Author name code: goedbloed ADS astronomy entries on 2022-09-14 author:"Goedbloed, J.P." ------------------------------------------------------------------------ Title: Advanced Magnetohydrodynamics Authors: Goedbloed, J. P.; Keppens, Rony; Poedts, Stefaan Bibcode: 2010adma.book.....G Altcode: Preface; Part III. Flow and Dissipation: 12. Waves and instabilities of stationary plasmas; 13. Shear flow and rotation; 14. Resistive plasma dynamics; 15. Computational linear MHD; Part IV. Toroidal Plasmas: 16. Static equilibrium of toroidal plasmas; 17. Linear dynamics of static toroidal plasmas; 18. Linear dynamics of stationary toroidal plasmas; Part V. Nonlinear Dynamics: 19. Computational nonlinear MHD; 20. Transonic MHD flows and shocks; 21. Ideal MHD in special relativity; Appendices; References; Index. Title: PHOENIX: MHD spectral code for rotating laboratory and gravitating astrophysical plasmas Authors: Blokland, J. W. S.; van der Holst, B.; Keppens, R.; Goedbloed, J. P. Bibcode: 2007JCoPh.226..509B Altcode: The new PHOENIX code is discussed together with a sample of many new results that are obtained concerning magnetohydrodynamic (MHD) spectra of axisymmetric plasmas where flow and gravity are consistently taken into account. PHOENIX, developed from the CASTOR code [W. Kerner, J.P. Goedbloed, G.T.A. Huysmans, S. Poedts, E. Schwarz, J. Comput. Phys. 142 (1998) 271], incorporates purely toroidal, or both toroidal and poloidal flow and external gravitational fields to compute the entire ideal or resistive MHD spectrum for general tokamak or accretion disk configurations. These equilibria are computed by means of FINESSE [A.J.C. Beliën, M.A. Botchev, J.P. Goedbloed, B. van der Holst, R. Keppens, J. Comp. Physics 182 (2002) 91], which discriminates between the different elliptic flow regimes that may occur. PHOENIX makes use of a finite element method in combination with a spectral method for the discretization. This leads to a large generalized eigenvalue problem, which is solved by means of Jacobi-Davidson algorithm [G.L.G. Sleijpen, H.A. van der Vorst, SIAM J. Matrix Anal. Appl. 17 (1996) 401]. PHOENIX is compared with CASTOR, PEST-1 and ERATO for an internal mode of Soloviev equilibria. Furthermore, the resistive internal kink mode has been computed to demonstrate that the code can accurately handle small values for the resistivity. A new reference test case for a Soloviev-like equilibrium with toroidal flow shows that, on a particular unstable mode, the flow has a quantifiable stabilizing effect regardless of the direction of the flow. PHOENIX reproduces the Toroidal Flow induced Alfvén Eigenmode (TFAE, [B. van der Holst, A.J.C. Beliën, J.P. Goedbloed, Phys. Rev. Lett. 84 (2000) 2865]) where finite resistivity in combination with equilibrium flow effects causes resonant damping. Localized ideal gap modes are presented for tokamak plasmas with toroidal and poloidal flow. Finally, we demonstrate the ability to spectrally diagnose magnetized accretion disk equilibria where gravity acts together with either purely toroidal flow or both toroidal and poloidal flow. These cases show that the MHD continua can be unstable or overstable due to the presence of a gravitational field together with equilibrium flow-driven dynamics [J.P. Goedbloed, A.J.C. Beliën, B. van der Holst, R. Keppens, Phys. Plasmas 11 (2004) 28]. Title: Unstable magnetohydrodynamical continuous spectrum of accretion disks. A new route to magnetohydrodynamical turbulence in accretion disks Authors: Blokland, J. W. S.; Keppens, R.; Goedbloed, J. P. Bibcode: 2007A&A...467...21B Altcode: 2007astro.ph..3581B Context: We present a detailed study of localised magnetohydrodynamical (MHD) instabilities occurring in two-dimensional magnetized accretion disks.
Aims: We model axisymmetric MHD disk tori, and solve the equations governing a two-dimensional magnetized accretion disk equilibrium and linear wave modes about this equilibrium. We show the existence of novel MHD instabilities in these two-dimensional equilibria which do not occur in an accretion disk in the cylindrical limit.
Methods: The disk equilibria are numerically computed by the FINESSE code. The stability of accretion disks is investigated analytically as well as numerically. We use the PHOENIX code to compute all the waves and instabilities accessible to the computed disk equilibrium.
Results: We concentrate on strongly magnetized disks and sub-Keplerian rotation in a large part of the disk. These disk equilibria show that the thermal pressure of the disk can only decrease outwards if there is a strong gravitational potential. Our theoretical stability analysis shows that convective continuum instabilities can only appear if the density contours coincide with the poloidal magnetic flux contours. Our numerical results confirm and complement this theoretical analysis. Furthermore, these results show that the influence of gravity can either be stabilizing or destabilizing on this new kind of MHD instability. In the likely case of a non-constant density, the height of the disk should exceed a threshold before this type of instability can play a role.
Conclusions: This localised MHD instability provides an ideal, linear route to MHD turbulence in strongly magnetized accretion disk tori. Title: Stationary field-aligned MHD flows at astropauses and in astrotails. Principles of a counterflow configuration between a stellar wind and its interstellar medium wind Authors: Nickeler, D. H.; Goedbloed, J. P.; Fahr, H. -J. Bibcode: 2006A&A...454..797N Altcode: 2012arXiv1203.5500N Context: .A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvénic or as a super-Alfvénic tail flow. An example is our own heliosphere and its heliotail.
Aims: . We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few governing parameters, like the inner Alfvén Mach number and the outer Alfvén Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points (neutral points) of the magnetic field within these flows.
Methods: . Within the framework of a one-fluid approximation, it is possible to obtain solutions of the governing MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfvén Mach number for the corresponding stationary equilibria is finite.
Results: .The topological structure, i.e. the distribution of magnetic neutral points, determines the geometrical structure of the interstellar gas - stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail/astrosheath region beyond the reverse shock.
Conclusions: .The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfvén Mach numbers in the case of subalfvénic flows. Title: Magneto-rotational overstability in accretion disks Authors: Blokland, J. W. S.; van der Swaluw, E.; Keppens, R.; Goedbloed, J. P. Bibcode: 2005A&A...444..337B Altcode: 2005astro.ph..4381B We present analytical and numerical studies of magnetorotational instabilities occuring in magnetized accretion disks. These calculations are performed for general radially stratified disks in the cylindrical limit. We elaborate on earlier analytical results and confirm and expand them with numerical computations of unstable eigenmodes of the full set of linearised compressible MHD equations. We compare these solutions with those found from approximate local dispersion equations from WKB analysis. In particular, we investigate the influence of a nonvanishing toroidal magnetic field component on the growth rate and oscillation frequency of magnetorotational instabilities in Keplerian disks. These calculations are performed for a constant axial magnetic field strength. We find the persistence of these instabilities in accretion disks close to equipartition. Our calculations show that these eigenmodes become overstable (complex eigenvalue), due to the presence of a toroidal magnetic field component, while their growth rate reduces slightly. Furthermore, we demonstrate the presence of magneto-rotational overstabilities in weakly magnetized sub-Keplerian rotating disks. We show that the growth rate scales with the rotation frequency of the disk. These eigenmodes also have a nonzero oscillation frequency, due to the presence of the dominant toroidal magnetic field component. The overstable character of the MRI increases as the rotation frequency of the disk decreases. Title: Transonic instabilities in accretion disks Authors: Goedbloed, J. P.; Keppens, R. Bibcode: 2005AIPC..784..639G Altcode: In two previous publications, we have demonstrated that stationary rotation of magnetized plasma about a compact central object permits an enormous number of different MHD instabilities, with the well-known magneto-rotational instability as just one of them. We here concentrate on the new instabilities found that are driven by transonic transitions of the poloidal flow. A particularly promising class of instabilities, from the point of view of MHD turbulence in accretion disks, is the class of trans-slow Alfvén continuum modes, that occur when the poloidal flow exceeds a critical value of the slow magnetosonic speed. When this happens, virtually every magnetic/flow surface of the disk becomes unstable with respect to highly localized modes of the continuous spectrum. The mode structures rotate, in turn, about the rotating disk. These structures lock and become explosively unstable when the mass of the central object is increased beyond a certain critical value. Their growth rates then become huge, of the order of the Alfvén transit time. These instabilities appear to have all requisite properties to facilitate accretion flows across magnetic surfaces and jet formation. Title: Response to ``Comment on `Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas' '' [Phys. Plasmas 12, 064701 (2005)] Authors: Goedbloed, J. P. Bibcode: 2005PhPl...12f4702G Altcode: Contrary to the Comment by McClements and Thyagaraja that the two-fluid equations for stationary axisymmetric equilibria are easier to deal with numerically than the corresponding ideal magnetohydrodynamics (MHD) equations, since they resolve the Alfvén singularity of the latter whereas transonic transitions do not create substantial numerical difficulties, the opposite proposition is maintained. The numerical solution of the single (MHD) or two (two-fluid) Bernoulli equations already eliminates the Alfvén singularity, but it presents major complications (such as the possible nonexistence, multiplicity, and hyperbolicity of the solutions) in the construction of stationary equilibria that are accurate enough to permit spectral analysis of the waves and instabilities of those equilibria. Furthermore, it is shown that imposing charge neutrality on the two-fluid equations not only obscures the solution procedure of the two independent Bernoulli equations but also eliminates the possibility of a self-consistent description of the charge imbalances that occur in rotating and gravitating astrophysical plasmas, such as Goldreich-Julian charges in magnetospheres of pulsars and massive black holes. Title: Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas Authors: Goedbloed, J. P. Bibcode: 2004PhPl...11L..81G Altcode: It is shown that the core equations of both the magnetohydrodynamics and the two-fluid description of stationary axisymmetric equilibrium flows may be derived from variational principles in terms of the core variables of the respective descriptions. The latter replace the primitive variables because of the stream function constraints associated with axisymmetry. This yields a concise representation of stationary flows in tokamaks, accretion disks, and jets, and permits accurate numerical implementation. Since hyperbolic flows occur in both descriptions, the limitation of the variational principles to elliptic flow regimes presents an intricate problem. Title: Principles of Magnetohydrodynamics Authors: Goedbloed, J. P. Hans; Poedts, Stefaan Bibcode: 2004prma.book.....G Altcode: Part I. Plasma Physics Preliminaries: 1. Introduction; 2. Elements of plasma physics; 3. 'Derivation' of the macroscopic equations; Part II. Basic Magnetohydrodynamics: 4. The MHD model; 5. Waves and characteristics; 6. Spectral theory; 7. Waves and instabilities on inhomogeneous plasmas; 8. Magnetic structures and dynamics; 9. Cylindrical plasmas; 10. Initial value problem and wave damping; 11. Resonant absorption and wave heating; Appendices; References; Index. Title: Transsonic instabilities in tokamaks and astrophysical accretion flows Authors: Goedbloed, J. P. (Hans); Beliën, A. J. C.; van der Holst, B.; Keppens, R. Bibcode: 2004AIPC..703...42G Altcode: Waves and instabilities of transonically rotating toroidal plasmas present a very complex problem of interest for the two unrelated fields of magnetically-dominated laboratory plasmas and gravitationally-dominated astrophysical plasmas. The complexity originates from the transonic transitions of the poloidal flow which causes the character of the rotating equilibrium states to change dramatically, from elliptic to hyperbolic or vice versa, when the poloidal velocity surpasses certain critical speeds. Associated with these transitions the different types of magnetohydrodynamic (MHD) shocks may appear. Obviously, at such transitions the possible waves and instabilities of the system also change dramatically. We have investigated these changes for the two mentioned physical systems, starting from the point of view that the continuous spectrum of magnetohydrodynamics presents the best organizing principle for the structure of the complete spectrum since it is the most robust part of it. We found a new class of local MHD instabilities, that we called trans-slow Alfvén continuum modes, which are due to poloidal flows exceeding the critical slow magnetosonic speed. They operate both in laboratory plasmas (tokamaks), in the absence of gravitational effects, and in astrophysical plasmas (accretion tori), when the gravitational field of a compact object dominates the flow. They become extremely violent when the mass of the central object is large, providing a new route to MHD turbulence in plasmas rotating about a massive central object. Title: Transsonic Instabilities in Laboratory and Astrophysical Plasmas Authors: Goedbloed, J. P. > Bibcode: 2004PhST..107..159G Altcode: Waves and instabilities of transsonically rotating axisymmetric plasmas present a highly complex problem that is of interest for two unrelated fields of research, viz. laboratory tokamak confinement for the eventual thermonuclear energy production and the dynamics of a vast number of astrophysical plasmas rotating about compact objects, broadly indicated as accretion disks. The complexity originates from the transsonic transitions of the poloidal flow which causes the character of the rotating equilibrium states to change dramatically, from elliptic to hyperbolic or vice versa, when the poloidal velocity surpasses certain critical speeds. Associated with these transitions the different types of magnetohydrodynamic (MHD) shocks may appear. Obviously, at such transitions the possible waves and instabilities of the system also change dramatically. We investigate these changes for the two mentioned classes of physical systems, starting from the point of view that the continuous spectrum of magnetohydrodynamics presents the best organizing principle for the structure of the complete spectrum of waves and instabilities since it is the most robust part of it, for that reason called the “essential spectrum” by mathematicians. The physical importance of the problem is that it provides the simplest approach to local waves and instabilities of the system and, possibly, to the onset of MHD turbulence in accretion disks. Title: Three-dimensional magnetohydrodynamic simulations of in situ shock formation in the coronal streamer belt Authors: Zaliznyak, Yu.; Keppens, R.; Goedbloed, J. P. Bibcode: 2003PhPl...10.4478Z Altcode: 2004astro.ph..3122Z A numerical study of an idealized magnetohydrodynamic (MHD) configuration consisting of a planar wake flow embedded into a three-dimensional (3D) sheared magnetic field is presented. The simulations investigate the possibility for in situ development of large-scale compressive disturbances at cospatial current sheet-velocity shear regions in the heliosphere. Using a linear MHD solver, the systematical investigation of the destabilized wavenumbers, corresponding growth rates, and physical parameter ranges for dominant 3D sinuous-type instabilities in an equilibrium wake-current sheet system was done. Wakes bounded by sufficiently supersonic (Mach number Ms>2.6) flow streams are found to support dominant fully 3D sinuous instabilities when the plasma beta is of order unity. Fully nonlinear, compressible 2.5D and 3D MHD simulations show the self-consistent formation of shock fronts of fast magnetosonic type. They carry density perturbations far away from the wake's center. Shock formation conditions are identified in sonic and Alfvénic Mach number parameter space. Depending on the wake velocity contrast and magnetic field magnitude, as well as on the initial perturbation, the emerging shock patterns can be plane-parallel as well as fully three-dimensionally structured. Similar large-scale transients could therefore originate at distances far above coronal helmet streamers or at the location of the ecliptic current sheet. Title: Adaptive Mesh Refinement for conservative systems: multi-dimensional efficiency evaluation Authors: Keppens, R.; Nool, M.; Tóth, G.; Goedbloed, J. P. Bibcode: 2003CoPhC.153..317K Altcode: 2004astro.ph..3124K Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic simulations, AMR is used in combination with several shock-capturing, conservative discretization schemes. Solution accuracy and execution times are compared with static grid simulations at the corresponding high resolution and time spent on AMR overhead is reported. Our examples reach corresponding efficiencies of 5 to 20 in multi-dimensional calculations and only 1.5-8% overhead is observed. For AMR calculations of multi-dimensional magnetohydrodynamic problems, several strategies for controlling the ∇.B=0 constraint are examined. Three source term approaches suitable for cell-centered B representations are shown to be effective. For 2D and 3D calculations where a transition to a more globally turbulent state takes place, it is advocated to use an approximate Riemann solver based discretization at the highest allowed level(s), in combination with the robust Total Variation Diminishing Lax-Friedrichs method on the coarser levels. This level-dependent use of the spatial discretization acts as a computationally efficient, hybrid scheme. Title: Analogies of Rapidly Rotating Tokamaks and Accretion Disks Authors: Goedbloed, J. P.; Belien, A. J. C.; van der Holst, B. Bibcode: 2003AIPC..669..642G Altcode: Equilibrium, waves, and instabilities of tokamaks and accretion disks that are rotating with arbitrary transonic velocities have been solved by means of advanced numerical and analytical techniques. The different transonic flow regimes yield a surprisingly large number of new MHD waves and instabilities that (1) are relevant for turbulent processes in accretion disks, (2) provide a clear correspondence between tokamaks and accretion disk dynamics, with different influence of rotation profiles, gravity, and magnetic pressure, (3) provide a new angle on rapid transition phenomena in transonic MHD flows of rotating astrophysical plasmas. The new angle entails a complete revision of all previously obtained spectral results. The reason is that transonic flows upset the standard theoretical approach to plasma dynamics, consisting of a separate study of the equilibrium state and of the perturbations of this background. We will discuss a new approach to this dichotomy consisting of a study of the similarities of the nonlinear stationary flow patterns and the different linear wave structures that occur when the background speed traverses the full range of critical speeds (from `slow magnetosonic' to `Alfvén' to `fast magnetosonic'). This has required the development of new computational tools that yield the mentioned plethora of new waves and instabilities. Title: Computer simulations of solar plasmas Authors: Goedbloed, J. P.; Keppens, R.; Poedts, S. Bibcode: 2003SSRv..107...63G Altcode: Plasma dynamics has been investigated intensively for toroidal magnetic confinement in tokamaks with the aim to develop a controlled thermonuclear energy source. On the other hand, it is known that more than 90% of visible matter in the universe consists of plasma, so that the discipline of plasma-astrophysics has an enormous scope. Magnetohydrodynamics (MHD) provides a common theoretical description of these two research areas where the hugely different scales do not play a role. It describes the interaction of electrically conducting fluids with magnetic fields that are, in turn, produced by the dynamics of the plasma itself. Since this theory is scale invariant with respect to lengths, times, and magnetic field strengths, for the nonlinear dynamics it makes no difference whether tokamaks, solar coronal magnetic loops, magnetospheres of neutron stars, or galactic plasmas are described. Important is the magnetic geometry determined by the magnetic field lines lying on magnetic surfaces where also the flows are concentrated. Yet, transfer of methods and results obtained in tokamak research to solar coronal plasma dynamics immediately runs into severe problems with trans‘sonic’ (surpassing any one of the three critical MHD speeds) stationary flows. For those flows, the standard paradigm for the analysis of waves and instabilities, viz. a split of the dynamics in equilibrium and perturbations, appears to break down. This problem is resolved by a detailed analysis of the singularities and discontinuities that appear in the trans‘sonic’ transitions, resulting in a unique characterization of the permissible flow regimes. It then becomes possible to initiate MHD spectroscopy of axi-symmetric transonic astrophysical plasmas, like accretion disks or solar magnetic loops, by computing the complete wave and instability spectra by means of the same methods (with unprecedented accuracy) exploited for tokamak plasmas. These large-scale linear programs are executed in tandem with the non-linear (shock-capturing, massively parallel) Versatile Advection Code to describe both the linear and the nonlinear phases of the instabilities. Title: Stability and waves of transonic laboratory and space plasmas Authors: Goedbloed, J. P. Bibcode: 2003SSRv..107..353G Altcode: The properties of magnetohydrodynamic waves and instabilities of laboratory and space plasmas are determined by the overall magnetic confinement geometry and by the detailed distributions of the density, pressure, magnetic field, and background velocity of the plasma. Consequently, measurement of the spectrum of MHD waves (MHD spectroscopy) gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward as well as the inverse spectral problems. This terminology entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in space. Here, helioseismology (which could be considered as one of the forms of MHD spectroscopy) may serve as a luminous example. The required study of magnetohydrodynamic waves and instabilities of both laboratory and space plasmas has been conducted for many years starting from the assumption of static equilibrium. Recently, there is a outburst of interest for plasma states where this assumption is violated. In fusion research, this interest is due to the importance of neutral beam heating and pumped divertor action for the extraction of heat and exhaust needed in future tokamak reactors. Both result in rotation of the plasma with speeds that do not permit the assumption of static equilibrium anymore. In astrophysics, observations in the full range of electromagnetic radiation has revealed the primary importance of plasma flows in such diverse situations as coronal flux tubes, stellar winds, rotating accretion disks, and jets emitted from radio galaxies. These flows have speeds which substantially influence the background stationary equilibrium state, if such a state exists at all. Consequently, it is important to study both the stationary states of magnetized plasmas with flow and the waves and instabilities they exhibit. We will present new results along these lines, extending from the discovery of gaps in the continuous spectrum and low-frequency Alfvén waves driven by rotation to the nonlinear flow patterns that occur when the background speed traverses the full range from sub-slow to super-fast. Title: Waves and Instabilities in Accretion Disks: Magnetohydrodynamic Spectroscopic Analysis Authors: Keppens, R.; Casse, F.; Goedbloed, J. P. Bibcode: 2002ApJ...569L.121K Altcode: 2002astro.ph..3237K A complete analytical and numerical treatment of all magnetohydrodynamic waves and instabilities for radially stratified, magnetized accretion disks is presented. The instabilities are a possible source of anomalous transport. While recovering results on known hydrodynamic and both weak- and strong-field magnetohydrodynamic perturbations, the full magnetohydrodynamic spectra for a realistic accretion disk model demonstrate a much richer variety of instabilities accessible to the plasma than previously realized. We show that both weakly and strongly magnetized accretion disks are prone to strong nonaxisymmetric instabilities. The ability to characterize all waves arising in accretion disks holds great promise for magnetohydrodynamic spectroscopic analysis. Title: Transonic Magnetohydrodynamic Flows in Laboratory and Astrophysical Plasmas Authors: Goedbloed, J. P. Bibcode: 2001PhST...98...43G Altcode: Magnetohydrodynamic (MHD) waves control the dynamics of plasma, the main constituent of the universe. They occur as the natural response to global excitation. Frequency and wave forms are determined by the magnetic confinement geometry and distribution of background equilibrium variables. Hence, measurement of the spectrum of MHD waves gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward and inverse spectral problems. This activity has been called MHD spectroscopy, [1, Goedbloed et al. Phys. Control. Fusion 35 B277 (1993)] in analogy with quantum mechanical spectroscopy which also involves eigenvalue problems of linear operators. The terminology also entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in astrophysics. Title: Magnetohydrodynamic waves in laboratory and astrophysical plasmas Authors: Goedbloed, J. P. Bibcode: 2000AIPC..537..109G Altcode: 2000wdss.conf..109G The study of magnetohydrodynamic waves and instabilities of both laboratory and astrophysical plasmas has been conducted for many years starting from the assumption of static equilibrium. Recently, there is an outburst of interest for plasma states where this assumption is violated. In fusion research, this interest is due to the importance of neutral beam heating and pumped divertor action for the extraction of heat and exhaust needed in future tokamak reactors. Both result in rotation of the plasma with speeds that do not permit the assumption of static equilibrium anymore. In astrophysics, observations in the full range of electromagnetic radiation has revealed the primary importance of plasma flows in such diverse situations as coronal flux tubes, stellar winds, rotating accretion disks, and jets emitted from radio galaxies. These flows have speeds which substantially influence the background stationary equilibrium state, if such a state exists at all. Consequently, it is important to study both the stationary states of magnetized plasmas with flow and the waves and instabilities they exhibit. We will present new results along these lines, extending from the discovery of gaps in the continuous spectrum and low-frequency Alfvén waves driven by rotation to the nonlinear flow patterns that occur when the background speed traverses the full range from sub-slow to super-fast. The solutions obtained may bridge the gap between insights from linear and nonlinear analyses. . Title: Stellar Winds, Dead Zones, and Coronal Mass Ejections Authors: Keppens, R.; Goedbloed, J. P. Bibcode: 2000ApJ...530.1036K Altcode: 1999astro.ph.10152K Axisymmetric stellar wind solutions are presented that were obtained by numerically solving the ideal magnetohydrodynamic (MHD) equations. Stationary solutions are critically analyzed using the knowledge of the flux functions. These flux functions enter in the general variational principle governing all axisymmetric stationary ideal MHD equilibria. The magnetized wind solutions for (differentially) rotating stars contain both a ``wind'' and a ``dead'' zone. We illustrate the influence of the magnetic field topology on the wind acceleration pattern by varying the coronal field strength and the extent of the dead zone. This is evident from the resulting variations in the location and appearance of the critical curves for which the wind speed equals the slow, Alfvén, and fast speed. Larger dead zones cause effective, fairly isotropic acceleration to super-Alfvénic velocities as the polar, open field lines are forced to fan out rapidly with radial distance. A higher field strength moves the Alfvén transition outward. In the ecliptic, the wind outflow is clearly modulated by the extent of the dead zone. The combined effect of a fast stellar rotation and an equatorial dead zone in a bipolar field configuration can lead to efficient thermocentrifugal equatorial winds. Such winds show both a strong poleward collimation and some equatorward streamline bending due to significant toroidal field pressure at midlatitudes. We discuss how coronal mass ejections are then simulated on top of the transonic outflows. Title: Stationary and Time-Dependent MHD Simulations of the Solar Wind Authors: Keppens, R.; Goedbloed, J. P. Bibcode: 1999ESASP.448.1177K Altcode: 1999ESPM....9.1177K; 1999mfsp.conf.1177K No abstract at ADS Title: Numerical simulations of stellar winds: polytropic models Authors: Keppens, R.; Goedbloed, J. P. Bibcode: 1999A&A...343..251K Altcode: 1999astro.ph..1380K We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spherically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arrive at axisymmetric, polytropic, magnetized, rotating models. These represent 2D generalisations of the analytical 1D Weber-Davis wind solution, which we obtain in the process. Axisymmetric wind solutions containing both a `wind' and a `dead' zone are presented. Since we are solving for steady-state solutions, we efficiently exploit fully implicit time stepping. The method allows us to model thermally and/or magneto-centrifugally driven stellar outflows. We particularly emphasize the boundary conditions imposed at the stellar surface. For these axisymmetric, steady-state solutions, we can use the knowledge of the flux functions to verify the physical correctness of the numerical solutions. Title: Growth and saturation of the Kelvin-Helmholtz instability with parallel and antiparallel magnetic fields Authors: Keppens, Rony; Tóth, G.; Westermann, R. H. J.; Goedbloed, J. P. Bibcode: 1999JPlPh..61....1K Altcode: 1999astro.ph..1166K Available from http://journals.cambridge.org/bin/bladerunner?REQUNIQ=1105385252&REQSESS=958582&118000REQEVENT=&REQINT1=18471&REQAUTH=0 Title: Numerical Simulations of Stellar Winds Authors: Keppens, R.; Goedbloed, J. P. Bibcode: 1999SSRv...87..223K Altcode: We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We model thermally and magneto-centrifugally driven stellar outflows as generalizations of the well-known Parker and Weber-Davis wind solutions. To obtain steady-state solutions efficiently, we exploit fully implicit time stepping. Title: Two-dimensional equilibrium in coronal magnetostatic flux tubes: an accurate equilibrium solver Authors: Beliën, A. J. C.; Poedts, S.; Goedbloed, J. P. Bibcode: 1997CoPhC.106...21B Altcode: To study linearized magnetohydrodynamic (MHD) waves, continuous spectra, and instabilities in coronal magnetic flux tubes that are anchored in dense chromospheric and photospheric regions, a two-dimensional numerical code, called PARIS, has been developed. PARIS solves the pertinent nonlinear Grad-Shafranov type, partial differential equation for the magnetic flux on a flux coordinate grid. Both a straight field line coordinate system and an orthogonal flux coordinate system are exploited. Isoparametric bicubic Hermite finite elements have been adopted to solve the Grad-Shafranov-like equation. These elements allow for a continuous representation of the flux and the gradient of the flux throughout the tube and can be aligned conveniently along the boundary of the tube. These properties are important to obtain an accurate representation of the solution on flux coordinate grids. An analytical test case is used to show that accurate solutions have been obtained, even for a small number of grid points. The equilibria calculated by PARIS are used to study the continuous spectra of two-dimensional magnetic flux tubes. One illustrative example is given here; extensive results are presented elsewhere (A.J.C. Beliën, S. Poedts and J.P. Goedbloed, Astron. Astrophys. 322 (1997) 995). The equilibria obtained by PARIS are also well suited to calculate the stability and the normal mode MHD spectrum. Title: Continuous magnetohydrodynamic spectra of two-dimensional coronal magnetostatic flux tubes. Authors: Belieen, A. J. C.; Poedts, S.; Goedbloed, J. P. Bibcode: 1997A&A...322..995B Altcode: In this paper we derive the equations for the continuous ideal magnetohydrodynamic (MHD) spectrum of two-dimensional coronal loops, including gravity and expansion, in general curvilinear coordinates. The equations clearly show the coupling between Alfven and slow magnetosonic continuum waves when both pressure and geodesic curvature of the magnetic field lines are present. Gravity always gives rise to Alfven-slow mode coupling when the magnetic field is twisted. Numerical calculations show that the coupling of Alfven and slow magnetosonic continuum waves can be strong, especially for Alfven-like continuum waves, when the magnetic flux concentration near the bases of flux tubes is taken into account. Amplitude ratios of the parallel and perpendicular displacement components of 0.4 were obtained for concentration of the flux with a factor of 4. Gravity has less effect on the coupling of Alfven and slow magnetosonic continuum waves than the concentration of flux but it has a large influence on the low frequency slow magnetosonic-like continuum branches. Title: Nonlinear MHD Simulations of Wave Dissipation in Flux Tubes Authors: Poedts, S.; Tóth, G.; Beliën, A. J. C.; Goedbloed, J. P. Bibcode: 1997SoPh..172...45P Altcode: 1997ESPM....8...45P The phase mixing and resonant dissipation of Alfvén waves is studied in both the 'closed' magnetic loops and the 'open' coronal holes observed in the hot solar corona. The resulting energy transfer from large to small length scales contributes to the heating of these magnetic structures. The nonlinear simulations show that the periodically varying shear flows that occur in the resonant layers are unstable. In coronal holes, the phase mixing of running Alfvén waves is speeded up by the 'flaring out' of the magnetic field lines in the lower chromosphere. Title: Nonlinear wave heating of solar coronal loops. Authors: Poedts, S.; Goedbloed, J. P. Bibcode: 1997A&A...321..935P Altcode: The heating of magnetically closed structures (loops) in the solar corona by the resonant absorption of incident waves is studied by means of numerical simulations in the framework of nonlinear resistive magnetohydrodynamics (MHD). It is shown that the dynamics in the resonant layer is indeed very nonlinear for typical coronal parameters. The effect of the nonlinearity on the efficiency of the resonant heating mechanism is investigated. It turns out that this heating mechanism may be less efficient than concluded from the linear MHD studies. As a matter of fact, the modification of the background magnetic field results in a shift of the resonance positions in time which in turn yields broader dissipation layers. Title: Critical Issues in Transonic Magnetohydrodynamic Flows Authors: Goedbloed, J. P.; Lifschitz, A. E. Bibcode: 1997ESASP.404..417G Altcode: 1997cswn.conf..417G No abstract at ADS Title: Slow Magnetosonic Waves and Instabilities in Expanded Flux Tubes Anchored in Chromospheric/Photospheric Regions Authors: Beliën, A. J. C.; Poedts, S.; Goedbloed, J. P. Bibcode: 1997ESASP.404..193B Altcode: 1997cswn.conf..193B No abstract at ADS Title: Visualization of resonant absorption in solar coronal loops by simulation of soft X-ray images. Authors: Belien, A. J. C.; Poedts, S.; Spoelder, H. J. W.; Leenders, R.; Goedbloed, J. P. Bibcode: 1996ComPh..10..573B Altcode: 1996CoPhy..10..573B One of the proposed mechanisms to explain the heating of the solar corona is resonant absorption of magnetic Alfven waves. Numerical studies of this mechanism often involve large scale computations and produce large amounts of data that need to be visualized. In this article the authors present a method to visualize numerically calculated density and temperature evolutions of heating calculations by simulating the soft X-ray observations of the soft X-ray telescope aboard the Yohkoh satellite. The visualization method is applied to two different model calculations of the heating of coronal magnetic loops by the resonant absorption of Alfven waves. For these two cases, information on the variations of temperature and density can be extracted conveniently from the generated images. The resulting images reveal features that are characteristic of the resonant absorption process. This suggests that signatures of resonant absorption can be extracted from real soft X-ray observations of coronal loops. Title: Calculation of Soft X-ray Images from MHD Simulations of Heating of Coronal Loops Authors: Belien, A. J. C.; Poedts, S.; Goedbloed, J. P. Bibcode: 1996mpsa.conf..423B Altcode: 1996IAUCo.153..423B No abstract at ADS Title: Symmetry of Magnetohydrodynamic Flows Authors: Goedbloed, J. P.; Lifschitz, A. Bibcode: 1996ApL&C..34..261G Altcode: No abstract at ADS Title: Magnetohydrodynamic Continua and Stratification Induced Alfvén Eigenmodes in Coronal Magnetic Loops Authors: Beliën, A. J. C.; Poedts, S.; Goedbloed, J. P. Bibcode: 1996PhRvL..76..567B Altcode: The continuous spectra of a 2D inhomogeneous, cylindrical magnetic flux tube are studied and applied to solar coronal loops. The density is stratified radially as well as longitudinally, while other equilibrium quantities only vary in the radial direction. Stratification causes gaps to appear in the continuous spectrum, and it is shown that discrete global, stratification-induced Alfvén eigenmodes occur in these gaps. These global modes may be important for the heating of coronal loops. Title: 2D and 3D Nonlinear MHD Simulations of Coronal Loop Heating by Alfven Waves Authors: Poedts, S.; Goedbloed, J. P. Bibcode: 1996mpsa.conf..425P Altcode: 1996IAUCo.153..425P No abstract at ADS Title: Alfven wave heating of coronal loops: photospheric excitation. Authors: Halberstadt, G.; Goedbloed, J. P. Bibcode: 1995A&A...301..559H Altcode: Alfven resonant heating of bounded coronal loops is investigated numerically in a two-dimensional model. A coronal loop is modelled as a cylindrical, magnetized plasma column, that is bounded by the high density photospheric plasma. Alfven wave excitation is assumed to be due to the convective motion of the photosphere. The excitation of coronal loops at the foot points by this photospheric motion, which is not incorporated in most existing models, is the main topic in the work described here. The dynamics of the heating of coronal loops due to the excited Alfven waves is treated by numerically solving the fully resistive linearized equations of magnetohydrodynamics for the described model. In previous work (Goedbloed & Halberstadt 1994), it was shown that pure Alfven and pure fast magnetosonic waves no longer exist in bounded loops. In the present paper the general role of the fast wave component for Alfven heating is investigated. In particular, it is shown that the coupling of Alfven and fast waves gives rise to a new kind of eigenmodes, that consist of a global fast wave contribution and a localized and damped Alfven tail. These waves are efficiently excited by compressional fluid motion, and yield high Ohmic dissipation rates. Title: Alfven heating of line-tied coronal loops. Surface excitation revisited. Authors: Halberstadt, G.; Goedbloed, J. P. Bibcode: 1995A&A...301..577H Altcode: Alfven resonant heating of closed coronal loops is investigated by linear magnetohydrodynamics simulations. The main subject of the presented work is the excitation of waves by the motion of the high density photospheric plasma. In recent two-dimensional calculations, the photospheric energy was introduced directly at the foot points of the loop (Strauss & Lawson 1989; Halberstadt 1994a). This enables the direct excitation of Alfven waves by purely incompressible motion, and a high rate of energy transfer from the photosphere to the dissipative layers is assured. In this paper it is emphasized that a realistic model of loop excitation by convective motion mainly involves plasma compression and therefore the introduced photospheric energy must be transferred across the magnetic field lines to reach the resonant layers. This is simulated by an excitation source which is localized towards the end points of the loop and which has an energy flux in the cross field line direction only. Both the dissipation rate, and the coupling between the source and the loop are investigated. The presence of global modes in the Alfven spectrum simultaneously enhances the coupling and the dissipation rate. An estimate of the attainable X-ray flux is made. Title: Magnetohydrodynamic waves in fusion and astrophysical plasmas. Authors: Goedbloed, J. P. Bibcode: 1995AIPC..345..465G Altcode: Macroscopic plasma dynamics in both controlled thermonuclear confinement machines and in the atmospheres of X-ray emitting stars is described by the equations of magnetohydrodynamics. This provides a vast area of overlapping research activities which is presently actively pursued. In this lecture the author concentrates on some important differences in the dynamics of the two confined plasma systems related to the very different geometries that are encountered and, thus, the role of the different boundary conditions that have to be posed. As a result, the basic MHD waves in a tokamak are quite different from those found in a solar magnetic flux tube. The result is that, whereas the three well-known MHD waves can be traced stepwise in the curved geometry of a tokamak, their separate existence is eliminated right from the start in a line-tied coronal loop because line-tying in general conflicts with the phase relationships between the vector components of the three velocity fields. The consequences are far-reaching, viz. completely different resonant frequencies and continuous spectra, absence of rational magnetic surfaces, and irrelevance of local marginal stability theory for coronal magnetic loops. Title: The Influence of Line-Tying on Coronal Perturbations in a Gravitationally Stratified Equilibrium Authors: van der Linden, R. A. M.; Hood, A. W.; Goedbloed, J. P. Bibcode: 1994SoPh..154...69V Altcode: We study the influence of gravitational stratification of the solar atmosphere on the stability of coronal magnetic structures. In particular we question whether the (presumably stabilizing) influence of the anchoring of the magnetic field lines in the solar photosphere (`line-tying') can be adequately modelled by either `rigid wall' or `flow-through' boundary conditions on the coronal perturbations, as is commonly done. Using the ideal MHD model without gravitational effects,inertial line-tying alone cannot lead to afull stabilization, as marginal stability cannot be crossed by including only the rapid density increase at the photospheric interface. Title: Magnetohydrodynamic waves in coronal flux tubes Authors: Goedbloed, J. P.; Halberstadt, G. Bibcode: 1994A&A...286..275G Altcode: The problem of the basic MHD waves of a coronal flux loop is investigated for the simplest configuration conceivable, viz. a plasma in a rectangular box, with an oblique magnetic field, and line-tied at the ends. The basic waves found are completely different from those found in a periodic box, representative for tokamak plasmas. They consist of an interwoven structure of Alfven and slow components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. The implications for stability are the existence of a global excess of stability in coronal loops, as opposed to local marginal stability at rational magnetic surfaces in tokamaks. The relationship to flares is pointed out. Pure Alfven and pure slow modes are only found as singular limiting cases of cluster spectra of Alfven-fast or slow-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfven wave heating. The waves consist of large amplitude Alfven components in the corona and fast components with a small but rapidly varying amplitude in the photospheric boundary layer, so that they appear to have all the right characteristics for effective transfer of energy from the photosphere to the corona. Title: On the Quality of Resonant Absorption as a Coronal Loop Heating Mechanism Authors: Poedts, S.; Belien, A. J. C.; Goedbloed, J. P. Bibcode: 1994SoPh..151..271P Altcode: The qualityQ of a resonance is defined as the ratio of the total energy contained in the system to the dissipation per driving cycle. Hence, a `good quality' resonance is one with little losses, i.e., little dissipation per driving cycle. However, for heating coronal plasmas by means of resonant absorption of waves, `bad' quality resonances are required. Here, the quality of the MHD resonances that occur when an inhomogeneous coronal loop is excited by incident waves is investigated for typical coronal loop parameter values in the frame work of linear, resistive MHD. It is shown that the resonances in coronal loops have bad quality and, hence, yield a lot of Ohmic heating per driving cycle compared to the total energy stored in the loop. As a consequence, the time scales of the heating process are relatively short and resonant absorption turns out to be a viable candidate for the heating of the magnetic loops observed in the solar corona. Title: 3D nonlinear wave heating of coronal loops Authors: Poedts, S.; Goedbloed, J. P. Bibcode: 1994SSRv...68..103P Altcode: The heating of solar coronal loops by the resonant absorption or phase-mixing of incident wave energy is investigated in the framework of 3D nonlinear magnetohydrodynamics (MHD) by means of numerical simulations. Title: MHD waves in coronal flux tubes Authors: Goedbloed, J. P.; Halberstadt, G. Bibcode: 1994SSRv...68..121G Altcode: The basic MHD waves of a coronal flux loop are investigated for the rectangular box model of a plasma with oblique magnetic field and line-tied at the ends. The waves found are completely different from those in a periodic box, representative for tokamaks. They consist of a mixture of Alfvén components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. Pure Alfvén modes are only found as singular limiting cases of cluster spectra of Alfvén-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfvén wave heating. The waves consist of large amplitude Alfvén components in the corona and fast components with a small but rapidly varying amplitude in the boundary layer, so that they appear to have the right signature for effective transfer of energy from the photosphere to the corona. Title: Nonlinear wave heating of the solar corona Authors: Poedts, S.; Goedbloed, J. P. Bibcode: 1994smf..conf..396P Altcode: No abstract at ADS Title: The continuous ALfven spectrum of line-tied coronal loops Authors: Halberstadt, G.; Goedbloed, J. P. Bibcode: 1993A&A...280..647H Altcode: The effect of the photospheric boundary conditions on Alfven continuum waves in coronal magnetic loops is considered. A coronal loop is modeled as effectively line-tied to the photospheric plasma, such that the foot points of the loop are forced to follow the photospheric velocity perturbations. Starting from recent work on the nature of magnetohydrodynamic (MHD) waves in line-tied magnetic loops (Goedbloed & Halberstadt 1993), we derive an expression for the Alfven continuum frequencies in a line-tied cylindrical plasma, which reveals that the line-tied Alfven continuum no longer depends on the poloidal magnetic field and that the corresponding eigenmodes have a global ballooning character. Subsequently, we derive a variational principle by which the Alfven and slow continuum frequencies in a line-tied cylinder with density variation along the field lines can be obtained. It is shown that the line-tied Alfven continuum determines the coronal heating due to resonant absorption in coronal loops that are excited at the foot points. Title: Resonant Heating of Line-Tied Coronal Loops Authors: Halberstadt, G.; Goedbloed, J. P. Bibcode: 1993ASSL..183..583H Altcode: 1993pssc.symp..583H No abstract at ADS Title: Coronal heating: the role of resonant absorption. Authors: Poedts, Stefaan; Goedbloed, J. P. Bibcode: 1992ESASP.348..253P Altcode: 1992cscl.work..253P The efficiency and time scales of Alfvén wave heating of solar coronal loops is investigated by means of numerical simulations in the framework of both linear and nonlinear dissipative magnetohydrodynamics. The coronal loops are modeled by cylindrical plasma columns that are excited by waves that are incident on them. Parameter studies are presented of the efficiency of the coupling of the external source to the coronal loop plasma, the fraction of the power supplied by the external source that is actually absorbed and converted into heat, the quality of the resonances that occur, the basic time scales of the resonant absorption mechanism, and the temporal evolution of the energetics of the driven dissipative system. The results of these investigations indicate that resonant absorption is a viable heating mechanism for solar coronal loops. Title: Line-Tying Effects on Stability and Heating of Solar Coronal Loops (With 2 Figures) Authors: Halberstadt, G.; Goedbloed, J. P.; Poedts, S. M.; van der Linden, R. A. M. Bibcode: 1991mcch.conf..489H Altcode: No abstract at ADS Title: Stability of solar coronal loops Authors: Goedbloed, J. P. Bibcode: 1990CoPhC..59...39G Altcode: The equations of magnetohydrodynamics do not contain an intrinsic length scale determining the size of phenomena. Hence, size only enters through the external geometrical properties of the configurations considered. This is one of the reasons why tokamaks and solar coronal loops may be considered as similar objects. The equations of MHD do not distinguish between the two. It is only the geometry and, hence, the boundary conditions that discriminate between them. Whereas for tokamaks toroidal periodicity and normal confinement provide the appropriate boundary conditions, for coronal loops line-tying at the photosphere and some prescription for the behavior across the ``edge'' of the loop determine the solutions. The latter is a more complicated problem and gives rise to even more complex dynamics than encountered in tokamaks. Here, we consider the influence of the two mentioned groups of boundary conditions for the problem of the stability and disruption of a solar coronal loop.

We consider the stability properties of a single loop with twisted magnetic field lines under the simultaneous influence of photospheric line-tying and constraining by neighboring flux loops. The loops would be violently unstable without these two ingredients (i.e. for the corresponding tokamak problem). It is shown that line-tying alone in not sufficient for stability, but the neighboring flux tubes provide a normal boundary condition similar to a conducting shell in tokamaks. This stabilization gets lost on the time scale associated with reconnection of the tangetial magnetic field discontinuities present in the many-loop system. On this time scale the magnetic energy, which has been built up during the twisting of the field lines, gets released, resulting in a disruption of the loop. This process may be considered as the single loop variant of Parker's solar flare model. Title: Kink modes in coronal loops. Authors: Goedbloed, J. P.; Goossens, M.; Poedts, S. Bibcode: 1989plap.work..103G Altcode: Spectral theory of magnetohydrodynamic waves and instabilities has been extensively developed. With proper modifications results obtained for tokamaks can be transferred to the study of stability of coronal flux loops and heating of the corona by means of Alfvén waves. In tokamaks external kink modes are stabilized by the geometric constraint that the modes should fit into the torus. In current-carrying coronal loops the opposite problem arises, viz. the apparent absence of external kink modes, as evidenced by their long life-time, spanning many orders of magnitude of the characteristic growth-time of these instabilities. Anchoring of the foot points of the field lines in the photosphere is generally considered to be the responsible agent for stabilization. Given the overall MHD stability of a coronal magnetic loop structure, the subtle analysis of Alfvén wave heating by means of the continuous spectrum may be undertaken. Here, an additional complication is encountered which turns out to be quite beneficial though from the point of view of heating efficiency. This gives rise to improper modes which have both a global character and a non-integrable part which admits quasi-dissipation. Title: Stabilization of external kink modes by means of a limiter Authors: Freidberg, J. P.; Goedbloed, J. P.; Rohatgi, R. Bibcode: 1983PhRvL..51.2105F Altcode: It is shown that poloidal ring limiters are very effective in stabilizing ideal external kink modes in a tokamak. With one poloidal limiter all external modes are stable for qa>1. However, toroidal limiters have negligible influence on stability. Reversed-field pinches require a finite number of poloidal limiters (typically six) to stabilize the strong external kink modes that would result if the conducting wall were removed. Title: Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields. II. Linear pinch. Authors: Goedbloed, J. P. Bibcode: 1971Phy....53..501G Altcode: The marginal-stability analysis, developed in a previous paper 1), is applied to the stability problem of a linear pinch with a distributed current. Complete stability criteria are derived from the marginal equation of motion and it is shown that this method is equivalent to the application of the energy principle. For a sharp-pinch model of a dense plasma surrounded by a force-free magnetic field of constant α kinks, unstable modes of the surface-layer, and of the force-free region are shown to be absent if α is properly chosen. Explicit expressions for the growth rates of unstable configurations are derived. An appendix is devoted to the stability with respect to resistive tearing modes. Title: Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields. I. Plane plasma layer. Authors: Goedbloed, J. P. Bibcode: 1971Phy....53..412G Altcode: A marginal-stability analysis is applied to the stability problem of a plane plasma layer under the influence of gravity. Complete stability criteria are derived from the marginal equation of motion and it is shown that this method is equivalent to the application of the energy principle. Ideal magnetohydrodynamic instabilities, as occurring in simple plasma-vacuum systems, can be suppressed by replacing the vacuum by a force-free magnetic field, that is a field satisfying the relation ∇ × B = α B. Force-free fields of constant α are investigated in particular. By proper choice of α the gravitational instabilities, of nonlocal and of surface-layer type, are absent in a plane plasma layer supported from below by a horizontal force-free magnetic field. An appendix is devoted to a rigorous treatment of the influence of singular points of the marginal equation of motion on the stability analysis. Title: Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields. III: Shearless magnetic fields. Authors: Goedbloed, J. P. Bibcode: 1971Phy....53..535G Altcode: The marginal-stability analysis, as given in two previous papers, is further elaborated for magnetic fields of constant direction in the plane case and for magnetic fields of constant pitch in the cylindrical case. For these shearless magnetic fields discontinuities arise in the stability criteria. The physical significance of these discontinuities is discussed. From the marginal-stability analysis the principle of exchange of stabilities is derived. This theory is applied to constant-pitch magnetic fields, which are shown to be necessarily unstable. Growth rates of the instabilities of these fields are calculated, correcting earlier results of Ware. Simple modifications of some constant-pitch models, namely Van der Laan's model of a constant-pitch force-free field and Alfvén's model of a constant-pitch field with parabolic pressure profile, prove to yield completely stable pinch configurations of a sharp or diffuse kind. An appendix is devoted to toroidal effects.