamma = 4/3 polytrope admits self-similar solutions which can be derived by analytic methods. An axisymmetric magnetic field in a stratified stellar atmosphere is assumed. The solutions admit a large variety of magnetic structures, including those in the form of loops, moving through the corona with large scale coherence and sharp small scale features. The Lagrangian velocity of an individual transient feature is found to accelerate or decelerate according to a positive or negative gain in momentum by the plasma in a self-similar distribution of the Lorentz force, the pressure gradient, and the gravitational force. In both cases, the net force decreases with time so that, at large radial distances, the motion becomes inertial. The physical implications are discussed, arguring in favor of the transient beginning as a fully nonlinear MHD motion that ejects both magnetic field and plasma out of the gravitational bond of the sun. Title: Some nonlinear problems in astrophysics Authors: Lerche, I.; Low, B. C. Bibcode: 1982PhyD....4..293L Altcode: Astrophysical magnetic fields, in the hydromagnetic approximation, pose a rich class of nonlinear problems. Of primary interest is the behavior and properties of the magnetic field interacting with the plasma in the presence of gravity. Substantial progress has been made recently with these problems arising in the study of interstellar clouds, stellar structures and magnetospheres, and structures on the Sun, such as prominences, sunspots and coronal magnetic fields. This paper reviews recent theoretical work, concentrating on steady state problems and emphasizing the use of analytic methods.

The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Nonlinear force-free magnetic fields. Authors: Low, B. C. Bibcode: 1982RvGSP..20..145L Altcode: 1982RvGeo..20..145L The nonlinear properties of force-free magnetic fields are reviewed with particular reference to the mechanisms for the sudden release of stored energy in flares during the quasi-steady evolution of solar fields. It is shown that in the solar atmosphere, force-free fields with a nonconstant scalar function in the field equations are more likely to occur than those with a constant scalar function, and the nonlinear properties of these fields may give rise to many interesting physical effects. Consideration is then given to two possible mechanisms of field evolution: a model in which a force-free field in a medium of infinite electrical conductivity evolves in response to slowly changing boundary conditions brought about by photospheric motions in the solar active region, and a model in which a field in a medium of small finite electrical conductivity evolves in response to the slow Ohmic dissipation of the electric current. Title: The Vertical Filamentary Structures of Quiescent Prominences Authors: Low, B. C. Bibcode: 1982SoPh...75..119L Altcode: We present a simple magnetostatic theory of the thin vertical filaments that make up the quiescent prominence plasma as revealed by fine spatial resolution Hα photographs. A class of exact equilibrium solutions is obtained describing a horizontal row of long vertical filaments whose weights are supported by bowed magnetic field lines. A free function is available to generate different assortments of filament sizes and spacings, as well as different density and temperature variations. The classic Kippenhahn-Schlüter solution for a long sheet without filamentary structures is a particular member of this class of solutions. The role of the magnetic field in supporting and thermally shielding the filament plasma is illustrated. It is found that the filament can have a sharp transition perpendicular to the local field, whereas the transition in the direction of the local field is necessarily diffuse. A consequence of the filamentary structure is that its support by the Lorentz force requires the electric current to have a component along the magnetic field. This electric current flowing into the rarefied region around the prominence can contain substantial energy stored in the form of force-free magnetic fields. This novel feature has implications for the heating and the disruption of prominences. Title: Eruptive solar magnetic fields Authors: Low, B. C. Bibcode: 1981ApJ...251..352L Altcode: The quasi-steady evolution of solar magnetic fields in response to gradual photospheric changes is considered, with particular attention given to the threshold of a sudden eruption in the solar atmosphere. The formal model of an evolving, force-free field dependent on two Cartesian coordinates is extended to a field which is not force free but in static equilibrium with plasma pressure and gravity. The basic physics is illustrated through the evolution of a loop-shaped electric current sheet enclosing a potential bipolar field with footpoints rooted in the photosphere. A free-boundary problem is posed and then solved for the equilibrium configuration of the current sheet in a hydrostatically supported isothermal atmosphere. As the footpoints move apart to spread a constant photospheric magnetic flux over a larger region, the equilibria available extend the field to increasing heights. Title: Equilibrium configuration of the magnetosphere of a star loaded with accreted magnetized mass Authors: Uchida, Y.; Low, B. C. Bibcode: 1981JApA....2..405U Altcode: No abstract at ADS Title: On the Presence of Electric Currents in the Solar Atmosphere - Part One - a Theoretical Framework Authors: Hagyard, M.; Low, B. C.; Tandberg-Hanssen, E. Bibcode: 1981SoPh...73..257H Altcode: An elementary analysis based on Ampére's Law is given to separate the general magnetic field above the photosphere into two parts B=B1+B*. The field B1 is a potential field due to electric currents below the photosphere. The field B* is produced by electric currents above the photosphere combined with the induced mirror currents. By symmetry, B* has a set of field lines lying entirely in the plane z = 0 taken to be the photosphere. This set of field lines can be constructed from given vector magnetograph measurements and represents all the information on the electric currents above the photosphere that a magnetograph can provide. Theoretical illustrations are given and the implications for data analysis are discussed. Title: A class of analytic solutions for the thermally balanced magnetostatic prominence sheet Authors: Low, B. C.; Wu, S. T. Bibcode: 1981ApJ...248..335L Altcode: A theoretical study is presented for the nonlinear interplay between magnetostatic equilibrium and energy balance in a Kippenhahn-Schlueter type solar prominence sheet. A class of theoretical models is presented, expressed in closed analytic forms, thus facilitating the direct illustration of the nonlinear physical properties. The model couples the equilibrium between magnetic field, plasma pressure, and weight on the one hand, with the balance between a rho-squared T radiative loss, a rho wave heating (where rho equals plasma density, and T equals plasma temperature), and thermal conduction channeled along magnetic field lines on the other. The steady solutions are divided into three classes, and are characterized by the total wave heating in the prominence sheet which is greater than, equal to, or less than the total radiative loss. The compaction of the plasma along the field lines, under its own weight, and the energy transport effects determine which of the three basic behaviors obtains in a particular situation. A discussion is presented of the implications of the steady solutions for the formation of prominences. Title: The field and plasma configuration of a filament overlying a solar bipolar magnetic region Authors: Low, B. C. Bibcode: 1981ApJ...246..538L Altcode: This paper presents an analytic model for a finite-size straight filament suspended horizontally in a steady state over a bipolar magnetic region. The equations of magnetostatic equilibrium are integrated exactly. The solution obtained illustrates the roles played by the electric current, magnetic field, pressure, and plasma weight in the balance of force everywhere in space. A specific example of a filament of diameter 50,000 km, with a density two orders of magnitude over the corona and supported by a magnetic field of about 4 gauss is included. The filament temperature can take values ranging from a small fraction to a few times the coronal temperature, depending on the internal electric current of the filament. To produce a cool filament, such as the quiescent prominence, the solution is required to have an internal field with a strong component along the filament, giving rise to helical structures. A hot filament such as the X-ray coronal loop can be produced as a twisted magnetic flux tube embedded in a strong background field aligned parallel to the filament and having lower density and temperature. The basic steps of construction can be used to develop models more realistic than the ones presented for their analytic simplicity. Title: On the Expulsion of Magnetised Plasmas through Solar and Stellar Atmospheres Authors: Low, B. C. Bibcode: 1981BAAS...13..837L Altcode: No abstract at ADS Title: The Magnetohydrodynamics of an Expanding Stellar Envelope Authors: Low, B. C. Bibcode: 1981BAAS...13..792L Altcode: No abstract at ADS Title: A Variational Approach to the Question of Temporal Stability of Equilibrium Models of Solar Prominences - Part One - the Formal Theory Authors: Lerche, I.; Low, B. C. Bibcode: 1981SoPh...69..327L Altcode: Using a Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences, we derive seven quantities which, by analogy to the concepts of energy, momentum and angular momentum, are conserved under circumstances corresponding to ignorable coordinates of classical mechanics. In a pragmatic sense it is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigen-frequencies for the perturbation equations when numerical techniques are employed. Title: On the equilibrium of heated self-gravitating masses - Cooling by conduction Authors: Lerche, I.; Low, B. C. Bibcode: 1980ApJ...242.1144L Altcode: An investigation is given of the equilibrium states available to a self-gravitating mass of gas, cooling by conduction, and being heated at a rate proportional to the local gas density. The plane geometry situation is shown to be reducible to quadratures for the pressure, density, temperature, and gravitational potential. For a constant thermal conductivity it is shown that the gas density has either a central maximum or a central minimum, depending on the ratio of the thermal conductivity to a parameter taken to be a measure of the rate of heating. For a thermal conductivity which is a positive power of the temperature, it is shown that the gas density always has a central minimum and a maximum at the outer boundary of the configuration. For cylindrical and spherical geometrical configurations the same general properties are obtained. The physical origin of this behavior is discussed, and it is suggested that these exploratory calculations provide an effect which may not only aid in understanding thin filamentary structure observed in supernova remnants, but also help to assuage the difficulties of producing maser activity in the interior regions of 'cocoon' protostars. Title: On equilibrium states of heated self-gravitating gas clouds cooling by conduction in an external gravitational field Authors: Lerche, I.; Low, B. C. Bibcode: 1980ApJ...242.1156L Altcode: Exact analytic solutions are presented for equilibrium states of a self-gravitating one-dimensional cloud of gas, embedded in an external gravitational field due to a plane of 'stars' being heated at a rate proportional to the local gas density, and cooling by thermal conduction. It is found that the general topology of the solutions is such that the gas density has a minimum on the plane of 'stars', rising to an infinite but integrable peak away from the plane so that the total mass of gas in the cloud is finite. The results may be of interest in investigations of interstellar molecular clouds and of filamentary structures in supernova remnants as well as in the modeling of gas distributions around 'cocoon' protostars. Title: The heating of a thermally conducting stratified medium. II. A simple plane model on an atmosphere. Authors: Lerche, I.; Low, B. C. Bibcode: 1980ApJ...241..459L Altcode: Exact solutions of the following theoretical problem are presented: A plane atmosphere is in hydrostatic equilibrium with a uniform gravity. The ideal gas law is assumed. Heat is generated everywhere at a rate proportional to the local density. The atmosphere is maintained in a steady state through cooling by thermal conduction and radiation. This problem is reducible to quadratures for a thermal conductivity which is an arbitrary, but prescribed, function of the temperature, and for a radiative loss which is expressible as the product of the density and an arbitrary, but prescribed, function of the pressure. The analysis is carried out for the case of power law thermal conductivity, and a radiative loss proportional to the square of the density and to the first power of the temperature. The radiative cooling function adopted here has the basic mathematical form for an optically thin medium. The solutions reproduce the macroscopic ordering of a hot 'corona' separated from a 'photosphere' by a layer of temperature minimum. The analytic solutions allow direct illustration of the interplay between steady energy transport and the requirements of hydrostatic equilibrium. Title: Eruptive Solar Magnetic FIELDS# Authors: Low, B. C. Bibcode: 1980BAAS...12..902L Altcode: No abstract at ADS Title: On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields Authors: Lerche, I.; Low, B. C. Bibcode: 1980MNRAS.192..611L Altcode: The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines. Title: On the resistive diffusion of force-free magnetic fields Authors: Low, B. C. Bibcode: 1980JPlPh..24..181L Altcode: Reid and Laing recently conjectured on the general behaviour of resistive force- free magnetic fields in a slab model following a numerical study. However, the basic properties of resistive force-free magnetic fields had been established previously. We use and extend some results from the previous work to show that the conjecture of Reid and Laing is incorrect. A general analytic treatment of the problem provides the correct physical properties that Reid and Laing were unable to deduce from their numerical solutions. A criticism is also given of the results presented in another numerical study treating cylindrical resistive forcefree magnetic fields, by the same authors. Title: On the Equilibrium of a Cylindrical Plasma Supported Horizontally by Magnetic Fields in Uniform Gravity Authors: Lerche, I.; Low, B. C. Bibcode: 1980SoPh...67..229L Altcode: We consider the mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity. This configuration is what may be expected if a quiescent prominence were to condense in a region initially filled with a uniform magnetic field. A set of exact solutions describing the equilibrium situation is presented. Although the plasma distribution is assumed to be cylindrically symmetric to obtain tractibility of the problem, exact force balance between plasma pressure, the Lorentz force and gravity is achieved everywhere in space. The set of solutions covers a particular case of a uniform temperature as well as cases where the temperature rises from zero at the center of the plasma cylinder to rapidly reach a constant asymptotic value outside the cylinder. The physical properties of these solutions are described. A suggestion is made for future development, based on the present work, to construct a prominence model in which the requirements of both mechanical and radiative equilibrium are satisfied. Title: Exact Static Equilibrium of Vertically Oriented Magnetic Flux Tubes - Part One - the Schluter-Temesvary Sunspot Authors: Low, B. C. Bibcode: 1980SoPh...67...57L Altcode: A method is prescribed for generating exact solutions of magnetostatic equilibrium describing a cylindrically symmetric magnetic flux tube oriented vertically in a stratified medium. Given the geometric shape of the field lines, compact formulae are presented for the direct calculation of all the possible distributions of pressure, density, temperature and magnetic field strength compatible with these field lines under the condition of static equlibrium. The plasma satisfies the ideal gas law and gravity is uniform in space. A particular solution is obtained by this method for a medium sized sunspot whose magnetic field obeys the similarity law of Schlüter and Temesváry (1958). With this solution, it is possible for the first time to illustrate explicitly the confinement of the magnetic field of the cool sunspot by the hotter external plasma in an exact relationship involving both magnetic pressure and field tension as well as the support of the weight of the plasma by pressure gradients. It is found that the cool region of the sunspot is not likely to extend much more than a few density scale heights below the photosphere. The sunspot field approaches being potential in the neighbourhood of the photosphere so that the Lorentz force exerting on the photosphere is less than what the magnetic pressure would suggest. This accounts for how the sunspot field can be confined in the photosphere where its magnetic pressure is often observed to even exceed the normal photospheric pressure. The energy mechanism operating in the sunspot and the question of mechanical stability are not treated in this paper. Title: Evolving force-free magnetic fields. III - States of nonequilibrium and the preflare stage Authors: Low, B. C. Bibcode: 1980ApJ...239..377L Altcode: The paper considers whether a neighboring magnetostatic equilibrium exists to allow a magnetic field initially in a force-free configuration to accommodate any imposed weak pressure. The following problem is treated. The foot points of the field are fixed and the plasma is frozen into the field lines under the approximation of infinite electrical conductivity. A weak pressure is introduced. It is determined infinitesimal plasma displacements exist to adjust the field lines to a new equilibrium without changing the field line connectivity. The analysis is carried out for the bipolar force-free fields forming one of two evolutionary sequences modeling the development of the preflare stage. It was found that for the force-free field corresponding to the quasi-static stage of evolution, the neighboring magnetostatic equilibrium always exists and the imposed gas pressure can be accommodated with a slight departure of the field from being exactly force free. Title: The heating of a thermally conducting stratified medium. I - Self-gravitating gas threaded by magnetic fields Authors: Lerche, I.; Low, B. C. Bibcode: 1980ApJ...239..360L Altcode: Two theoretical problems are presented to illustrate the equilibrium structure of a gravitating gas threaded by magnetic fields. The gas is heated everywhere at a rate proportional to the local density and cooled by thermal conduction channeled along the magnetic field. Emphasis is placed on the influence of anisotropic thermal conduction on the distribution of the gas. In the first problem, the magnetic field has straight field lines that are nearly parallel. The simple field line geometry allows us to calculate, in closed form, the equilibria configurations of a gas slab which is cooled nonuniformly by thermal conduction along field lines which leave the gas slab at varying angles. The problem involves the gas having a free boundary, which is one of the unknowns to be determined. A discussion is given of the set of all possible equilibria so constructed. In the second problem there is no electric current flowing in the gas but there is a potential magnetic field having curved field lines. Exact solutions of equilibriums are presented to illustrate the heating of stellar and galactic coronas. Title: Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium Authors: Lerche, I.; Low, B. C. Bibcode: 1980ApJ...238.1088L Altcode: Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation. Title: Cylindrical Prominences and the Magnetic Influence of the Photospheric Boundary Authors: Lerche, I.; Low, B. C. Bibcode: 1980SoPh...66..285L Altcode: We construct exact, non-linear, solutions for an horizontal, cylindrical, current-carrying, prominence supported against solar gravity by the action of a Lorentz force. The solutions incorporate the photosphere boundary condition, proposed by van Tend and Kuperus (1978), and analyzed by them for line filaments. Our solutions have finite radius for the prominence material and, as well as satisfying the equations of magnetostatic equilibrium, they allow for the continuity of gas pressure, and of the normal and tangential components of magnetic field across the circular prominence boundary. We show that an infinity of solutions is possible and we illustrate the basic behavior by investigation of a special case. Title: Exact Magnetostatic Models of Filament Prominences Authors: Low, B. C. Bibcode: 1980BAAS...12..477L Altcode: No abstract at ADS Title: On Magnetostatic Equilibrium in a Stratified Atmosphere Authors: Low, B. C. Bibcode: 1980SoPh...65..147L Altcode: This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction. Title: The False Equilibrium of a Force-Free Magnetic Field Authors: Low, B. C. Bibcode: 1980IAUS...91..283L Altcode: No abstract at ADS Title: On exact equilibrium states in external gravitational fields of heated, self-gravitating gas clouds cooling by conduction and radiation. Authors: Lerche, I.; Low, B. C. Bibcode: 1980PhyD...10..203L Altcode: No abstract at ADS Title: Evolving force-free magnetic fields. IV. A variational formulation of the problem. Authors: Low, B. C. Bibcode: 1978ApJ...224..668L Altcode: A theoretical model of evolving force-free magnetic fields is reformulated by taking the distribution of photospheric footpoints as the starting point of the model. A previously considered case of two-dimensional geometry is treated, and the equations for the force-free fields above the photosphere are derived from a variational principle. It is shown that the approach adopted leads to a formidable nonlinear boundary-value problem and that the physical relationship between photospheric footpoint motions and magnetic-field evolution can be more fruitfully investigated by using the original formulation in which the starting point is to take as given the value of the longitudinal field and a transverse field at the photosphere. The questions of the existence and uniqueness of the solution to the nonlinear boundary-value problem are briefly considered. Title: Evolving force-free magnetic fields. II. Stability of field configurations and the accompanying motion of the medium. Authors: Low, B. C. Bibcode: 1977ApJ...217..988L Altcode: Two features of magnetic field evolution in the solar atmosphere are examined for understanding solar flare phenomena. A stability analysis of the force-free configurations of the magnetic field in Paper I (1977), treated as static fields with their foot points rooted in the photosphere, reveals that they are stable when subject to infinitesimal perturbations which depend on two Cartesian coordinates. As a result, the quasi-static evolution of intense magnetic fields in the solar atmosphere may be understood in terms of successive infinitesimal displacements of photospheric magnetic foot points and the relaxation to a new stable force-free configuration following each infinitesimal displacement of magnetic foot points. Furthermore, a kinematic approach is described for obtaining information on the plasma motion during the evolution of a magnetic field. The kinematic velocities that satisfy the governing induction equation are found to have contrasting flow patterns associated with qualitatively different mass transport. Title: A self-consistent model of a thermally balanced quiescent prominence in magnetostatic equilibrium in a uniform gravitational field. Authors: Lerche, I.; Low, B. C. Bibcode: 1977SoPh...53..385L Altcode: We present a theoretical model of quiescent prominences in the form of an infinite vertical sheet. Self-consistent solutions are obtained by integrating simultaneously the set of nonlinear equations of magnetostatic equilibrium and thermal balance. The basic features of the models are: (1) The prominence matter is confined to a sheet and supported against gravity by a bowed magnetic field. (2) The thermal flux is channelled along magnetic field lines. (3) The thermal flux is everywhere balanced by Low's (1975b) hypothetical heat sink which is proportional to the local density. (4) A constant component of the magnetic field along the length of the prominence shields the cool plasma from the hot surrounding. We assume that the prominence plasma emits more radiation than it absorbs from the radiation fields of the photosphere, chromosphere and corona, and we interpret the above hypothetical heat sink to represent the amount of radiative loss that must be balanced by a nonradiative energy input. Using a central density and temperature of 1011 particles cm−3 and 5000 K respectively, a magnetic field strength between 2 to 10 gauss and a thermal conductivity that varies linearly with temperature, we discuss the physical properties implied by the model. The analytic treatment can also be carried out for a class of more complex thermal conductivities. These models provide a useful starting point for investigating the combined requirements of magnetostatic equilibrium and thermal balance in the quiescent prominence. Title: Evolving force-free magnetic fields. I. The development of the preflare stage. Authors: Low, B. C. Bibcode: 1977ApJ...212..234L Altcode: Two boundary value problems are solved analytically to obtain nonlinear force-free magnetic fields overlying given time-dependent distributions of bipolar photospheric magnetic fields. We follow the evolution in time of these two magnetic fields to show the development of conditions likely to lead to solar flares. For the first magnetic field, the photosphere moves as two almost rigid plates sliding past each other along the magnetic neutral line. For the second magnetic field, the photospheric velocity at large distances from the magnetic neutral line has a growing uniform shear. The preflare stage for each magnetic field is described. In particular, the model demonstrates that the presence of large horizontal photospheric velocity shear across the magnetic neutral line prior to a flare eruption is closely associated with either a parallel or a perpendicular horizontal magnetic field along the magnetic neutral line. Title: Dynamics of solar magnetic fields. VI. Force-free magnetic fields and motions of magnetic foot-points. Authors: Low, B. C.; Nakagawa, Y. Bibcode: 1975ApJ...199..237L Altcode: A mathematical model is developed to consider the evolution of force-free magnetic fields in relation to the displacements of their foot-points. For a magnetic field depending on only two Cartesian coordinates and time, the problem reduces to solving a nonlinear elliptic partial differential equation. As illustration of the physical process, two specific examples of evolving force-free magnetic fields are examined in detail, one evolving with rising and the other with descending field lines. It is shown that these two contrasting behaviors of the field lines correspond to sheared motions of their foot-points of quite different characters. The physical implications of these two examples of evolving force-free magnetic fields are discussed. Title: Nonisothermal magnetostatic equilibria in a uniform gravity field. II. Sheet models of quiescent prominences. Authors: Low, B. C. Bibcode: 1975ApJ...198..211L Altcode: We use the mathematical formulation of Low to construct magnetostatic models of the quiescent prominence in the form of a vertical infinite sheet of material which is both denser and cooler than its surrounding. A magnetic field of about 2 gauss serves to support the weight of the prominence and to confine the prominence material in a thin sheet. By a suitable choice of a certain free function in the mathematical model, the variation of the prominence temperature corresponds to a medium with a 5/2 power-law thermal conductivity, neglecting the magnetic effect on thermal conduction. It is shown that a static balance obtains everywhere between the conducted heat input and a hypothetical heat sink which is proportional to the local material density. This heat sink simulates the effect of the radiative loss of the prominence. The gross observed prominence features are reproduced. Title: Nonisothermal magnetostatic equlibria in a uniform gravity field. I. Mathematical formulation. Authors: Low, B. C. Bibcode: 1975ApJ...197..251L Altcode: The magnetostatic equilibrium equations of a two-dimensional plasma in a uniform gravity field are derived without assuming a constant gas temperature. Pressure and temperature are transformed into functions of the magnetic vector potential and the vertical height, and the vector equilibrium equation for Cartesian and cylindrical coordinate systems is reduced to a single scalar nonlinear elliptic partial differential equation. The general properties of the derived equations and their general implications are discussed, and it is shown that photospheric conditions at any one time in general do not determine unique magnetostatic equilibrium configurations above the photosphere. Title: Evolving Force-Free Magnetic Fields in Response to Photospheric Motions Authors: Low, B. C.; Nakagawa, Y. Bibcode: 1975BAAS....7..347L Altcode: No abstract at ADS Title: Resistive diffusion of force-free magnetic fields in a passive medium. IV. The dynamical theory. Authors: Low, B. C. Bibcode: 1974ApJ...193..243L Altcode: The subsequent resistive diffusion of an initially force-free magnetic field in a tenuous medium, initially at rest, is considered. The inertia of the medium is taken into account. The one-dimensional case is treated by an expansion of both the momentum and the hydromagnetic induction equations of the parameter epsilon = An/V0 in the limit of epsilon being much less than 1. Here A(-1) is a typical length scale, n the constant resistive coefficient, and V0 the Alfven speed. It is found that within the Alfven transit time a small nonzero Lorentz force sets in and accelerates the medium to move in a manner such that the magnetic field may remain almost force-free for an extended period of time. Title: Resistive Diffusion of Force-Free Magnetic Fields in a Passive Medium. III. Acceleration of Flare Particle Authors: Low, B. C. Bibcode: 1974ApJ...189..353L Altcode: We have previously suggested that solar flares are triggered by the resistive diffusion of force-free magnetic fields in a passive medium. We consider a one-dimensional model in which an increasingly large electric field is induced by a rapidly evolving magnetic field. We estimate, in the case of solar flares, the energies to which protons and electrons may be directly accelerated by such an induced electric field. Sabject headings: flares, solar - hydromagnetics Title: Resistive diffusion of force-free magnetic fields in a passive medium. Authors: Low, B. C. Bibcode: 1974BAAS....6..264L Altcode: No abstract at ADS Title: Erratum: Resistive Diffusion of Force-Free Magnetic Fields in a Passive Medium Authors: Low, B. C. Bibcode: 1973ApJ...186..775L Altcode: No abstract at ADS Title: Resistive Diffusion of Force-Free Magnetic Fields in a Passive Medium. 11. a Nonlinear Analysis of the One-Dimensional Case Authors: Low, B. C. Bibcode: 1973ApJ...184..917L Altcode: We investigate the force-free magnetic field B = [cos (z, t), sin (z, t), 0] to ascertain when it may develop infinite field gradients while undergoing resistive diffusion in a passive medium (Low). A complete analysis of the nonlinear evolution of B is given, subject to the conditions (i) 4L(z, 0) is an odd and increasing function of the Cartesian coordinate z and (ii) ( I 00, t) = I o for all time, where o is finite and independent of time. if the total rotation of B along the z-axis exceeds half a revolution, i.e., > , we find that B always develops infinite field gradients after a finite period of time, irrespective of the initial distribution (z, 0). The modest criterion > supports our suggestion that this type of instability triggers the eruption of flares in the solar chromosphere. if < , we find that B always evolves toward a uniform field, irrespective of the initial distribution (z, 0). The marginal case = admits an unstable steady state. We use the properties of this steady state to show how a quantitative theory of homologous flares might be constructed. Subject headings: flares, solar - hydromagnetics Title: Resistive Diffusion of Force-Free Magnetic Fields in a Passive Medium Authors: Low, B. C. Bibcode: 1973ApJ...181..209L Altcode: A force-free magnetic field B(x, t) satisfying V x B = aB for nonconstant a will change its shape as it undergoes resistive diffusion. We consider the resistive diffusion of such a force-free magnetic field in a tenuous compressible medium, which is free to move to accommodate the changing magnetic-field configuration. This process is nonlinear, contrary to the usual magnetic field diffusion in a fixed medium. We show that the force-free magnetic field may evolve slowly for an extended period of time, whereupon it abruptly develops steep gradients and passes into an explosive phase. We suggest that it is this process that sets the stage for the onset of solar flares. Subject headings: flares, solar - hydromagnetics - magnetic fields Title: Erratum: Root Mean Square Fluctuation of a Weak Magnetic Field in an Infinite Medium of Homogeneous Stationary Turbulence Authors: Low, B. C. Bibcode: 1972ApJ...178..277L Altcode: No abstract at ADS Title: Root Mean Square Fluctuation of a Weak Magnetic Field in an Infinite Medium of Homogeneous Stationary Turbulence Authors: Low, B. -C. Bibcode: 1972ApJ...173..549L Altcode: This paper considers the generation of magnetic field by statistically homogeneous, stationary velocity turbulence. The generation of rms magnetic fluctuation is explicitly demonstrated in the limit of short turbulence correlation time. It is shown that the fluctuation ( B2) associated with a growing or stationary mean field (B grows with time such that ( B1)/( tends to a steady value, which is a monotonically decreasing function of the growth rate of (B) As an application, we estimate ( B1)/(B) to be of order one for the galactic medium, in agreement with observational results. In the case of a decaying (B), we show that the associated (bB1) eventually decays in time, proceeding at a rate slower than that of the decay of (B). Title: Kinematic-Dynamo Action Under Incompressible, Isotropic Velocity Turbulence Authors: Lerche, I.; Low, B. C. Bibcode: 1971ApJ...168..503L Altcode: We demonstrate that incompressible, isotropic velocity turbulence on its own iii an infinite medium leads to regenerative dynamo action. Earlier work has demonstrated that (i) incompressible velocity turbulence possessing a net helicity generates dynamo action in an infinite medium; (ii) isotropic, compressible velocity turbulence generates dynamo action in an infinite medium. The present results show first that regenerative dynamo action is not peculiar to the assumption of either nonisotropy or compressibility, and second that the turbulent Lorentz force (which is never isotropic no matter whether the velocity turbulence is isotropic or not) is the main cause of purely turbulent dynamo action. The fact that incompressible, isotropic turbulence generates dynamo activity just underscores these facts.