A formulation of non-ideal localized (or ballooning) modes in the solar corona

The stability equations for localized (or ballooning) modes in the solar atmosphere are formulated. Dissipation due to viscosity, resistivity, and thermal conduction are included using the general forms due to Braginskii (1965). In addition, the effect of gravity, plasma radiation, and coronal heating are included. The resulting equations are one-dimensional and only involve derivatives along the equilibrium magnetic field. Thus, the stabilising influence of photospheric line-tying, which is normally neglected in most numerical simulations, can be studied in a simple manner. Two applications to sound wave propagation and thermal instabilities in a low-beta plasma are considered with a view to determining realistic coronal boundary conditions that model the lower, denser levels of the solar atmosphere in a simple manner.Research Assistant of the Belgian National Fund for Scientific Research.     

Resistive ballooning line-tied boundary conditions

Ideal and resistive ballooning modes are investigated for different ratios of a two-layer stratified density region representing a model for the photospheric/coronal boundary. Construction of the ballooning equations using a WKB approach is justified by comparison between the values of the growth rate obtained using Hain-Lüst and ballooning equations together with a WKB integral relation. Different values of the density ratio, radius, and resistivity are considered. Sausage-type and kink-type instabilities are found. One of these, depending on the value of r remained unstable for large density ratios. The other instability tended to marginal stability as the density ratio was increased, and allowed parallel and perpendicular flows across the boundary. This is contrary to the predictions of both the rigid-wall and flow-through conditions.     

Effect of rotation and self-gravity on the propagation of MHD waves

Magnetohydrodynamics waves and instabilities in rotating, self-gravitating, anisotropic and collision-less plasma were investigated. The general dispersion relation was obtained using standard mode analysis by constructing the linearized set of equations. The wave mode solutions and stability properties of the dispersion relations are discussed in the propagations transverse and parallel to the magnetic field. These special cases are discussed considering the axis of rotation to be in transverse and along the magnetic field. In the case of propagation transverse to the magnetic field with axis of rotation parallel to the magnetic field, we derived the dispersion relation modified by rotation and self-gravitation. In the case of propagation parallel to the magnetic field with axis of rotation perpendicular to the magnetic field, we obtained two separate modes affected by rotation and self-gravitation. This indicates that the Slow mode and fire hose instability are not affected by rotation. Numerical analysis was performed for oblique propagation to show the effect of rotation and self-gravitation. It is found that rotation has an effect of reducing the value of the phase speeds on the fast and Alfven wave modes, but self-gravitation affect only on the Slow modes, thereby reducing the phase speed compare to the ideal magneto hydrodynamic (MHD) case.     

The visco-resistive stability of arcades in the corona of the Sun

The stability of ballooning modes in coronal arcades is studied using linear visco-resistive MHD. Rigid wall conditions are adopted for modelling the photospheric line-tying of the magnetic field. The full Braginskii viscosity stress tensor is used and particular attention is given to the effect of the viscosity coefficient ₃ which was left out of an earlier investigation by Van der Linden, Goossens, and Hood (1987, 1988). The numerical results for shearless arcades show that the coefficient ₃ has a stabilizing effect. However, for realistic values of the equilibrium quantities the stabilizing effect by ₃ can be neglected in comparison with the strong stabilizing effect of the perpendicular viscosity. The effect of magnetic field strength and mode number on stability are determined. In particular it is found that there exists a critical field strength for every mode number such that the mode is stable for weaker fields and unstable for stronger fields.     

The relevance of the ballooning approximation for magnetic,thermal, and coalesced magnetothermal instabilities

Approximate solutions of the linearized non-adiabatic MHD equations, obtained using the ballooning method, are compared with exact numerical solutions of the full equations (including the effects of optically thin plasma radiation). It is shown that the standard ballooning method, developed within the framework of ideal linear MHD, can be generalized to non-ideal linear MHD. The localized (ballooning) spectrum has to be used with caution, but can give valuable (though limited) information on non-ideal stability.The numerical analysis also confirms and quantifies the interesting connection between magnetic and thermal instabilities. The existence of such a coupling is inherent in many qualitative discussions of magnetic disruptions. Finally, the hitherto unrecognized role of the thermal continuum in the unstable part of the magnetothermal spectrum is investigated.Research Assistant of the National Fund for Scientific Research, Belgium.     

Saturated magnetic field amplification at supernova shocks

Cosmic ray streaming instabilities at supernova shocks are discussed in the quasi-linear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the non-resonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear growth rate is calculated using kinetic theory for a streaming distribution. We show that the non-resonant instability is actually driven by a compensating current in the background plasma. The non-resonant instability can develop into a non-linear regime generating turbulence. The saturation of the amplified magnetic fields due to particle diffusion in the turbulence is derived analytically. It is shown that the evolution of parallel and perpendicular cosmic ray pressures is predominantly determined by non-resonant diffusion. However, the saturation is determined by resonant diffusion which tends to reduce the streaming motion through pitch angle scattering. The saturated level can exceed the mean background magnetic field.     

Magnetogravitational instability of an infinite homogeneous rotating plasma through a porous medium with finite electrical and thermal conductivities

The gravitational instability of an infinite homogenous rotating plasma through a porous medium in the presence of a uniform magnetic field with finite electrical and thermal conductivities has been studied. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained, which is further reduced for the special cases of rotation, parallel and perpendicular to the megnetic field acting in the vertical direction. Longitudinal and transverse modes of propagation are discussed separately. It is found that the joint effect of various parameters is simply to modify the Jeans's condition of instability. The effect of finite electrical conductivity is to remove the effect of magnetic field where as the effect of thermal conductivity is to replace the adiabatic velocity of sound by the isothermal one. Rotation has its effect only along the magnetic field in the transverse mode of propagation for an inviscid plasma, thereby stabilizing the system. Porosity reduces the effect of both, the magnetic field and the rotation, in the transverse mode of propagation in both the cases of rotation. The effect of viscosity is to remove the rotational effects parallel to the magnetic field in the transverse mode of propagation.     

Counterstreaming magnetized plasmas with kappa distributions – II. Perpendicular wave propagation

The analysis of the stability and the dispersion properties of a counterstreaming plasma system with kappa distributions are extended here with the investigation of perpendicular instabilities. Purely growing filamentation (Weibel-like) modes propagating perpendicular to the background magnetic field can be excited in streaming plasmas with or without an excess of parallel temperature. In this case, however, the effect of suprathermal tails of kappa populations is opposite to that obtained for parallel waves: the growth rates can be higher and the instability faster than for Maxwellian plasmas. The unstable wavenumbers also extend to a markedly larger broadband making this instability more likely to occur in space plasmas with anisotropic distributions of kappa-type. The filamentation instability of counterstreaming magnetized plasmas could provide a plausible mechanism for the origin of two-dimensional transverse magnetic fluctuations detected at different altitudes in the solar wind.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

修正的粘滞律及有磁吸积盘的稳定性研究

本文采用修正的粘滞定律及磁流体力学研究了薄吸积盘内区及外区的稳定性问题。运用微扰方法导出了色散方程，分析了四种情况下吸积盘的不稳定性，结果表明：在同时考虑磁场和修正的粘滞律时，吸积盘中存在着三种振荡模式，其中粘滞模式总是稳定的，磁声速模式（包括向里、向外传播两种模式）通常是不稳定的。这些结果为解释ＢＬ Ｌａｃ天体、Ｓｅｙｆｅｒｔ星系、类星体等活动星系核的光变现象提供了理论依据。     

Effect of thermal conductivity on the gravitational instability of a magnetized rotating plasma through a porous medium in the presence of suspended particles

The self-gravitational instability of an ionized, thermally-conducting, magnetized, rotating plasma flow through a porous medium has been studied in the presence of suspended particles. The ionized gas-particle medium has been considered rotating along and perpendicular to the vertical magnetic field. Propagation of the plasma waves has been studied for the longitudinal and the transverse modes for both the cases of rotation. A general dispersion relation has been derived with the help of relevant perturbation equations, using the method of normal mode analysis. The Jeans criterion determines the condition of gravitational instability in all the cases with some modifications introduced by the various parameters considered. Thermal conductivity replaces the adiabatic sonic speed by the isothermal one. Considering the longitudinal mode of propagation with perpendicular rotational axis, for an inviscid plasma with adiabatic behaviour the effect of both, the rotation and the suspended particles has been removed by the magnetic field. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the viscosity removes the effect of both, the rotation and the suspended particles. Porosity reduces the effect of both, the rotation and the magnetic field, whereas the concentration of the suspended particles reduces the rotational effect.     

Magnetohydrodynamic instabilities and turbulence in accretion disks

In this paper we review the possibilities for magnetohydrodynamic processes to handle the angular momentum transport in accretion disks. Traditionally the angular momentum transport has been considered to be the result of turbulent viscosity in the disk, although the Keplerian flow in accretion disks is linearly stable towards hydrodynamic perturbations. It is on the other hand linearly unstable to some magnetohydrodynamic (MHD) instabilities. The most important instabilities are the Parker and Balbus-Hawley instabilities that are related to the magnetic buoyancy and the shear flow, respectively. We discuss these instabilities not only in the traditional MHD framework, but also in the context of slender flux tubes, that reduce the complexity of the problem while keeping most of the stability properties of the complete problem. In the non-linear regime the instabilities produce turbulence. Recent numerical simulations describe the generation of magnetic fields by a dynamo in the resulting turbulent flow. Eventually such a dynamo may generate a global magnetic field in the disk. The relation of the MHD-turbulence to observations of accretion disks is still obscure. It is commonly believed that magnetic fields can be highly efficient in transporting the angular momentum, but emission lines, short-time scale variability and non-thermal radiation, which a stellar astronomer would take as signs of magnetic variability, are more commonly observed during periods of low accretion rates. Received October 12, 1995 / Accepted November 16, 1995     

Thermal stability of a corona heated by fast mode waves

It has been proposed that dissipation of hydromagnetic waves is an important heat source for the solar corona. We consider damping by collisionless processes and by electron thermal conduction and ion viscosity, and calculate the wave energy density such that heating balances the energy radiated by the plasma. We then analyze the thermal stability of the wave heated medium. The fastest growing instabilities are condensations perpendicular to the fieldlines. The instability may be important for producing coronal fine structure, and in loops and streamers.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magneto-gravitational instability of a fluid through porous medium including finite ion Larmor radius

The magneto-gravitational instability of an infinite, homogenous, and infinitely conducting plasma flowing through a porous medium is studied. The finite ion Larmor radius (FLR) effects and viscosity are also incorporated in the analysis. The prevalent magnetic field is assumed to be uniform and acting in the vertical direction. A general dispersion relation has been obtained from the relevant linearized perturbation equations of the problem. The wave propagation parallel and perpendicular to the direction of the magnetic field have been discussed. It is found that the condition of the instability is determined by the Jeans criterion for a self-gravitating, infinitely conducting, magnetized fluid through a porous medium. Furthermore, for transverse perturbation FLR is found to have stabilizing influence when the medium is considered inviscid.     

Limits for the Firehose Instability in Space Plasmas

Electromagnetic instabilities in high-β plasmas, where β is the ratio of the kinetic plasma energy to the magnetic energy, have a broad range of astrophysical applications. The presence of temperature anisotropies T _∥ /T _⊥ >1 (where ∥ and ⊥ denote directions relative to the background magnetic field) in solar flares and the solar wind is sustained by the observations and robust acceleration mechanisms that heat plasma particles in the parallel direction. The surplus of parallel kinetic energy can excite either the Weibel-like instability (WI) of the ordinary mode perpendicular to the magnetic field or the firehose instability (FHI) of the circularly polarized waves at parallel propagation. The interplay of these two instabilities is examined. The growth rates and the thresholds provided by the kinetic Vlasov – Maxwell theory are compared. The WI is the fastest growing one with a growth rate that is several orders of magnitude larger than that of the FHI. These instabilities are however inhibited by the ambient magnetic field by introducing a temperature anisotropy threshold. The WI admits a larger anisotropy threshold, so that, under this threshold, the FHI remains the principal mechanism of relaxation. The criteria provided here by describing the interplay of the WI and FHI are relevant for the existence of these two instabilities in any space plasma system characterized by an excess of parallel kinetic energy.     

Radiative and reconnection instabilities: Compressible and viscous effects

Filaments and flares are prominent indicators of the magnetic fields of solar activity. These instability phenomena arise from the influence of weak transport effects (radiation and resistivity, respectively) on coronal magnetodynamics and energy flow. We have previously shown that the filament and flare (tearing or reconnection) mechanisms are resistively coupled in sheared magnetic fields of the kind existing in active regions. The present paper expands this treatment to include the effects of compressibility and viscosity, which are most prominent at short wavelengths. The results show that compressibility affects the radiative mode, including a modest increase of its growth rate, and that viscosity modifies the tearing mode, partially through a decrease of its growth rate. A comprehensive discussion of the mode structures and flows is presented. The strongest effect found is a reversal, at very long wavelengths, of the radiative cooling of the resistive interior layer of the tearing mode, caused by compressional heating.     

Effect of rotation and finite Larmor radius on magneto-gravitational instability of Hall plasma in the presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetized Hall plasma is considered with the inclusion of finite Larmor radius corrections and the effect of suspended particles. A general dispersion relation is obtained from the linearized set of equations. The particular cases of the effect of rotation along and perpendicular to the direction of the magnetic field are considered. The effects of Hall current, finite Larmor radius, and suspended particles on the waves propagated parallel and perpendicular to the uniform magnetic field are investigated along with the uniform rotation of the medium. It is found that in the presence of suspended particles, magnetic field, Hall current, rotation and finite Larmor radius, the Jeans criterion determines the condition of gravitational instability of a gas-particle medium.