Author name code: leer ADS astronomy entries on 2022-09-14 author:"Leer, Egil" ------------------------------------------------------------------------ Title: Solar wind originating in funnels: fast or slow? Authors: Janse, Å. M.; Lie-Svendsen, Ø.; Leer, E. Bibcode: 2007A&A...474..997J Altcode: Aims:We model a hydrogen-helium solar wind originating in funnels, regions of rapid flux tube expansion at the base of the solar corona.
Methods: The time-dependent model describes the particle density, flow speed, temperature parallel and perpendicular to the magnetic field, and the heat flow for each ionization state of hydrogen and helium, and for electrons.
Results: For a large range of heating parameters, the funnel has two co-existing solutions: both a slow and a fast solar wind solution result from the same heating parameters, depending on the initial state from which the model was started. Though the fast and the slow solar wind can co-exist it is difficult to change from a fast solar wind to a slow solar wind or vice versa. A significant change in the heating parameters is required to “flip” the solution, and it takes a long time, about one month, to reach the other steady state solution. When either the funnel or helium is removed from the model, we no longer have two co-existing states. Title: The Impact of Solar Eruptions on the Upper Chromosphere, Transition Region, and Corona Authors: Lie-Svendsen, Øystein; Leer, Egil Bibcode: 2006ApJ...643.1286L Altcode: We study how the solar atmosphere and wind respond to sudden and large increases in the coronal energy input, with the aim of better understanding the impact of fast coronal mass ejections on the lower solar atmosphere. We apply a gyrotropic multifluid model extending from the chromosphere to 1 AU and that accounts for radiative losses in the transition region. The energy is deposited as pushing of coronal plasma by a large-amplitude Alfvén wave (simulating expulsion of flux ropes) and by thermal heating of electrons and protons. Both mechanisms lead to rapid acceleration of coronal plasma close to the Sun, with speeds of order 1000-2000 km s-1, and the resulting solar wind structures with large-amplitude shocks do not depend sensitively on the form of energy deposition in the corona. The response of the low corona and transition region does depend sensitively on the form of energy input, however. Alfvén wave pushing leads to very low coronal temperatures and densities and a strong reduction in Lyα radiation from the transition region, and only the plasma already present in the corona is expelled. Thermal heating leads to much higher coronal temperatures and densities and large downward heat fluxes, causing a strong heating of the upper chromosphere and a resulting large upflow of chromospheric material. In this case chromospheric material constitutes 50% or more of the matter ejected from the Sun as a result of the heating. Heating also leads to a sudden and large increase in the Lyα radiation during the event. Although the lower atmosphere responds rapidly to the increased energy input, it takes half a day or more for the transition region and corona to be restored to its preeruption state. Without electron or proton coronal heating, electrons never reach the temperatures required to produce the high ion charge states that are observed in some CMEs. Title: The Helium Abundance of Quiescent Coronal Loops Authors: Killie, Mari Anne; Lie-Svendsen, Øystein; Leer, Egil Bibcode: 2005ApJ...632L.155K Altcode: Coronal loops are modeled using a code that solves a newly developed set of transport equations, in which a more accurate description of thermal forces and heat conduction is contained. The plasma consists of hydrogen and helium, and ionization and recombination, as well as radiative loss, have been accounted for. When the loop is anchored in a ``well-mixed'' chromosphere with a helium abundance of approximately 10%, the helium density of the coronal part of the loop becomes larger than the hydrogen density within 1-3 days. In steady state, the loop is completely dominated by helium, with a helium density more than 10 times the hydrogen density. For a loop based in a stratified chromosphere with very little helium in the upper part, a moderate coronal helium abundance can be maintained. In this latter case, helium does not ``drain'' from the loop, and we get an extreme increase in the helium abundance from the upper chromosphere to the corona. These results suggest that the chromosphere underlying closed field regions of the Sun is highly stratified and that both helium and minor ion abundances are far from constant throughout the chromosphere. Title: Modeling Helium in the Solar Wind with New Gyrotropic Transport Equations Authors: Janse, A. M.; Lie-Svendsen, Ø.; Leer, E. Bibcode: 2005ESASP.592..487J Altcode: 2005ESASP.592E..88J; 2005soho...16E..88J No abstract at ADS Title: Modeling Helium in Closed Coronal Structures Authors: Killie, M. A.; Lie-Svendsen, Ø.; Leer, E. Bibcode: 2005ESASP.592..147K Altcode: 2005ESASP.592E..22K; 2005soho...16E..22K No abstract at ADS Title: Release of Helium from Closed-Field Regions of the Sun Authors: Endeve, Eirik; Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil Bibcode: 2005ApJ...624..402E Altcode: Using a numerical model that extends from the chromosphere into the supersonic solar wind, we study the dynamics of previously closed coronal flux tubes that open, allowing plasma to be expelled from the corona. In particular, we study whether the opening of flux tubes may provide a source of helium-rich material for the solar wind. We use higher order moment fluid equations to describe the plasma, which consists of hydrogen (neutral and protons), helium (neutral, singly ionized, and α-particles), and electrons. The helium abundance decreases rapidly with altitude in a closed flux tube, caused by the collisional coupling between α-particles and protons leading to a small α-particle scale height. When the flux tube is rapidly opened, protons escape from the Sun immediately. The coronal α-particles leave the corona only much later, 10-20 hr after the protons, when the collisional coupling to protons has eased, allowing their temperature to become sufficiently high for them to escape. Title: Mode Conversion in Magneto-Atmospheres Authors: Bogdan, T. J.; Carlsson, M.; Hansteen, V.; Heggland, L.; Leer, E.; McMurry, A. D.; Stein, R. F. Bibcode: 2004AGUFMSH13A1162B Altcode: Numerical simulations of wave propagation in a simple magneto-atmosphere are employed to illustrate the complex nature of wave transformation and conversion taking place in solar and stellar atmospheres. An isothermal atmosphere threaded by a potential poloidal magnetic field, and a superposed uniform toroidal field, is treated in a local cartesian approximation. Spatial variations are restricted to the two poloidal dimensions, but the toroidal field ensures that all three MHD waves are present in the simulation. As in our previous purely two-dimensional simulations (Bogdan et al. ApJ 599, 626-60, 2003), mode mixing and transformation take place at surfaces where the magnetic and thermal pressures are equal. In the present case, the upward propagating acoustic-gravity (MAG) wave is converted into roughly equal parts transmitted fast, intermediate (Alfven), and slow magneto-acoustic-gravity waves in passing through this mixing layer. Unlike the fast and slow waves, the Alfven wave is weakly damped, and is able to deposit its energy and momentum in the upper chromosphere and corona. The fast and slow MAG waves are decoupled on either side of mixing layer owing to their disparate propagation speeds. Under certain fortuitous circumstances, the Alfven wave also decouples from the fast and slow MAG waves. Title: Improved Transport Equations for Fully Ionized Gases Authors: Killie, Mari Anne; Janse, Åse Marit; Lie-Svendsen, Øystein; Leer, Egil Bibcode: 2004ApJ...604..842K Altcode: We have developed fluid transport equations for fully ionized gases that improve the description of Coulomb collisions. The aim has been to develop simple and versatile equations that can easily be implemented in numerical models and thus be applied to a large variety of space plasmas, while they still accurately describe thermal forces and energy flows in collision-dominated plasmas. Based on exact solutions to the Boltzmann equation in the collision-dominated limit, the correction term to the velocity distribution function that account for particle flows is assumed to be proportional to the third power of the velocity, leading to a near isotropic core distribution. Applying the fluid equations derived from this new velocity distribution to a collision-dominated electron-proton plasma with a small temperature gradient, the resulting electron heat flux, as well as the thermal force between electrons and protons, deviate less than 25% from the exact results of classical transport theory. The new equations predict a factor of 4 reduction in the thermal force acting on heavy, minor ions caused by an imposed heat flux, compared with fluid equations that are in common use today. The improved description of thermal forces is expected to be important for modeling the composition of stellar atmospheres. Title: Helmet Streamers Gone Unstable: Two-Fluid Magnetohydrodynamic Models of the Solar Corona Authors: Endeve, Eirik; Holzer, Thomas E.; Leer, Egil Bibcode: 2004ApJ...603..307E Altcode: The equations of magnetohydrodynamics (MHD) are used to study heating of electrons and protons in an axially symmetric model of the solar corona, extending from the coronal base to 15 solar radii. To study heating of electrons and protons separately, as well as the collisional coupling between the particle species, we use a two-fluid description of the electron-proton plasma. A steady coronal heat input, uniform base pressure, and dipole field boundary conditions produce a magnetic field configuration similar to that seen with white-light coronagraphs during quiet-Sun conditions: a helmet streamer is formed in the inner corona around the equator, surrounded by coronal holes at higher latitudes. The plasma inside the helmet streamer is in hydrostatic equilibrium, while in the coronal holes a transonic solar wind is accelerated along the field. The collisional coupling between electrons and protons becomes weak close to the coronal base. In the case of proton heating, the thermal structure along open and closed field lines is very different, and there is a large pressure jump across the streamer-coronal hole boundary. When the equations are integrated on a long timescale, the helmet streamer becomes unstable, and massive plasmoids are periodically released into the solar wind. These plasmoids contribute significantly to the total mass and energy flux in the solar wind. The mass of the plasmoids is reduced when electrons are heated. Title: Helium Abundance in the Corona and Solar Wind: Gyrotropic Modeling from the Chromosphere to 1 AU Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil Bibcode: 2003ApJ...596..621L Altcode: We have developed a solar wind model including helium that extends from the chromosphere to 1 AU. The model is based on the gyrotropic approximation to the 16-moment set of fluid transport equations, which allows it to accommodate temperature anisotropies, as well as nonclassical heat transport. We find that, as in a pure electron-proton solar wind, the flow geometry close to the Sun also has a large impact on helium. In a radially expanding flow, downward proton heat conduction from the corona leads to a high transition region pressure and a large thermal force that pulls helium ions into the corona. In this case α-particles may easily become the dominant species in the corona, resulting in a polar wind type of solar wind in which the light protons are accelerated outward in the electric field set up by the α-particles and electrons. By contrast, applying the same form for the coronal heating in a rapidly expanding geometry intended to simulate a coronal hole, protons become collisionless closer to the Sun, and therefore the downward proton heat flux is smaller, resulting in a lower transition region pressure and a lower thermal force on helium. In this case the helium abundance is low everywhere and helium is unimportant for the acceleration of the solar wind. For the low coronal proton and α-particle densities found in the rapidly expanding flow, where asymptotic flow speeds are typically significantly higher than the gravitational escape speed at the solar surface, the solar wind helium mass flux is determined by the amount of helium available at the top of the chromosphere. In the radially expanding flow, with asymptotic flow speeds lower than the escape speed, the helium mass flux depends on the amount of energy available in the corona to lift helium out of the gravitational potential. In both cases the frictional coupling between helium and hydrogen in the chromosphere, using currently accepted elastic cross sections, is too weak to pull a sufficient number of helium atoms up to the top of the chromosphere and thus obtain a mass flux in agreement with observations. A better understanding of the chromosphere is therefore called for. Title: Thermal forces and the coronal helium abundance Authors: Hansteen, V. H.; Lie-Svendsen, Ø.; Leer, E. Bibcode: 2003AIPC..679..620H Altcode: The interaction between protons and minor ions in the chromosphere-corona transition region produces an upward force on the minor ions and an enhanced coronal abundance. In this presentation we compare a ``classical'' hydrodynamical model of a hydrogen - helium solar wind and a model based on a 16-moment fluid description where the heat flux is treated in a self-consistent manner. Title: The effect of time-dependent coronal heating on the solar wind from coronal holes Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil Bibcode: 2003AIPC..679..299L Altcode: We have modelled the solar wind response to a time-dependent energy input in the corona. The model, which extends from the upper chromosphere to 1 AU, solves the time-dependent transport equations based on the gyrotropic approximation to the 16-moment set of transport equations, which allow for temperature anisotropies. Protons are heated perpendicularly to the magnetic field, assuming a coronal heating function that varies sinusoidally in time. We find that heating with periods less than about 3 hours does not leave visible manifestations in the solar wind (the oscillations are efficiently damped near the Sun) heating with periods of order 10 hours leads to perturbations comparable to Ulysses observations; while heating with periods of order 100 hours results in a series of steady-state solutions. Mass flux perturbations tend to be larger than perturbations in wind speed. Heating in coronal holes with periods of order 30 hours leads to large mass flux perturbations near Earth, even when the amplitude of the change in heating rate in the corona is small. Title: 2D MHD Models of the Large Scale Solar Corona Authors: Endeve, Eirik; Holzer, Thomas E.; Leer, Egil Bibcode: 2003AIPC..679..331E Altcode: By solving the equations of ideal MHD the interaction of an isothermal coronal plasma with a dipole-like magnetic field is studied. We vary the coronal temperature and the magnetic field strength to investigate how the plasma and the magnetic field interact to determine the structure of the large scale solar corona. When our numerical calculations are initiated with an isothermal solar wind in a dipole magnetic field, the equations may be integrated to a steady state. Open and closed regions are formed. In the open regions the atmosphere expands into a super-sonic wind, and in the closed regions the plasma is in hydrostatic equilibrium. We find that the magnetic field configuration in the outer corona is largely determined by the equatorial current sheet. Title: Two-dimensional Magnetohydrodynamic Models of the Solar Corona: Mass Loss from the Streamer Belt Authors: Endeve, Eirik; Leer, Egil; Holzer, Thomas E. Bibcode: 2003ApJ...589.1040E Altcode: The equations of magnetohydrodynamics (MHD) are used to study an axially symmetric model of the large-scale solar corona, extending from the coronal base to 15 solar radii. We use a uniform heating of the inner corona to investigate the energy output when the magnetic field is given as a dipole at the coronal base. The heat input produces a large-scale magnetic field structure similar to that found by Pneuman and Kopp, with coronal holes in the polar regions and a helmet streamer around the equator. We pay special attention to the energy balance in the system, and find that the role of heat conduction is important in determining the thermal structure in magnetically closed regions. Insufficient energy loss to the transition region leads to a high temperature inside the closed region. In the coronal holes a solar wind is accelerated into interplanetary space, and the temperature is lower. As the difference in pressure scale height along open and closed flux tubes is large, the helmet streamer does not relax to a steady state; it opens periodically to eject mass into interplanetary space. These mass ejections may contribute significantly to the mass and energy flux in the solar wind. Title: Book Review: Energy conversion and particle acceleration in the solar corona / Springer, 2003 Authors: Leer, Egil Bibcode: 2003SoPh..218..361L Altcode: 2003SoPh..218..361K No abstract at ADS Title: Effect of time-dependent coronal heating on the solar wind Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil Bibcode: 2002JGRA..107.1325L Altcode: We have used a higher-order fluid model to study the effect of time-dependent coronal heating of protons on the solar wind, both for the fast wind from rapidly expanding coronal holes and for slower winds from a radially expanding geometry. The model extends from the chromosphere to 1 AU in order to capture the coupling between the chromosphere and corona and therefore the supply of plasma to the solar wind. The protons are heated in the perpendicular direction (relative to the magnetic field), assuming a simple sinusoidal variation with time. With a short time period for the heating, less than about 3 hours, the oscillations are efficiently damped in the inner part of the solar wind, even when the amplitude of the change in heating rate is large, leading to essentially steady state solutions near Earth. Heating with a period of 10 hours or so leads to perturbations in the wind near Earth that are comparable to Ulysses observations. Heating with a period of order 100 hours leads to essentially a series of steady state solutions. The mass flux perturbations are in general larger than the perturbations in wind speed, and for heating of coronal holes with periods of order 30 hours the mass flux perturbations are amplified in the wind by the interaction between the fast and slow components of the wind. In this case even moderate changes in the heating rate in the corona can produce solar wind interaction regions with forward and reversed shocks and large mass flux perturbations near Earth. Title: The Effect of Transition Region Heating on the Solar Wind from Coronal Holes Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil; Holzer, Thomas E. Bibcode: 2002ApJ...566..562L Altcode: Using a 16 moment solar wind model extending from the chromosphere to 1 AU, we study how the solar wind is affected by direct deposition of energy in the transition region, in both radially expanding geometries and rapidly expanding coronal holes. Energy is required in the transition region to lift the plasma up to the corona, where additional coronal heating takes place. The amount of energy deposited determines the transition region pressure and the number of particles reaching the corona and, hence, how the solar wind energy flux is divided between gravitational potential and kinetic energy. We find that when only protons are heated perpendicularly to the magnetic field in a rapidly expanding coronal hole, the protons quickly become collisionless and therefore conduct very little energy into the transition region, leading to a wind much faster than what is observed. Only by additional deposition of energy in the transition region can a reasonable mass flux and flow speed at 1 AU be obtained. Radiative loss in the transition region is negligible in these low-mass flux solutions. In a radially expanding geometry the same form of coronal heating results in a downward heat flux to the transition region substantially larger than what is needed to heat the upwelling plasma, resulting in a higher transition region pressure, a slow, massive solar wind, and radiative loss playing a dominant role in the transition region energy budget. No additional energy input is needed in the transition region in this case. In the coronal hole geometry the solar wind response to transition region heating is highly nonlinear, and even a tiny input of energy can have a very large influence on the asymptotic properties of the wind. By contrast, the radially expanding wind is quite insensitive to additional deposition of energy in the transition region. Title: Coupling Between Chromosphere and Corona: Why it Matters for the Solar Wind Authors: Lie-Svendsen, {; Hansteen, V. H.; Leer, E. Bibcode: 2001AGUSM..SH21B02L Altcode: The solar wind is driven by energy input which must be deposited mainly in the corona. In some sense, therefore, the solar wind ``starts'' in the corona, and most solar wind models have their lower boundary here. However, the underlying chromosphere and transition region is not only a ``passive'' supplier of solar wind plasma. Energy must be supplied as well in the upper chromosphere and transition region to ionize and heat the outflowing gas from chromospheric to coronal temperatures. While this energy input is usually small compared to the energy deposited in the corona, it nevertheless can have a crucial influence on the solar wind because the amount of energy deposited in the transition region limits the mass flux of the wind. Using a higher-order (16-moment) fluid solar wind model that extends from the chromosphere to 1~AU, we find that when protons are heated in the corona they may quickly become collisionless so that the heat flux deviates strongly from classical heat conduction, making it difficult to transport sufficient amounts of energy downwards to the transition region. The problem is most acute in the rapidly expanding magnetic field of coronal holes, where we find that adding even a small energy input in the transition region therefore can increase the solar wind mass flux by a factor ten or more, and not doing so leads to a wind much faster than what is observed even in high-speed streams. Title: Coronal heating and solar wind acceleration; gyrotropic electron-proton solar wind Authors: Endeve, Eirik; Leer, Egil Bibcode: 2001SoPh..200..235E Altcode: In coronal holes the electron (proton) density is low, and heating of the proton gas produces a rapidly increasing proton temperature in the inner corona. In models with a reasonable electron density in the upper transition region the proton gas becomes collisionless some 0.2 to 0.3 solar radii into the corona. In the collisionless region the proton heat flux is outwards, along the temperature gradient. The thermal coupling to electrons is weak in coronal holes, so the heat flux into the transition region is too small to supply the energy needed to heat the solar wind plasma to coronal temperatures. Our model studies indicate that in models with proton heating the inward heat conduction may be so inefficient that some of the energy flux must be deposited in the transition region to produce the proton fluxes that are observed in the solar wind. If we allow for coronal electron heating, the energy that is needed in the transition region to heat the solar wind to coronal temperatures, may be supplied by heat conduction from the corona. Title: A 16-moment solar wind model: From the chromosphere to 1 AU Authors: Lie-Svendsen, Øystein; Leer, Egil; Hansteen, Viggo H. Bibcode: 2001JGR...106.8217L Altcode: We present a solar wind fluid model extending from the chromosphere to Earth. The model is based on the gyrotropic approximation to the 16-moment set of transport equations, in which we solve for the density, drift speed, temperature parallel and perpendicular to the magnetic field, and transport of parallel and perpendicular thermal energy along the magnetic field (heat flux). The solar wind plasma is created dynamically through (photo) ionization in the chromosphere, and the plasma density in the transition region and corona is computed dynamically, dependent on the type of coronal heating applied, rather than being set arbitrarily. The model improves the description of proton energy transport in the transition region, where classical heat conduction is only retrieved in the collision-dominated limit. This model can serve as a ``test bed'' for any coronal heating mechanism. We consider heating of protons by a turbulent cascade of Alfvén waves in rapidly expanding coronal holes. The resulting high coronal proton temperatures lead to a downward proton energy flux from the corona which is much smaller than what classical transport theory predicts, causing a very low coronal density and an extremely fast solar wind with a small mass flux. Only when some of the wave energy is forcibly deposited in the lower transition region can a realistic solar wind be obtained. Because of the poor proton heat transport, in order to produce a realistic solar wind any viable heating mechanism must deposit some energy in the transition region, either directly or via explicit heating of coronal electrons. Title: Solar Wind: Theory Authors: Leer, E. Bibcode: 2000eaa..bookE2308L Altcode: The supersonic outflow of electrically charged particles, mainly electrons and protons from the solar CORONA, is called the SOLAR WIND. The solar wind was described theoretically by E N PARKER, in 1958. Parker's theory was verified experimentally by in situ observations by Soviet and American spaceprobes. On its way to Venus, in 1962, the MARINER II spacecraft observed the solar wind for 104 days... Title: The electron velocity distribution in the high-speed solar wind: Modeling the effects of protons Authors: Lie-Svendsen, Øystein; Leer, Egil Bibcode: 2000JGR...105...35L Altcode: The evolution of the electron velocity distribution function (VDF) in high-speed solar wind streams is modeled taking the expanding geometry, the polarization electric field, and Coulomb collisions into account. The VDF we find at the orbit of Mercury is composed of an isotropic, collision-dominated core, a trapped, anisotropic population called ``halo'' in this study, and a narrow, high-energy ``strahl'' that escapes along the magnetic field. The distribution function is very similar to the electron VDF observed in the low-density, high-speed solar wind by Pilipp et al. [1987] and Phillips et al. [1989]. The main features of the VDF can be obtained by considering only electron self-collisions; the effect of proton collisions is to make the distribution function more isotropic. At low energies, collisions with protons dominate the angular scattering, but electron self-collisions alone are frequent enough to keep the core of the distribution function quite isotropic. The expanding geometry produces an anisotropic halo and a narrow strahl. The angular scattering by protons reduces the anisotropy of the trapped halo particles and broadens the lower-energy part of the strahl. Along the magnetic field the resulting electron velocity distribution is composed of a relatively cold core and a halo-strahl spectrum that is ``flatter'' than the coronal spectrum. The two-temperature electron distribution function often observed in the solar wind may therefore be produced by Coulomb collisions and should not be taken as a ``proof'' of a non-Maxwellian (two-temperature) distribution function in the corona. Title: Advances in Modelling the Fast Solar Wind Authors: Hansteen, V. H.; Leer, E.; Lie-Svendsen, Ø. Bibcode: 1999ESASP.448.1091H Altcode: 1999mfsp.conf.1091H; 1999ESPM....9.1091H No abstract at ADS Title: Electron Heat Conduction in the Solar Transition Region: Validity of the Classical Description Authors: Lie-Svendsen, Øystein; Holzer, Thomas E.; Leer, Egil Bibcode: 1999ApJ...525.1056L Altcode: We have studied the transport of energy in the solar transition region, with the aim of finding out whether classical transport theory is applicable in this region. We use a test particle approximation, where test electrons move in a prescribed, background Maxwellian electron-proton plasma. This approximation is validated by comparing with the Spitzer-Härm result in the collision-dominated limit, where the Spitzer-Härm result should be valid. We find that the test particle approximation yields velocity distribution functions in good agreement with Spitzer and Härm, and the test particle energy flux is only 25% lower than the correct result. Then, applying the model to conditions believed to be found in the solar transition region, we obtain essentially the same good agreement with the classical result, showing that classical transport theory is sufficient to describe heat transport in the solar transition region. When the transition region pressure (density) is reduced to unrealistically low values, while the temperature profile is kept unchanged, a significant fraction of the energy flux is carried by nonthermal electrons from the corona. But the total energy flux is never larger than the classical Spitzer-Härm value. The heat flux is independent of density at high densities (the classical result), and decreases monotonically as the transition region pressure is reduced. Title: The origin of the high speed solar wind Authors: Hansteen, Viggo H.; Leer, Egil; Holzer, Thomas E. Bibcode: 1999AIPC..471...17H Altcode: 1999sowi.conf...17H The outflow of coronal plasma into interplanetary space is a consequence of the coronal heating process. Therefore the formation of the corona and the acceleration of the solar wind should be treated as a single problem. The deposition of energy into the corona through some mechanical or electromagnetic energy flux is balanced by the various sinks available to the corona, and the sum of these processes determines the coronal structure, i.e. its temperature and density. Heating of the extended solar corona leads to high proton and ion temperatures and relatively low electron temperatures. This is due to the low heat conductivity in the proton (ion) gas as compared to the electrons. To a fairly good approximation we can say that most of the energy flux deposited in the protons and ions is lost as kinetic and gravitational energy flux in the solar wind flow, whereas a large fraction of the energy flux added to the electrons is conducted back into the transition region and lost as radiation. In order to drive high speed wind most of the energy must be deposited in the ions. Title: A study of solar wind acceleration based on gyrotropic transport equations Authors: Olsen, Espen Lyngdal; Leer, Egil Bibcode: 1999JGR...104.9963O Altcode: The gyrotropic transport equations are used to describe an electron-proton solar wind from the 500,000 K level in the upper transition region and out to 30 solar radii. These equations allow for different temperatures parallel and perpendicular to the magnetic field, as well as transport of parallel and perpendicular thermal energy along the field. We find that in models with significant coronal proton heating, the electron temperature is much lower than the proton temperature. The electron gas is collision dominated, the thermal anisotropy is small, and the heat flux is close to a ``classical'' heat flux. The proton gas is collision dominated in the upper transition region, but the temperature increases rapidly in the inner corona, and the protons become collisionless close to the Sun. The proton heat flux is proportional to the temperature gradient very close to the Sun, but in the extended corona it deviates substantially from a classical heat flux. In models where the proton heating is in the direction perpendicular to the magnetic field, a large perpendicular temperature is produced locally, but the perpendicular thermal motion couples into parallel thermal motion, and the parallel temperature increases outward from the Sun. We obtain a maximum parallel temperature that is comparable to the maximum perpendicular temperature. This result seems to hold for all models where the energy flux necessary to drive high-speed wind is deposited in the corona as heat. The result is not in agreement with UVCS/SOHO observations of the 1216 Å Ly-α line in large coronal holes. These observations are consistent with a much larger random proton motion perpendicular to the magnetic field than parallel to the field. Such anisotropies can be obtained in models of high-speed solar wind if we allow for a significant fraction of the energy flux from the Sun to be in the form of low-frequency, transverse waves. These waves accelerate the solar wind without heating the corona, and they contribute to the line broadening in the direction perpendicular to the magnetic field. Title: Erratum: ``An eight-moment approximation two-fluid model of the solar wind'' Authors: Olsen, Espen Lyngdal; Leer, Egil Bibcode: 1999JGR...104..597O Altcode: 1999JGR...104..596O Abstract Available from AGU Title: Working Group 1 Report: Solar Wind Models from the Sun to 1 AU: Constraints by "in situ" and Remote Sensing Measurements Authors: Leer, E.; Marsch, E. Bibcode: 1999SSRv...87...67L Altcode: The goal of Working Group 1 was to discuss constraints on solar wind models. The topics for discussion, outlined by Eckart Marsch in his introduction, were: (1) what heats the corona, (2) what is the role of waves, (3) what determines the solar wind mass flux, (4) can stationary, multi-fluid models describe the fast and slow solar wind, or (5) do we need time dependent fluid models, kinetic models, and/or MHD models to describe solar wind acceleration. The discussion in the working group focused on observations of "temperatures" in the corona, mainly in coronal holes, and whether the observations of line broadening should be interpreted as thermal broadening or wave broadening. Observations of the coronal electron density and the flow speed in coronal holes were also discussed. There was only one contribution on observations of the distant solar wind, but we can place firm constraints on the solar wind particle fluxes and asymptotic flow speeds from observations with Ulysses and other spacecraft. Theoretical work on multi-fluid models, higher-order moment fluid models, and MHD models of the solar wind were also presented. Title: Erratum: "An eight-moment approximation two-fluid model of the solar wind&quot Authors: Lyngdal Olsen, Espen; Leer, Egil Bibcode: 1999JGR...104..596L Altcode: No abstract at ADS Title: An eight-moment model parameter study of the solar wind: dependence on variations in coronal heating Authors: Olsen, Espen Lyngdal; Leer, Egil; Lie-Svendsen, Oystein Bibcode: 1998A&A...338..747O Altcode: The eight-moment two-fluid model describes, self-consistently, the proton (and electron) heat flux in the solar wind. This is a crucial parameter in solar wind models with a high coronal proton temperature. In the present study the eight-moment description is used to study how the solar wind outflow from an electron-proton corona responds to variations in coronal heating. Most of the energy flux is deposited in the proton gas. We find that the asymptotic flow speed of the solar wind is only weakly dependent on the amplitude of the energy flux, but it increases with increasing dissipation length. When most of the energy flux is dissipated in the extended corona, where the protons are collisionless, we obtain flow speeds characteristic of high-speed solar wind streams: For a dissipation length of 1 to 2 solar radii the asymptotic flow speed is 700-1000 km s(-1) . A relatively modest electron heating in the inner corona may lead to an increased transition region pressure and hence a large increase in the solar wind proton flux. This increase in proton flux may be so large that there is not enough energy available to drive a high-speed wind. Title: Acceleration of the Solar Wind: A New View Authors: Hansteen, V. H.; Leer, E. Bibcode: 1998HiA....11..838H Altcode: No abstract at ADS Title: The Solar Wind Authors: Leer, E. Bibcode: 1998ESASP.417...11L Altcode: 1998cesh.conf...11L No abstract at ADS Title: Heating of the corona and acceleration of high speed solar wind Authors: Evje, H. O.; Leer, E. Bibcode: 1998A&A...329..735E Altcode: We present a parameter study of the corona--solar wind system. The corona is heated by an energy flux from the sun. This energy flux is lost as heat conductive flux into the transition region and as solar wind energy flux. We consider two-fluid models where most of the energy flux is deposited in the proton gas. Heating of the inner corona leads to a significant (electron) heat conductive flux into the transition region and a relatively high coronal electron density. This gives a relatively low coronal proton temperature, a large solar wind proton flux, and a relatively low asymptotic flow speed. In rapidly expanding flow geometries, where the thermal coupling between electrons and protons is weaker, heating of the protons in the inner corona may lead to a somewhat higher proton temperature, and higher asymptotic flow speed, but in order to drive high speed solar wind, a significant fraction of the energy flux from the sun must be deposited in the outer corona, where the protons are collisionless. In such a model only a small fraction of the energy flux is lost as inward heat flux, the transition region pressure is low, and the solar wind proton flux is quite small. The proton temperature in the outer corona is high, and a larger fraction of the energy flux deposited in the proton gas may be lost as solar wind kinetic energy flux. Title: Understanding the Solar Wind Authors: Leer, E.; Hansteen, V. H.; Holzer, T. E. Bibcode: 1998cvsw.conf..263L Altcode: No abstract at ADS Title: The Role of Helium in the Outer Solar Atmosphere Authors: Hansteen, V. H.; Leer, E.; Holzer, T. E. Bibcode: 1997ApJ...482..498H Altcode: We construct models of the outer solar atmosphere comprising the region from the mid-chromosphere and into the solar wind in order to study the force and energy balance in models with a significant helium abundance. The corona is created by dissipation of an energy flux from the Sun. The energy flux is lost as radiation from the top of the chromosphere and as gravitational and kinetic solar wind energy flux. We find that in models with significant ion heating of the extended corona most of the energy flux is lost in the solar wind. The ion temperatures are higher than the electron temperature in these models, and the α-particle temperature is much higher than the proton temperature, so there is energy transfer from the α-particle fluid to the protons and electrons, but this energy exchange between the different species is relatively small. To a fairly good approximation we can say that the energy flux deposited in the protons and α-particles is lost as kinetic and gravitational energy flux in the proton and α-particle flow. How this energy flux is divided between gravitational and kinetic energy flux (i.e., how large the particle fluxes and flow speeds are) depends upon details of the heating process. We also find that mixing processes in the chromosphere play an important role in determining the coronal helium abundance and the relative solar wind proton and α-particle fluxes. Roughly speaking, we find that the relative α-particle and proton fluxes are set by the degree of chromospheric mixing, while the speeds are set by the details of the coronal heating process. Title: The Coronal Helium Abundance and the Solar Wind Authors: Hansteen, Viggo H.; Hassler, Donald M.; Leer, Egil; Holzer, Thomas E.; Woods, Thomas N. Bibcode: 1997SPD....28.0154H Altcode: 1997BAAS...29Q.889H The coronal Helium abundance depends on the rate Helium is brought into the corona via the transition region from the chromosphere and on the rate that Helium is removed from the corona in the Solar wind. Recent multi-fluid models of the combined chromosphere, corona, solar wind system show that the corona may have a significant Helium abundance; perhaps even exceeding 50% of the Hydrogen number density. These models also indicate that in order to reproduce the Solar wind at 1AU ions (alpha -particles as well as protons) may be required to be the most important recipient of the coronal heating process. In these models the role of electrons in the energetics of the Solar wind is much reduced compared to the standard thermally driven winds. A measurement of the coronal Helium abundance will serve to fix these theoretical ideas and may give important clues as to mixing processes in the chromosphere as well as to coronal heating processes. Consequently, we will discuss the current state of observations (i.e. SOHO), and their limitations, as well as plans for future observations (i.e. sounding rocket, Spartan). Title: Kinetic electrons in high-speed solar wind streams: Formation of high-energy tails Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil Bibcode: 1997JGR...102.4701L Altcode: We study the evolution of the electron velocity distribution function in high-speed solar wind streams from the collision-dominated corona and into the collisionless interplanetary space. The model we employ solves the kinetic transport equation with the Fokker-Planck collision operator to describe Coulomb collisions between electrons. We use a test particle approach, where test electrons are injected into a prescribed solar wind background. The density, temperature, and electric field associated with the background are computed from fluid models. The test electrons are in thermal equilibrium with the background at the base of the corona, and we study the evolution of the velocity distribution of the test electrons as a function of altitude. We find that velocity filtration, due to the energy dependence of the Coulomb cross section, is a small effect and is not capable of producing significant beams in the distribution or a temperature moment that increases with altitude. The distribution function is mainly determined by the electric field and the expanding geometry and consists of a population with an almost isotropic core which is bound in the electrostatic potential and a beam-like high-energy tail which escapes. The trapped electrons contribute significantly to the even moments of the distribution function but almost nothing to the odd moments; the drift speed and energy flux moments are carried solely by the tail. In order to describe the high-speed solar wind observed near 0.3 AU by the Helios spacecraft, we use a multifluid model where ions are heated preferentially. The resulting test electron distribution at 0.3 AU, in this background, is in very good agreement with the velocity distributions observed by the Helios spacecraft. Title: Coronal Hole Structure and the High Speed Solar Wind Authors: Holzer, T. E.; Leer, E. Bibcode: 1997ESASP.404...65H Altcode: 1997cswn.conf...65H; 1997soho....5...65H No abstract at ADS Title: Helium in the outer solar atmosphere Authors: Hansteen, V. H.; Leer, E.; Holzer, T. E. Bibcode: 1997AIPC..385..197H Altcode: 1997recs.conf..197H We construct models of the outer solar atmosphere comprising the region from the mid chromosphere and into the solar wind in order to study the force and energy balance in models with a significant helium abundance. The corona is created by dissipation of an energy flux from the Sun. The energy flux is lost as radiation from the top of the chromosphere and as gravitational and kinetic solar wind energy flux. We find that in models with significant ion heating of the extended corona most of the energy flux is lost in the solar wind. The ion temperatures are higher than the electron temperature in these models, and the α-particle temperature is much higher than the proton temperature. Roughly speaking we find that the relative α-particle and proton fluxes are set by the degree of chromospheric mixing while the speeds are set by the details of the coronal heating process. Title: Acceleration of the Solar Wind Authors: Holzer, T. E.; Hansteen, V. H.; Leer, E. Bibcode: 1997cwh..conf..239H Altcode: 2006mslp.conf..239H No abstract at ADS Title: Outflow of He+ from the polar ionosphere: Comparison of hydrodynamic and kinetic descriptions Authors: Leer, Egil; Lie-Svendsen, Øystein; Olsen, Espen Lyngdal; Hansteen, Viggo H. Bibcode: 1996JGR...10117207L Altcode: Singly ionized helium, a minor species in the polar ionosphere, is being propelled out along open magnetic field lines by an outward polarization electric field. In the present study we compare the kinetic and hydrodynamic descriptions of this transonic outflow treating the singly ionized helium as a test particle population in a static background of singly ionized oxygen and electrons. We find that the resultant He+ particle fluxes are equal in both the eight-moment hydrodynamic description and in the kinetic description based on the Fokker-Planck equation. A five-moment hydrodynamic description gives a flux that is some 40% lower. The increase of the He+ energy flux with altitude is also equal in the eight-moment hydrodynamic and in the kinetic descriptions. Title: An eight moment solar wind model Authors: Olsen, Espen Lyngdal; Leer, Egil Bibcode: 1996AIPC..382..157O Altcode: No abstract at ADS Title: An eight-moment approximation two-fluid model of the solar wind Authors: Olsen, Espen Lyngdal; Leer, Egil Bibcode: 1996JGR...10115591O Altcode: In fluid descriptions of the solar wind the heat conductive flux is usually determined by the use of the classical Spitzer-Härm expression. This expression for the heat flux is derived assuming the gas to be static and collision-dominated and is therefore strictly not valid in the solar wind. In an effort to improve the treatment of the heat conductive flux and thereby fluid models of the solar wind, we study an eight-moment approximation two-fluid model of the corona-solar wind system. We assume that an energy flux from the Sun heats the coronal plasma, and we solve the conservation equations for mass and momentum, the equations for electron and proton temperature, as well as the equations for heat flux density in the electron and proton fluid. The results are compared with the results of a ``classical'' model featuring the Spitzer-Härm expression for the heat conductive flux in the electron and proton gas. In the present study we discuss models with heating of the coronal protons; the electrons are only heated by collisional coupling to the protons. The electron temperature and heat flux are small in these cases. The proton temperature is large. In the classical model the transfer of thermal energy into flow energy is gradual, and the proton heat flux in the solar wind acceleration region is often too large to be carried by a reasonable proton velocity distribution function. In the eight-moment model we find a higher proton temperature and a more rapid transfer of thermal energy flux into flow energy. The heat fluxes from the corona are small, and the velocity distribution functions, for both the electrons and protons, remain close to shifted Maxwellians in the acceleration region of the solar wind. Title: A kinetic study of solar wind electrons Authors: Lie-Svendsen, Øystein; Leer, Egil Bibcode: 1996AIPC..382...58L Altcode: The evolution of the distribution function for a test population of electrons in an isothermal electron-proton corona has been studied using a Fokker-Planck description. The aim is to investigate whether a suprathermal tail forms due to the energy dependence of the Coulomb cross section. We find that a Maxwellian test population, injected into this background close to the coronal base with a temperature equal to that of the background electrons, maintains its shape throughout the transition from collision-dominated to collisionless flow. No significant suprathermal tail in the electron distribution function is seen in the outer corona. Title: An eight-moment approximation two-fluid model of the solar wind Authors: Lyngdal Olsen, Espen; Leer, Egil Bibcode: 1996JGR...10115591L Altcode: No abstract at ADS Title: Thermally Driven One-Fluid Electron-Proton Solar Wind: Eight-Moment Approximation Authors: Olsen, Espen Lyngdal; Leer, Egil Bibcode: 1996ApJ...462..982O Altcode: In an effort to improve the "classical" solar wind model, we study an eight-moment approximation hydrodynamic solar wind model, in which the full conservation equation for the heat conductive flux is solved together with the conservation equations for mass, momentum, and energy. We consider two different cases: In one model the energy flux needed to drive the solar wind is supplied as heat flux from a hot coronal base, where both the density and temperature are specified. In the other model, the corona is heated. In that model, the coronal base density and temperature are also specified, but the temperature increases outward from the coronal base due to a specified energy flux that is dissipated in the corona. The eight-moment approximation solutions are compared with the results from a "classical" solar wind model in which the collision-dominated gas expression for the heat conductive flux is used. It is shown that the "classical" expression for the heat conductive flux is generally not valid in the solar wind. In collisionless regions of the flow, the eight-moment approximation gives a larger thermalization of the heat conductive flux than the models using the collision-dominated gas approximation for the heat flux, but the heat flux is still larger than the "saturation heat flux." This leads to a breakdown of the electron distribution function, which turns negative in the collisionless region of the flow. By increasing the interaction between the electrons, the heat flux is reduced, and a reasonable shape is obtained on the distribution function. By solving the full set of equations consistent with the eight-moment distribution function for the electrons, we are thus able to draw inferences about the validity of the eight-moment description of the solar wind as well as the validity of the very commonly used collision-dominated gas approximation for the heat conductive flux in the solar wind. Title: Coronal heating, densities, and temperatures and solar wind acceleration Authors: Hansteen, Viggo H.; Leer, Egil Bibcode: 1995JGR...10021577H Altcode: The outflow of coronal plasma into interplanetary space is a consequence of the coronal heating process. Therefore the formation of the corona and the acceleration of the solar wind should be treated as a single problem. The deposition of energy into the corona through some ``mechanical'' energy flux is balanced by the various energy sinks available to the corona, and the sum of these processes determines the coronal structure, i.e., its temperature and density. The corona loses energy through heat conduction into the transition region and through the gravitational potential energy and kinetic energy put into the solar wind. We show from a series of models of the chromosphere-transition region-corona-solar wind system that most of the energy deposited in a magnetically open region goes into the solar wind. The transition region pressures and the coronal density and temperature structure may vary considerably with the mode and location of energy deposition, but the solar wind mass flux is relatively insensitive to these variations; it is determined by the amplitude of the energy flux. In these models the transition region pressure decreases in accordance with the increasing coronal density scale height such that the solar wind mass loss is consistent with the energy flux deposited in the corona. On the basis of the present study we can conclude that the exponential increase of solar wind mass flux with coronal temperature, found in most thermally driven solar wind models, is a consequence of fixing the transition region pressure. Title: Coronal Heating and Solar Wind Energy Balance Authors: Sandbaek, Ornulf; Leer, Egil Bibcode: 1995ApJ...454..486S Altcode: In this paper we present a parameter study of a two-fluid and a one-fluid model of the solar wind where coronal heating and solar wind acceleration is treated as one problem. To study the energy balance in the corona/solar wind system, we consider a "mechanical" energy flux emanating from the Sun which is transferred to the coronal plasma as heat with a characteristic dissipation length of a few tenths of a solar radius. The mechanical energy flux adding energy to the coronal plasma as heat is varied, and the dissipation length of the mechanical energy flux and the fraction of the energy added to protons (electrons) are varied. The low heat conductivity in the proton gas and the relatively weak thermal coupling between electrons and protons cause large temperature differences in the corona. In two-fluid models with electron heating and in one-fluid models, a larger fraction of the mechanical energy flux is lost as heat conduction and radiation than in two-fluid models with pure proton heating. In all models where an energy flux is added to the quasi-static corona as heat, the asymptotic flow speed is low. We demonstrate how a flux of Alfvén waves emanating from the Sun can accelerate the thermally driven solar wind to asymptotic flow speeds higher than the Sun's escape speed. Title: Eight-moment approximation solar wind models Authors: Olsen, Espen Lyngdal; Leer, Egil Bibcode: 1995sowi.confR..66O Altcode: Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds. Title: A kinetic study of solar wind electrons in the transition region from collision dominated to collisionless flow Authors: Lie-Svendsen, O.; Leer, E. Bibcode: 1995sowi.conf...30L Altcode: We have studied the evolution of the velocity distribution function of a test population of electrons in the solar corona and inner solar wind region, using a recently developed kinetic model. The model solves the time dependent, linear transport equation, with a Fokker-Planck collision operator to describe Coulomb collisions between the 'test population' and a thermal background of charged particles, using a finite differencing scheme. The model provides information on how non-Maxwellian features develop in the distribution function in the transition region from collision dominated to collisionless flow. By taking moments of the distribution the evolution of higher order moments, such as the heat flow, can be studied. Title: Stellar Winds Authors: Leer, E. Bibcode: 1995fras.conf..125L Altcode: No abstract at ADS Title: On the Relation between Coronal Heating, Flux Tube Divergence, and the Solar Wind Proton Flux and Flow Speed Authors: Sandbaek, Onulf; Leer, Egil; Hansteen, Viggo H. Bibcode: 1994ApJ...436..390S Altcode: A one-fluid solar wind model is used to investigate some relations between coronal heating, the flux tube divergence near the Sun, and the solar wind proton flux and flow speed. The effects of energy addition to the supersonic region of the flow are also studied. We allow for a mechanical energy flux that heats the corona, and an Alfven wave energy flux that adds energy, mainly to the supersonic flow, both as momentum and as heat. We find that the mechanical energy flux determines the solar wind mass flux, and in order to keep an almost constant proton flux at the orbit of Earth with changing flow geometry, that the mechanical energy flux must vary linearly with the magnetic field in the inner corona. This thermally driven wind generally has a low asymptotic flow speed. When Alfven waves are added to the thermally driven flow, the asymptotic flow speed is increased and is determined by the ratio of the Alfven wave and the mechanical energy fluxes at the coronal base. Flow speeds characteristic of recurrent high-speed solar wind streams can be obtained only when the Alfven wave energy flux, deposited in the supersonic flow, is larger than the mechanical energy flux heating the corona. Title: Coupling of the coronal He abundance to the solar wind Authors: Hansteen, V. H.; Leer, E.; Holzer, T. E. Bibcode: 1994SSRv...70..347H Altcode: Models of the transition region — corona — solar wind system are investigated in order to find the coronal helium abundance and to study the role played by coronal helium in controlling the the solar wind proton flux. The thermal force on α-particles in the transition region sets the flow of helium into the corona. The frictional coupling between α-particles and protons and/or the electric polarization field determines the proton flux in the solar wind as well as the fate of the coronal helium content. Title: Coupling of the Coronal Helium Abundance to the Solar Wind Authors: Hansteen, Viggo H.; Leer, Egil; Holzer, Thomas E. Bibcode: 1994ApJ...428..843H Altcode: Models of the transition region-corona-solar wind system are investigated in order to find the coronal helium abundance and to study the role played by coronal helium in controlling the solar wind proton flux. The thermal force on alpha-particles in the transition region sets the flow of helium into the corona. The frictional coupling between alpha-particles and protons and/or the electric polarization field determines the proton flux in the solar wind as well as the fate of the coronal helium content. The models are constructed by solving the time-dependent population and momentum equations for all species of hydrogen and helium in an atmosphere with a given temperature profile. Several temperature profiles are considered in order to very the roles of frictional coupling and electric polarization field in the solar wind, and the thermal force in the transition region. Steady-state solutions are found for coronae with a hydrogen flux at 1 AU of 1.0 x 109/cm2/sec or larger. For coronae with lower hydrogen fluxes, the helium flux into the corona is larger than the flux 'pulled out' by the solar wind protons, and solutions with increasing coronal helium content are found. The timescale for forming a helium-filled corona, that may allow for a steady outflow, is long compared to the mixing time for the corona. Title: Acceleration and Heating of Two-Fluid Solar Wind by Alfven Waves Authors: Sandbaek, Ornulf; Leer, Egil Bibcode: 1994ApJ...423..500S Altcode: Earlier model studies of solar wind driven by thermal pressure and Alfven waves have shown that wave amplitudes of 20-30 km/s at the coronal base are sufficient to accelerate the flow to the high speeds observed in quasi-steady streams emanating from large coronal holes. We focus on the energy balance in the proton gas and show that heat conduction from the region where the waves are dissipated may play an important role in determining the proton temperature at the orbit of Earth. In models with 'classical' heat conduction we find a correlation between high flow speed, high proton temperature, and low electron temperature at 1 AU. The effect of wave heating on the development of anisotropies in the solar wind proton gas pressure is also investigated in this study. Title: Neutral Hydrogen in the Solar Wind Acceleration Region Authors: Olsen, Espen Lyngdal; Leer, Egil; Holzer, Thomas E. Bibcode: 1994ApJ...420..913O Altcode: Observation of solar Ly alpha radiation scattered by coronal neutral hydrogen atoms can be used to investigate the acceleration region of the solar wind. In this paper we focus on the use of these observations to study Alfven waves, which can accelerate the solar wind plasma to flow speeds observed in high-speed streams if their amplitude at the coronal base is 20 km/s or larger. The wave amplitude is then larger than the proton thermal speed in the outer corona, so that the mean proton speed (averaged over a wave period) is significantly larger than the proton thermal speed. For low-frequency wave the hydrogen atoms follow the proton motion in the waves, while for higher frequencies the protons move relative to the neutrals. Nevertheless, in the higher frequency case, the rates for charge exchange and recombination are high enough to broaden the velocity distribution function of neutral hydrogen. Both the wave motion of the hydrogen atoms in low-frequency Alfven waves and the 'heating' by higher frequency waves lead to a broadening of the scattered solar Ly alpha line. For coronal base amplitudes of 20 km/s, the line broadening increases with heliocentric distance beyond 4-5 solar radii. Title: Diffusion Effects on the Helium Abundance of the Solar Transition Region and Corona Authors: Hansteen, Viggo H.; Holzer, Thomas E.; Leer, Egil Bibcode: 1993ApJ...402..334H Altcode: The diffusion of helium in the solar transition region is studied by solving the mass and momentum conservation equations for a hydrogen-helium plasma given a representative temperature profile. Steady state solutions show that two distinct atmospheres may result. In cases where the thermal force on alpha-particles is balanced by the partial pressure gradient force, helium is the dominant coronal species. On the other hand, if it is the frictional force between protons and alpha-particles which balances the thermal force on alpha-particles then hydrogen is the major coronal component. In order to explore which of these solutions are attainable within reasonable time scales, the time-dependent equations are solved, starting from an initial state with a uniform helium abundance of 10 percent. The atmosphere as a whole is close to hydrostatic equilibrium, but due the thermal forces the individual elements are not. This force inbalance leads to a differential flow between species. It is found that this differential flow leads to a significant enhancement of the coronal helium abundance. Even for the relatively shallow temperature gradient used the helium abundance in the lower corona increases to 30 percent over a 24 hr period. Title: Alfvén wave broadening of the scattered solar Ly-α line. Authors: Olsen, E. L.; Leer, E. Bibcode: 1993wpst.conf...83O Altcode: The authors study the effects of Alfvén waves from the sun on an electron-proton solar wind and the density, motion, and temperature of the neutral hydrogen gas in this background. The flow parameters are used to compute the width and intensity of the scattered solar Ly-α line. The authors find that the density of neutral hydrogen in the corona and inner solar wind is determined by the local balance between ionization and recombination. Both, high and low frequency Alfvén waves, may cause broadening of the scattered solar Ly-α line. Title: A Parameter Study of the Two-Fluid Solar Wind Authors: Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E. Bibcode: 1992ApJ...400..362S Altcode: A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind. Title: Solar wind from a corona with a large helium abundance Authors: Leer, Egil; Holzer, Thomas E.; Shoub, Edward C. Bibcode: 1992JGR....97.8183L Altcode: Observations of quasi-steady high-speed solar wind streams show that the proton mass flux density at 1 AU is remarkably constant, varying by less than 10% over long time periods. The observations are problematic, for simple theoretical models predict that the proton mass flux density is a sensitive function of the coronal base temperature, which is not expected to be unvarying to the degree required by the observations. In this paper we investigate the possibility that the presence of alpha particles in the coronal base region can reduce the sensitivity of the proton mass flux to base temperature. The equations of mass and momentum conservation are solved for electrons, protons, and alpha particles using a variety of assumed temperature profiles for each species. A wide range of base conditions are considered. We find that for an alpha particle to proton density ratio at the base as small as 10%, alpha particles can reduce the sensitivity of the proton mass flux density to variations in the base temperature. We also study the effects of enhanced collisional coupling and of Alfvén waves on the flux of protons and alpha particles. As an aid to future observational determination of the alpha particle density in the corona, we present calculations of the intensities of the resonantly scattered lines HeII λ304 and HI λ1216 for selected models. Title: Adiabatic Cooling of Solar Wind Electrons Authors: Sandbaek, Ornulf; Leer, Egil Bibcode: 1992JGR....97.1571S Altcode: In thermally driven winds emanating from regions in the solar corona with base electron densities of n0>=108 cm-3, a substantial fraction of the heat conductive flux from the base is transferred into flow energy by the pressure gradient force. The adiabatic cooling of the electrons causes the electron temperature profile to fall off more rapidly than in heat conduction dominated flows. Alfvén waves of solar origin, accelerating the basically thermally driven solar wind, lead to an increased mass flux and enhanced adiabatic cooling. The reduction in electron temperature may be significant also in the subsonic region of the flow and lead to a moderate increase of solar wind mass flux with increasing Alfvén wave amplitude. In the solar wind model presented here the Alfvén wave energy flux per unit mass is larger than in models where the temperature in the subsonic flow is not reduced by the wave, and consequently the asymptotic flow speed is higher. Title: A two-fluid model of the solar wind Authors: Sandbaek, O.; Leer, E.; Holzer, T. E. Bibcode: 1992sws..coll...95S Altcode: A method is presented for the integration of the two-fluid solar-wind equations which is applicable to a wide variety of coronal base densities and temperatures. The method involves proton heat conduction, and may be applied to coronal base conditions for which subsonic-supersonic solar wind solutions exist. Title: Coronal holes and the solar wind Authors: Leer, E. Bibcode: 1992HiA.....9..663L Altcode: No abstract at ADS Title: Magnetic reconnection in physics astrophysics: Summary of the workshop. Authors: Leer, E. Bibcode: 1992mrpa.work..207L Altcode: No abstract at ADS Title: The solar wind mass flux problem. Authors: Leer, E.; Holzer, T. E. Bibcode: 1991AnGeo...9..196L Altcode: 1991AnG.....9..196L The variation of the proton flux with coronal temperature and density in thermally driven solar wind models is discussed. It is shown that the rapid increase of the proton flux with increasing temperature can be reduced by adiabatic cooling of the expanding plasma. A significant coronal helium abundance can also act as a "regulator" for the solar wind proton flux. Title: Solar wind models Authors: Leer, Egil; Sandbaek, Ornulf Bibcode: 1991AdSpR..11a.197L Altcode: 1991AdSpR..11..197L Our understanding of the solar wind is based upon Parker's description of a thermally driven subsonic - supersonic outflow from a fully ionized electron-proton corona. The basic physical processes of thermally driven solar wind models are discussed. We also study the effect of alpha particles in the corona on the solar wind proton flux, and further discuss the acceleration of the solar wind by Alfvén waves. Title: Models of the solar wind and similar types of flow. Authors: Leer, E. Bibcode: 1991cwlt.conf..139L Altcode: Our current understanding of the solar wind and other types of flow is based upon Parker's theoretical model of an electron-proton solar wind (Parker, 1958). The electric field plays an important role for the dynamics of the electron-proton solar wind as well as in winds with several types of ions. The author discusses the role of the electric field in the solar wind and the polar wind, and shows how α-particles in the solar corona moderate variations in the solar wind proton flux with changing coronal conditions by exerting a collisional drag on the protons and modifying the electric field in the subsonic solar wind region. Title: Diagnostics of solar oscillation observations. Proceedings. Authors: Maltby, P.; Leer, E. Bibcode: 1991dsoo.conf.....M Altcode: No abstract at ADS Title: Coronae and winds in late-type stars. Proceedings. Authors: Leer, E.; Maltby, P. Bibcode: 1991cwlt.conf.....L Altcode: No abstract at ADS Title: Standing Shocks in the Inner Solar Wind Authors: Leer, Egil; Holzer, Thomas E. Bibcode: 1990ApJ...358..680L Altcode: It has been pointed out by several authors that the equations describing rapidly diverging flow in the solar wind and in related astrophysical systems allow for solutions with standing shocks in the acceleration region of the flow. The range of plasma and flow-geometry parameters that allow for such solutions are investigated. It is shown that, for reasonable geometries, shocks can occur only for a very narrow range of flow parameters in the case of the solar wind. Similar results can be expected for related astrophysical systems. Title: Flow of oxygen ions in the solar wind acceleration region Authors: Esser, Ruth; Leer, Egil Bibcode: 1990JGR....9510269E Altcode: A solar wind model with protons, electrons, OVII and OVI ions is studied. It is found that ionization and recombination processes lead to an approximately constant density ratio of the oxygen states (nOVI/nOVII~const<<1) in the solar wind acceleration region. Although ionization and recombination have a significant effect on the flow speed of the OVI ions, these processes are not fast enough to bring the speed of OVI up to the flow speed of the OVII ions. Title: Propagation of magnetohydrodynamic (MHD) waves in the solar transition region and corona. Authors: Leer, E.; Hansteen, V. Bibcode: 1990ppst.conf...81L Altcode: The propagation of MHD waves in the solar transition region and the corona is discussed. It is shown that the non-compressive Alfvén mode is the best candidate for energy transport into the corona and in the solar wind. Title: Physical processes in the solar transition-region and corona. Proceedings. Authors: Maltby, P.; Leer, E. Bibcode: 1990ppst.conf.....M Altcode: No abstract at ADS Title: Mini-Workshop on Flux Tubes in the Solar Atmosphere, held June 19-21, 1989, in Oslo, Norway Authors: Leer, E.; Maltby, P. Bibcode: 1989ftsa.conf.....L Altcode: No abstract at ADS Title: Mass loss mechanisms for cool stars Authors: Leer, E. Bibcode: 1988ASSL..143..297L Altcode: 1988acse.conf..297L The discussion of mass loss mechanisms for cool stars is based upon the understanding of thermally driven stellar winds. First the author discusses Parker's thermally driven solar wind model, and considers the effects of energy addition to the flow in the form of heat and momentum. On the basis of this general discussion he examines a few particular mechanisms to see if they can play a role in driving massive winds from cool giants and supergiants. Title: Drawing inferences about solar wind acceleration from coronal minor ion observations Authors: Esser, Ruth; Holzer, Thomas E.; Leer, Egil Bibcode: 1987JGR....9213377E Altcode: A parameter study is designed and carried out to illustrate the physical effects that can be studied through analysis and interpretation of coronal minor ion spectral line observations. It is shown that minor ion line width, together with the coronal Lyα line width and coronal white light observations, can yield important information concerning the transport and dissipation of energy carried outward from the coronal base by hydromagnetic waves. Although it is difficult to infer minor ion velocities through the Doppler dimming technique, the application of this technique using both radiatively and collisionally excited lines can provide constraints on the acceleration of coronal minor ions. It is concluded tha the observation of coronal minor ion spectral lines represents an important component of a concerted observational approach to the solar wind acceleration problem. It must be emphasized, however, that the measurement of line widths is the most important coronal minor ion observation to obtain. Title: Solar corona and solar wind. Authors: Leer, Egil Bibcode: 1987ESASP.275...11L Altcode: 1987sspp.symp...11L Parker's thermally driven solar wind model is reviewed. The model can describe the quiet solar wind quite well, but energy must be added to the flow to drive high speed streams. It is argued that the Solar and Heliospheric Observatory (SOHO) should be used to study possible acceleration mechanisms of the solar wind, in particular acceleration by magnetohydrodynamic (MHD) waves. In the inner corona a nonnegligible wave energy flow introduces a substantial nonthermal broadening of lines from heavy ions. Simultaneous observations of line widths and of the corona density profile in the source region of the solar wind, as well as the flow emanating from that region, should lead to a better understanding of the energy balance in the solar wind. Title: Wave Acceleration Mechanisms for the Solar Wind (R) Authors: Leer, E. Bibcode: 1987sowi.conf...89L Altcode: No abstract at ADS Title: Viscosity in the solar wind Authors: Holzer, T. E.; Leer, E.; Zhao, X. -P. Bibcode: 1986JGR....91.4126H Altcode: The effects of viscosity on a steady, radial, spherically symmetric solar wind with an embedded, non-radial magnetic field are reconsidered. The correct expression for the classical viscosity in the presence of a non-radial magnetic field is shown to be different from that used in the past, and a means of describing non-classical viscosity is presented. A physical interpretation of the classical and nonclassical description of viscosity is provided, and observational inferences are used in discussing the nature and degree of viscous effects in the solar wind. Title: A two-fluid solar wind model with Alfven waves: parameter study and application to observations Authors: Esser, Ruth; Leer, Egil; Habbal, Shadia R.; Withbroe, George L. Bibcode: 1986JGR....91.2950E Altcode: The effects of Alfven waves from the inner corona on the solar wind density profile, flow velocity and on the random motion of protons are studied. Different base densities, temperatures, and wave velocity amplitudes, as well as different flow geometries, are considered. The model calculations are compared to simultaneous observations of the electron density profile and the resonantly scattered Lyman alpha line. Present observations, out to 4 solar radii, can be used to place limits on the coronal base density and temperature, and put an upper limit on the wave amplitude. It is pointed out that future observations of the electron density and the Lyman alpha line, out to larger heliocentric distances, and of lines from heavier elements, should be used to place more stringent constraints on the amplitudes of MHD waves in the corona. Title: Solar Wind and Coronal Holes Authors: Leer, E.; Holzer, T. E. Bibcode: 1985ESASP.235....3L Altcode: 1985fmsh.work....3L; 1985shpp.rept....3L The authors discuss the basic physics of the solar wind emanating from coronal holes, and show that thermally driven solar wind models cannot explain the high flow speeds. The effect of MHD waves on both the solar wind and wind from late-type giants and supergiants is also considered. Title: Fast-mode magnetohydrodynamic waves in coronal holes and the solar wind Authors: Fla, T.; Habbal, S. R.; Holzer, T. E.; Leer, E. Bibcode: 1984ApJ...280..382F Altcode: Fast-mode MHD waves in the solar corona can propagate in any direction relative to the background magnetic field. In coronal holes, they refract into regions of low Alfven speed and are relatively difficult to damp. These characteristics lead to the possibility that fast-mode waves transport energy from magnetically closed coronal regions into coronal holes, that they are refracted into the central regions of coronal holes, and that they deposit most of their energy in the region of supersonic flow of high-speed solar wind streams emanating from coronal holes. To investigate whether this possibility might be realized and fast-mode waves might play a significant role in driving high-speed streams, a parameter study is carried out to examine the propagation and damping of fast-mode waves in various coronal hole models. This study indicates a broad range of coronal hole parameters for which fast-mode waves can play such a role and emphasizes the need for an improved knowledge of large-scale coronal magnetic structure, which is required before any firm conclusions can be drawn. Title: Alfven waves in stellar winds Authors: Holzer, T. E.; Fla, T.; Leer, E. Bibcode: 1983ApJ...275..808H Altcode: An analytic description of a stellar wind with waves which are undamped in the region of subsonic flow is developed for a range of stellar conditions, and numerical models with wave damping are applied to the massive winds from cool, low gravity stars, in an examination of the propagation and damping of Alfven waves in stellar winds. Attention is also given to the effects of these waves on the wind mass loss rate, asymptotic flow speed, and radial temperature profile. No evidence is found for the belief that winds driven by Alfven waves from cool, low gravity stars can exhibit both a very large mass loss rate and a very small asymptotic flow speed. It is noted that the radial temperature profile produced by invoking a constant damping length for the waves is different from that produced by self-consistent description of frictional wave damping for a wave frequency which is presumably consistent with the chosen constant damping length. Title: Theory of solar wind acceleration. Authors: Leer, E. Bibcode: 1983NASCP2280..147L Altcode: No abstract at ADS Title: The structure of cosmic ray shocks Authors: Axford, W. I.; Leer, E.; McKenzie, J. F. Bibcode: 1982A&A...111..317A Altcode: The acceleration of cosmic rays by steady shock waves has been discussed in brief reports by Leer et al. (1976) and Axford et al. (1977). This paper presents a more extended version of this work. The energy transfer and the structure of the shock wave is discussed in detail, and it is shown that even for moderately strong shock waves most of the upstream energy flux in the background gas is transferred to the cosmic rays. This holds also when the upstream cosmic ray pressure is very small. For an intermediate Mach-number regime the overall shock structure is shown to consist of a smooth transition followed by a gas shock (cf. Drury and Voelk, 1980). Title: Acceleration of the solar wind. Authors: Leer, E.; Holzer, T. E.; Fla, T. Bibcode: 1982SSRv...33..161L Altcode: In this review, we discuss critically recent research on the acceleration of the solar wind, giving emphasis to high-speed solar wind streams emanating from solar coronal holes. We first explain why thermally driven wind models constrained by solar and interplanetary observations encounter substantial difficulties in explaining high speed streams. Then, through a general discussion of energy addition to the solar wind above the coronal base, we indicate a possible resolution of these difficulties. Finally, we consider the question of what role MHD waves might play in transporting energy through the solar atmosphere and depositing it in the solar wind, and we conclude by examining, in a simple way, the specific mechanism of solar wind acceleration by Alfvén waves and the related problem of accelerating massive stellar winds with Alfvén waves. Title: Electron heating by fast mode magnetohydrodynamic waves in the solar wind emanating from coronal holes Authors: Habbal, S. R.; Leer, E. Bibcode: 1982ApJ...253..318H Altcode: It is shown that fast mode magnetohydrodynamic waves, propagating outwards from the sun in coronal hole regions, will dissipate primarily through collisionless interaction with electrons rather than with protons. This dissipation can lead to higher electron than proton temperatures in the accelerating region of the solar wind, provided the waves carry a sufficiently large energy flux. Title: Theory of Mass and Energy Flow in the Solar Wind Authors: Holzer, T. E.; Leer, E. Bibcode: 1981sowi.conf...28H Altcode: No abstract at ADS Title: Conductive solar wind models in rapidly diverging flow geometries Authors: Holzer, T. E.; Leer, E. Bibcode: 1980JGR....85.4665H Altcode: A detailed parameter study of conductive models of the solar wind has been carried out, extending the previous similar studies of Durney (1972) and Durney and Hundhausen (1974) by considering collisionless inhibition of thermal conduction, rapidly diverging flow geometries, and the structure of solutions for the entire n0-T0 plane (n0 and T0 are the coronal base density and temperature). Primary emphasis is placed on understanding the complex effects of the physical processes operative in conductive solar wind models. There are five points of particular interest that have arisen from the study: (1) neither collisionless inhibition of thermal conduction nor rapidly diverging flow geometries can significantly increase the solar wind speed at 1 AU; (2) there exists a firm upper limit on the coronal base temperature consistent with observed values of the coronal base pressure and solar wind mass flux density; (3) the principal effect of rapidly diverging flow geometries is a decrease in the solar wind mass flux density at 1 AU and an increase in the mass flux density at the coronal base; (4) collisionless inhibition of thermal conduction can lead to a solar wind flow speed that either increases or decreases with increasing coronal base density (n0) and temperature (T0, depending on the region of the n0-T0 plane considered; (5) there is a region of the n0-To plane at high coronal base densities where low-speed, high-mass-flux, transonic solar wind flows exist-a region not previously considered. Title: Energy addition in the solar wind. Authors: Leer, E.; Holzer, T. E. Bibcode: 1980JGR....85.4681L Altcode: A general study of energy addition, energy loss, and energy redistribution in the solar wind, for both spherically symmetric and rapidly diverging flow geometries, is presented. It is found that energy addition in the region of subsonic flow increases the solar wind mass flux but either has little effect on (for heat addition) or significantly reduces (for momentum addition) the solar wind flow speed at 1 AU. In contrast, energy addition in the region of supersonic flow has no effect on the solar wind mass flux but significantly increases the flow speed at 1 AU. It is also found that both momentum loss in the subsonic region and energy exchange (involving loss in the subsonic region and gain in the supersonic region) can lead to an increase in the asymptotic flow speed. This general study thus places certain constraints on viable mechanisms for driving high-speed solar wind streams and points to a number of specific, self-consistent studies of such mechanisms that need to be carried out in the future. Title: Alfvén-wave acceleration of the solar wind. Authors: Leer, E.; Fla, T.; Holzer, T. E. Bibcode: 1980NCimC...3..114L Altcode: The increase in mass flux and energy flux from the sun is calculated for an increasing Alfven-wave amplitude, in the lower corona and fixed values for the coronal pressure, the coronal temperature and the interplanetary magnetic field. The energy per mass and the flow speed at the orbit of the earth increase with the wave amplitude and reach a maximum for a wave amplitude of approximately 50 km/sec. For reasonable values of the coronal pressure and temperature and of the magnetic field, high-speed solar-wind streams can be driven by Alfven waves with an amplitude approximately equal to 20-25 km/sec in the lower corona. Title: Plasma drift in the polar ionosphere. Authors: Bratteng, O.; Leer, E. Bibcode: 1980FFV....42...37B Altcode: No abstract at ADS Title: Heating of Coronal Loops by Fast-Mode Magnetohydrodynamic Waves Authors: Habbal, Shadia Rifai; Leer, Egil; Holzer, Thomas E. Bibcode: 1979SoPh...64..287H Altcode: A possible mechanism for the formation and heating of coronal loops through the propagation and damping of fast mode waves is proposed and studied in detail. Loop-like field structures are represented by a dipole field with the point dipole at a given distance below the solar surface. The density of the medium is determined by hydrostatic equilibrium along the field lines in an isothermal atmosphere. The fast mode waves propagating outward from the coronal base are refracted into regions with a low Alfvén speed and suffer collisionless damping when the gas pressure becomes comparable to the magnetic pressure. The propagation and damping of these waves are studied for three different cases: a uniform density at the coronal base, a density depletion within a given flux tube, and a density enhancement within a given flux tube. The fast mode waves are found to be important in the formation and heating of the loops if the wave energy flux density is of the order 105 ergs cm-2 s-1 at the coronal base. Title: Constraints on the solar coronal temperature in regions of open magnetic field. Authors: Leer, E.; Holzer, T. E. Bibcode: 1979SoPh...63..143L Altcode: It is shown that the simultaneous consideration of observed values of the solar wind proton flux density at 1 AU and of the electron pressure at the base of the solar corona leads to relatively strong constraints on the coronal temperature in the region of subsonic solar wind flow. The extreme upper limit on the mean coronal temperature in the subsonic region is found to be about 2.6 × 106 K, but this upper limit is reduced to about 2.0 × 106 K if reasonable, rather than extreme, assumptions are made; the limit on the maximum temperature is about 0.5 × 106 K greater than the limit on the mean. It is also found that the same two observations limit the rate of momentum addition possible in the region of subsonic solar wind flow. Title: Discussion Authors: Wentzel, D.; Leer, E. Bibcode: 1979phsp.coll..231W Altcode: 1979IAUCo..44..231W No abstract at ADS Title: Heating of Coronal Loops by Fast Mode Mhd-Waves Authors: Habbal, S. R.; Holzer, T. E.; Leer, E. Bibcode: 1979phsp.coll..228H Altcode: 1979phsp.conf..228H; 1979IAUCo..44..228H This paper discusses the formation and heating of solar coronal loops by fast mode MHD waves which, unlike Alfven waves, have an acoustic component. These fast mode waves can carry a substantial energy flux along the wave normal only in coronal regions with a strong magnetic field. The propagation and damping of these waves in a two dimensional solar atmosphere is considered. It is noted that the damping occurs mainly in the region where beta = 2nkT/(B-squared/8pi) is larger than 0.05, and that most of the energy is transferred to the plasma in the region where beta approximately equals 0.2. In this case the plasma in the flux tube with a height approximately equal to 0.2R is heated most, and the wave energy flux from the base deposits more energy in this tube than is lost by radiation and heat conduction at the footpoints. Therefore, density and temperature perturbations across the field lines will develop and 'loops' may be formed. Heating mechanisms of the surrounding plasma in both large density and low density loops are then described. Title: Group velocity of whistlers in a two-ion plasma Authors: Leer, E.; Johansen, K. M.; Albrigtsen, R. Bibcode: 1978JGR....83.3125L Altcode: Computations of goup velocity of whistlers in a two-ion plasma show that a quasi-longitudinal (QL) right-handed polarized wave (electron wave) has a minimum group velocity at the so-called crossover frequency; a QL left-handed polarized wave has a maximum group velocity at the ion hybrid frequency. In an oxygen/hydrogen plasma this minimum occurs only for almost perpendicular waves, whereas in a helium/hydrogen plasma it occurs also for waves propagating off perpendicular to the magnetic field. We also find that a small concentration of helium in a hydrogen plasma introduces a 'stop band' for quasi-transverse waves with frequencies just above the helium gyrofrequency. The theoretical results are used to interpret satellite observations of quasi-tranverse low-frequency whistlers. Title: Oscillating echoes from the polar E layer Authors: Bratteng, O.; Leer, E. Bibcode: 1978JGR....83.1162B Altcode: Radio waves with a freuency of 4 MHz transmitted vertically into the polar ionosphere and reflected in the E layer occasionally show very stable oscillations in intensity. This phenomenon, which occurs mainly in the evening sector under quiet conditions, has been studied at Ny-Ălesund, Spitzbergen, by using a 4-MHz transmitter and four spaced receiving antennas. The observed oscillations can be explained as interference of waves reflected from a pair of enhanced ionization regions some 30 km apart and moving with a horizontal velocity of the order of 100 m/s. The low drift velocity is consistent with low magnetic activity. Title: Acceleration of cosmic rays by shock waves. Authors: Axford, W. I.; Leer, E.; Skadron, G. Bibcode: 1978cosm.conf..125A Altcode: No abstract at ADS Title: Stimulated Brillouin scattering in the ionosphere Authors: Dysthe, K. B.; Leer, E.; Trulsen, J.; Stenflo, L. Bibcode: 1977JGR....82..717D Altcode: We discuss the possibility of obtaining stimulated backscattering from the ionosphere. It is found that stimulated Brillouin scattering off ion modes and quasi modes may be possible with the signal power that is planned for the Eiscat radar. Title: The Acceleration of Cosmic Rays by Shock Waves Authors: Axford, W. I.; Leer, E.; Skadron, G. Bibcode: 1977ICRC...11..132A Altcode: 1977ICRC...15k.132A; 1978ICRC...11..132A The possibility of cosmic ray acceleration by shock waves has been considered by many workers during the last twenty years on the basis of various assumptions on the exact nature of the acceleration mechanism. The paper examines the question further on the assumption that the cosmic rays are constrained to move diffusively with respect to the background medium, and finds that acceleration is very efficient. The acceleration of cosmic rays in flows involving shocks and other compressional waves is considered in terms of one-dimensional steady flows and the diffusion approximation. The results suggest that very substantial energy conversion can occur. Title: Acceleration of Cosmic Rays at Shock Fronts (Abstract) Authors: Axford, W. I.; Leer, E.; Skadron, G. Bibcode: 1977ICRC....2..273A Altcode: 1977ICRC...15b.273A No abstract at ADS Title: Electrostatic waves in the ionosphere. Authors: Leer, E. Bibcode: 1977rpap.conf...55L Altcode: No abstract at ADS Title: Group velocity of whistlers Authors: Johansen, K. M.; Leer, E. Bibcode: 1976JGR....81.4503J Altcode: The dispersion relation of waves in a cold magnetoplasma can be given in the form ∑ı=0p Ai(k)ωı ≡ 0, where ω is the frequency and the coefficients Aı are functions of the wave vector k. The group velocity Vg can be expressed as Vg = -∑i=0p(∂Ai/∂k)ωı/∑i=0piAiωı-1. This equation is used for numerical studies of the slow and fast mode propagation in a one-ion plasma. The slow mode is always guided by the magnetostatic field B0, whereas the fast mode is guided only for frequencies in the ‘whistler band.’ The ‘nose frequency’ for the whistlers decreases as the angle θ = ∠(k, B0) increases. Title: Parametric excitation of standing electromagnetic waves. Authors: Leer, E. Bibcode: 1976PhyS...13...47L Altcode: The threshold for parametric excitation of standing electromagnetic waves by a standing electromagnetic pump wave with the same frequency is derived. A homogeneous plasma is considered, and a method based on energy balance is used. The threshold is found to depend on the amplitude of the electron motion in the pump wave and on the angle between the direction of this motion and the electric component of the excited wave. Waves in the same mode as the pump wave can be excited more easily than waves in the opposite mode. This instability may be important in ionospheric-modification experiments. Title: Plasma drift in the polar ionosphere, Ny Alesund, 6 - 10 September 1974. Authors: Leer, E.; Bratteng, O. Bibcode: 1976PhyNr...8..129L Altcode: No abstract at ADS Title: Heated Solar Atmosphere: A One-Fluid Model Authors: Leer, Egil Bibcode: 1974SoPh...35..467L Altcode: A one-fluid model of the solar atmosphere is considered. The corona is heated by waves propagating out from the Sun, and profiles for temperature, flow speed and number density are obtained. For a relatively quiet Sun the inwards heat flux in the inner corona is constant in T ≲ 5-6 × 105 K and the temperature maximum is reached for r — R⊙ = 0.4 — 0.5 R⊙ where R⊙ is the solar radius. The number density in the inner corona decreases with an increasing particle flux. Title: Solar Wind Heating Beyond 1 AU Authors: Holzer, Thomas E.; Leer, Egil Bibcode: 1973Ap&SS..24..335H Altcode: The effect of an interplanetary atomic hydrogen gas on solar wind proton, electron and α-particle temperatures beyond 1 AU is considered. It is shown that the proton temperature (and probably also the α-particle temperature) reaches a minimum between 2 AU and 4 AU, depending on values chosen for solar wind and interstellar gas parameters. Heating of the electron gas depends primarily on the thermal coupling of the protons and electrons. For strong coupling (when T p ≳T e ), the electron temperature reaches a minimum between 4 AU and 8 AU, but for weak coupling (Coulomb collisions only), the electron temperature continues to decrease throughout the inner solar system. A spacecraft travelling to Jupiter should be able to observe the heating effect of the solar wind-interplanetary hydrogen interaction, and from such observations it may be possible of infer some properties of the interstellar neutral gas. Title: A Two-Fluid Solar Wind Model with Anisotropic Proton Temperature Authors: Leer, E.; Axford, W. I. Bibcode: 1972SoPh...23..238L Altcode: A two-fluid model of the solar wind with anisotropic proton temperature and allowing for extended coronal proton-heating is considered for the case of a purely radial and of a spiral magnetic field. Proton-proton Coulomb-collisions together with a spiral interplanetary magnetic field are found to be sufficient to reduce the thermal anisotropy in the proton gas to a value in agreement with observations. Reasonable values are obtained for the flow-velocity, number density and the protontemperature near the orbit of the Earth. Title: Collisionless solar wind protons: A comparison of kinetic and hydrodynamic descriptions Authors: Leer, Egil; Holzer, Thomas E. Bibcode: 1972JGR....77.4035L Altcode: Kinetic and hydrodynamic descriptions of a collisionless solar wind proton gas are compared. Heat conduction and viscosity are neglected in the hydrodynamic formulation but are automatically included in the kinetic formulation. The fact that the results of the two models are very nearly the same indicates that heat conduction and viscosity are not important in the solar wind proton gas beyond approximately 0.1 AU. It is concluded that the hydrodynamic equations provide a valid description of the collisionless solar wind protons and, hence, that future models of the quiet solar wind should be based on a hydrodynamic formulation. Title: Galactic cosmic rays in interplanetary space. Authors: Leer, E. Bibcode: 1972PhyNr...6..193L Altcode: No abstract at ADS Title: Ion-reflection of downward-propagating whistlers at low latitudes Authors: Egeland, A.; Leer, E.; Holtet, J. A. Bibcode: 1970JATP...32.1983E Altcode: The real time a.c. (10-1500 Hz) electric field measurements, received on 2 May 1967 when the Satellite OV1-10 (altitude about 700 km) moved from 0° to 20° N geomagnetic latitude, are presented. Several long fractional hop whistlers, strongly influenced by ions, were observed. The main findings are: For downward propagating whistlers a frequency band is reflected. The width and the location of this band are latitude dependent. Whistler-pairs separated in time by 0.15 sec and with a 15 per cent difference in dispersion were observed. These pairs are probably generated by the same lightning stroke and propagate along different ray paths. Whistlers propagating on higher L-shells seem to be less connected to the magnetic fieldlines than those on lower L-shells. Resonance damping may be important for a limited frequency band. Title: Low latitude subprotonospheric and ion cyclotron whistlers generated by the same lightning discharge Authors: Egeland, A.; Leer, E. Bibcode: 1970P&SS...18D....E Altcode: No abstract at ADS Title: Low latitude subprotonospheric and ion cyclotron whistlers generated by the same lightning discharge Authors: Egeland, A.; Leer, E. Bibcode: 1970P&SS...18.1848E Altcode: No abstract at ADS Title: Exact motion of a charged particle in an arbitrary plane wave propagating along a constant homogeneous magnetic field. Authors: Leer, E. Bibcode: 1969PhFl...12.2206L Altcode: The classical relativistic equations of motion are solved for a charged particle moving in an arbitrary plane electromagnetic wave propagating along a constant homogenous magnetic field. The solutions are expressed by (proper time) evolution tensor factors, operating upon the initial value quantities. The calculations are performed in terms of tensor-component matrices. Elliptically polarized waves are then considered. At resonance frequency an expression for the increase in the kinetic energy is obtained. This expression shows that the kinetic energy increases indefinitely, and that the energy exchange is caused by the field component rotating in the same direction as the particle.