The thermal continuum in coronal loops: Instability criteria and the influence of perpendicular thermal conduction

The linear MHD spectrum is investigated for cylindrical equilibrium models under typical coronal conditions. Non-ideal effects are included and attention is focussed on the thermal instability and the influence of perpendicular thermal conduction. It is shown that, when thermal conduction across magnetic field lines is neglected, the classic Alfvén and slow continua are supplemented by a new thermal continuum. Surprisingly, the existence of this non-ideal continuous spectrum appears to have been overlooked for a very long time. Unlike the (still purely oscillatory) Alfvén continuum modes and the slow continuum modes (overstable or damped), the thermal continuum modes are exponentially growing or decaying in time. As with the Alfvén and slow continua, discrete modes may be present above or below the thermal continuum, depending upon the choice of equilibrium parameters. These modes are localized using a simple WKB approach. The knowledge of the thermal subspectrum is then exploited to find necessary and sufficient conditions for instability.The inclusion of perpendicular thermal conduction eliminates this thermal continuum, but replaces it by a dense set of eigenmodes located at the same values of the growth rate. It is shown that perpendicular thermal conduction has no significant influence on the thermal stability of the equilibrium, though individual modes may be strongly influenced. The corresponding eigenfunctions still have a nearly-singular behaviour, but in addition they may contain a rapid spatial oscillation on a scale proportional to some power of the perpendicular thermal conduction coefficient. This rapid oscillation is confined to the most unstable part of the equilibrium and may be of relevance for the formation of fine-scale structure (threads) in prominences.Research Assistant of the National Fund for Scientific Research (Belgium).     

Formation of fluctuations in a molecular slab via isobaric thermal instability

Frictional heating by the ion-neutral drift is calculated and its effect on the isobaric thermal instability is studied. Ambipolar drift heating of a one-dimensional self-gravitating magnetized molecular slab is used under the assumptions of quasi-magnetohydrostatic and local ionization equilibrium. We see that ambipolar drift heating is inversely proportional to density and its value in some regions of the slab can be significantly larger than the average heating rates of cosmic rays and turbulent motions. The results show that isobaric thermal instability can occur in some regions of the slab, and thus it may produce slab fragmentation and formation of astronomical unit scale condensations.     

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.     

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.     

Simulation of the Magnetothermal Instability

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (∂ P/∂z) (∂ ln T/∂ z) > 0, which we refer to as the Balbus criterion. We refer to the convective-type instability that results as the magnetothermal instability (MTI). We use the equations of MHD with anisotropic electron heat conduction to numerically simulate the linear growth and nonlinear saturation of the MTI in plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured from the simulations are in excellent agreement with the weak field dispersion relation. The addition of isotropic conduction, e.g. radiation, or strong magnetic fields can damp the growth of the MTI and affect the nonlinear regime. The instability saturates when the atmosphere becomes isothermal as the source of free energy is exhausted. By maintaining a fixed temperature difference between the top and bottom boundaries of the simulation domain, sustained convective turbulence can be driven. MTI-stable layers introduced by isotropic conduction are used to prevent the formation of unresolved, thermal boundary layers. We find that the largest component of the time-averaged heat flux is due to advective motions as opposed to the actual thermal conduction itself. Finally, we explore the implications of this instability for a variety of astrophysical systems, such as neutron stars, the hot intracluster medium of galaxy clusters, and the structure of radiatively inefficient accretion flows. J. M. Stone: Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544     

The formation of solar prominences by thermal instability in a current sheet

The energy balance equation for the upper chromosphere or lower corona contains a radiative loss term which is destabilizing, because a slight decrease in temperature from the equilibrium value causes more radiation and hence a cooling of the plasma; also a slight increase in temperature has the effect of heating the plasma. In spite of this tendency towards thermal instability, most of the solar atmosphere is remarkably stable, since thermal conduction is very efficient at equalizing any temperature irregularity which may arise. However, the effectiveness of thermal conduction in transporting heat is decreased considerably in a current sheet or a magnetic flux tube, since heat can be conducted quickly only along the magnetic field lines. This paper presents a simple model for the thermal equilibrium and stability of a current sheet. It is found that, when its length exceeds a certain maximum value, no equilibrium is possible and the plasma in the sheet cools. The results may be relevant for the formation of a quiescent prominence.     

Attenuation of small-amplitude oscillations in a prominence–corona model with a transverse magnetic field

Observations show that small-amplitude prominence oscillations are usually damped after a few periods. This phenomenon has been theoretically investigated in terms of non-ideal magnetoacoustic waves, non-adiabatic effects being the best candidates to explain the damping in the case of slow modes. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The magnetohydrodynamic equations are considered in their linearised form and terms representing thermal conduction, radiation and heating are included in the energy equation. The differential equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes.     

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.     

Turbulent transport and heating in the auroral plasma of the topside ionosphere

Using plasma parameters from a typical stormtime ionospheric energy balance model, we have investigated the effects of plasma turbulence on the auroral magnetoplasma. The turbulence is assumed to be comprised of electrostatic ion cyclotron waves. These waves have been driven to a nonthermal level by a geomagnetic field-aligned, current-driven instability. The evolution of this instability is shown to proceed in two stages and indicates an anomalous increase in field-aligned electrical resistivity and cross-field ion thermal conductivity as well as a decrease in electron thermal conductivity along the geomagnetic field. In addition, this turbulence heats ions perpendicular to the geomagnetic field and hence leads to a significant ion temperature anisotropy.     

Dissipation of an electron phase-space hole and its consequence on electron heating

An electron phase-space hole (electron hole) is considered to be unstable to the transverse instability. In this paper, two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations are used to explore the dissipation process of a one-dimensional (1D) electron hole in a weakly magnetized plasma and its consequence on electron heating, which consists of two stages. In the first stage, the electron hole is still kept as a quasi-1D structure, however, with the excitation of the transverse instability and the generation of the perpendicular electric field, the electrons are scattered and then heated along the perpendicular direction in the electron hole. In the second stage, the quasi-1D electron hole is broken into several 2D electron holes. The temperature of the electrons outside of these 2D electron holes also increase, and at last the velocity distribution of the electrons become almost isotropic in the whole simulation domain. Our results provide a new dissipation mechanism of an electron hole.     

The stability of electron beams in the flaring solar corona

The conditions required for the stability of a steady-state electron beam propagating in the solar corona are determined using the quasi-linear theory. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution function being given by an analytic solution of the linearized Fokker-Planck equation. It is shown that, when the gyrofrequency is less than the plasma frequency, the instability has a narrow angular range, with the maximum growth rate occuring along the magnetic field. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of the results for alternative models of hard X-ray bursts are discussed and it is argued that Langmuir instability will not occur on either the trap model or the thermal model. Such models would, therefore, be refuted by the detection of a large flux of plasma microwave radiation associated with hard X-ray emission.     

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.     

Magnetic and boundary effects on thermal instabilities in solar magnetic fields: Localized modes in a slab geometry

The coupling of thermal and ideal MHD effects in a sheared magnetic field is investigated. A slab geometry is considered so that the Alfvén mode can be decoupled from the system. With the total perturbed pressure approximately zero, the fast mode is eliminated and a system of linearized equations describing magnetic effects on the slow mode and thermal mode is derived. These modes evolve independently on individual fieldlines. One of the main features of this approach is that the influence of the dense photosphere can be included. A variety of different conditions that simulate the photospheric boundary are presented and the different results are discussed. A choice of field geometry and boundary conditions is made which removes mode rational surfaces so that there are no regions in which parallel thermal conduction can be neglected. This provides a stabilizing mechanism for the thermal mode. Growth rates are reduced by 30–40% and there is complete stabilization for sufficiently short fieldlines. The influence of dynamic and thermal boundary conditions on the formation of prominences is discussed.     

Growing electrostatic modes in the isothermal pair plasma of the pulsar magnetosphere

It is shown that a strongly magnetized isothermal pair plasma near the surface of a pulsar supports low-frequency (in comparison to electron cyclotron frequency) toroidal electrostatic plasma modes in the equatorial region. Physically, the thermal pressure coupled with the magnetic pressure creates the low frequency oscillations which may grow for particular case of inhomogeneities of the equilibrium magnetic field and the pair plasma density.     

Electron-acoustic instability driven by a crossfield hot electron-beam

On the basis of kinetic theory, the electron-acoustic instability is studied in a three component plasma consisting of a hot electron-beam and stationary cool electrons and ions. The transformation of the instability into the modified two-stream instability for wave propagation oblique to the confining magnetic field is also investigated. In our model both the electrons and ions are magnetized, with the beam drifting across the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is examined. In addition, we investigate the effect of anisotropies in the velocity distributions of the hot electron-beam and the cool electrons on the instability growth rate.     

Alfvénic drift Kelvin-Helmholtz instability in the presence of an equilibrium electric field

Alfvénic drift Kelvin-Helmholtz instability is discussed in the presence of equilibrium electric and magnetic fields which are perpendicular to each other. A dispersion relation is achieved with the help of WKB approximation and the instability criterion is established. A comparison is made with the previous studies and it is shown that the electric field has a stabilizing or destabilizing effect on the system according to the conditions discussed in the text.     

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.     

Radiation spectrum of a magnetized supercritical accretion disc with thermal conduction

we examine the effect of thermal conduction on the observational properties of a super critical hot magnetized flow. We obtained self-similar solution of a magnetized disc when the thermal conduction plays an important role. Follow of our first paper (Ghasemnezhad et al. in Astrophys. J. 750, 2012 (hereafter GKA12)) we have extended our solution on the observational appearance of the disc to show how physical condition such as thermal conduction, viscosity, and advection will change the observed luminosity of the disc, Continuous spectra and surface temperature of such discs was plotted. We apply the present model to black-hole X-ray binary LMC X-3 and narrow-line seyfert 1 galaxies, which are supposed to be under critical accretion rate. Our results show clearly that the surface temperature is strongly depends on the thermal conduction, the magnetic field and advection parameter. However we see that thermal conduction acts to oppose the temperature gradient as we expect and observed luminosity of the disc will reduce when thermal conduction is high. We have shown that in this model the spectra of critical accretion flows strongly depends on the inclination angle.     

Gravitational instability in isotropic MHD plasma waves

The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.     

Large-scale zonal flow and magnetic field generation due to drift-Alfven turbulence in ionosphere plasma

In the present work, the generation of large-scale zonal flows and magnetic field by short-scale collision-less electron skin depth order drift-Alfven turbulence in the ionosphere is investigated. The self-consistent system of two model nonlinear equations, describing the dynamics of wave structures with characteristic scales till to the skin value, is obtained. Evolution equations for the shear flows and the magnetic field is obtained by means of the averaging of model equations for the fast-high-frequency and small-scale fluctuations. It is shown that the large-scale disturbances of plasma motion and magnetic field are spontaneously generated by small-scale drift-Alfven wave turbulence through the nonlinear action of the stresses of Reynolds and Maxwell. Positive feedback in the system is achieved via modulation of the skin size drift-Alfven waves by the large-scale zonal flow and/or by the excited large-scale magnetic field. As a result, the propagation of small-scale wave packets in the ionospheric medium is accompanied by low-frequency, long-wave disturbances generated by parametric instability. Two regimes of this instability, resonance kinetic and hydrodynamic ones, are studied. The increments of the corresponding instabilities are also found. The conditions for the instability development and possibility of the generation of large-scale structures are determined. The nonlinear increment of this interaction substantially depends on the wave vector of Alfven pumping and on the characteristic scale of the generated zonal structures. This means that the instability pumps the energy of primarily small-scale Alfven waves into that of the large-scale zonal structures which is typical for an inverse turbulent cascade. The increment of energy pumping into the large-scale region noticeably depends also on the width of the pumping wave spectrum and with an increase of the width of the initial wave spectrum the instability can be suppressed. It is assumed that the investigated mechanism can refer directly to the generation of mean flow in the atmosphere of the rotating planets and the magnetized plasma.