MHD waves and instabilities of a temperature-anisotropic plasma in the solar corona as a source of its heating

The MHD instabilities of a temperature-anisotropic coronal plasma are considered. We show that aperiodic mirror instabilities of slow MHD waves can develop under solar coronal conditions for weak magnetic fields (B < 1 G) and periodic ion-acoustic instabilities can develop for strong magnetic fields (B > 10 G). We have found the instability growth rates and estimated the temporal and spatial scales of development and decay of the periodic instability. We show that the instabilities under consideration can play a prominent role in the energy balance of the corona and may be considered as a large-scale energy source of the wave coronal heating mechanism.     

Current‐driven instabilities in weakly ionized disks

Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall‐MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toroidal magnetic field is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas

Self-generated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that firehose and ordinary-mode instabilities can develop under the same conditions, which makes it challenging to separate the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron-temperature anisotropy T _∥>T _⊥, where ∥ and ⊥ denote directions with respect to the local mean magnetic field. In addition to the previously reported comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, with a focus on the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For stronger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding those of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the low β [<?1] regimes, here it is rigorously shown that only the high β [>?1] regimes are susceptible to these instabilities.     

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.     

Multicomponent theory of buoyancy instabilities in magnetized plasmas: the case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.     

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.     

Dynamo theory and liquid metal MHD experiments

High values of magnetic Reynolds number R_m are characteristic not only to astrophysics, but also to other interesting objects, including liquid metal (LM) flows. Since sixties LM experiments have been performed illustrating important predictions of the dynamo theory, for example, about the existence and features of the α effect. Consideration of so called “laminar” dynamos provides a theoretical base for direct experimental realization and examination of the dynamo process. First step results, gathered at subcritical conditions, confirm the statement that self-excitation in LM experiments can be achieved practically today. In such devices as LM (sodium) cooled fast breeders R_m can reach values up to 50 and specific MHD phenomena have been observed in operating fast reactors. Cautions against crisis like processes have been expressed. It is important for the dynamo theory to understand what kind of perturbed motion is able to coexist with the generated magnetic field. Fundamentally new ideas here are issuing from the theory of 2D MHD turbulence. LM MHD served for the first direct proves, confirming, that the predicted surprising features of 2D turbulence can be observed in reality. It is worth incorporating these already not new ideas in the dynamo theory. In such a way a field for new solutions could be established.     

Effect of Hall Current and Finite Larmor Radius Corrections on Thermal Instability of Radiative Plasma for Star Formation in Interstellar Medium (ISM)

The effects of finite ion Larmor radius (FLR) corrections, Hall current and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effects of finite electrical resistivity, thermal conductivity and permeability for star formation in interstellar medium have been investigated. A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion gets modified into radiative instability criterion. The finite electrical resistivity removes the effect of magnetic field and the viscosity of the medium removes the effect of FLR from the condition of radiative instability. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. Numerical calculation shows stabilizing effect of viscosity, heat-loss function and FLR corrections, and destabilizing effect of finite resistivity and permeability on the thermal instability. The outcome of the problem discussed the formation of star in the interstellar medium.     

An electrodynamic model of electric currents and magnetic fields in the dayside ionosphere of Venus

The electric current configuration induced in the ionosphere of Venus by the interaction of the solar wind has been calculated in previous papers (Cloutier and Daniell, Planet. Space Sci. 21, 463, 1973; Daniell and Cloutier. Planet. Space Sci.25, 621, 1977; Cloutier and Daniell, Planet. Space Sci.27, 1111, 1979) for average steady-state solar wind conditions and interplanetary magnetic field. This model is generalized to include the effects of (a) plasma depletion and magnetic field enhancement near the ionopause, (b) velocity-shear-induced MHD instabilities of the Kelvin-Helmholtz type within the ionosphere, and (c) variations in solar wind parameters and interplanetary magnetic field. It is shown that the magnetic field configuration resulting from the model varies in response to changes in solar wind and interplanetary field conditions, and that these variations produce magnetic field profiles in excellent agreement with those seen by the PIONEER-VENUS Orbiter. The formation of “flux-ropes” by the Kelvin-Helmholtz instability is shown to be a natural consequence of the model, with the spatial distribution and size of the flux-ropes determined by the magnetic Reynolds number.     

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。     

A magnetohydrodynamic model of whistler duct structure in the magnetosphere

In this study, the physical structure for the propagation of whistler waves within a duct in the Earth's magnetosphere is investigated by means of magnetohydrodynamic (MHD) theory. Expressions for the current density and induced magnetic field are determined analytically and evaluated in terms of two models for the duct plasma density distribution. It is found that once the duct is formed, forces associated with the current structure will maintain it. MHD instabilities are examined briefly and found to be unlikely to threaten duct maintenance in regions where whistlers are typically observed. Examination of some effects of field-aligned currents suggest that this may be a viable mechanism for duct formation.     

The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops

It has been proposed that the million-degree temperature of the corona is due to the combined effect of barely detectable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release; thus we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory; i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold.     

Magnetic equilibria and instabilities

Solar flares are understood as a process of explosive liberation of magnetic energy, coming after a slow phase of energy build-up. The slow evolution of magnetic equilibria may end up with (a) the termination of an equilibrium sequence, or (b) an instability. The distinction between the two can be made by drawing schematic potential curves. Case (a) has been extensively studied in two-dimensional models. The appearance of multiple solutions, or disappearance of a solution takes place as the system evolves away from the current-free configuration. Case (b) can be discussed in terms of ideal MHD or resistive MHD instabilities. A possible route to explosive energy release is suggested by combining these two cases.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

An MHD gadget for cosmological simulations

Various radio observations have shown that the hot atmospheres of galaxy clusters are magnetized. However, our understanding of the origin of these magnetic fields, their implications on structure formation and their interplay with the dynamics of the cluster atmosphere, especially in the centres of galaxy clusters, is still very limited. In preparation for the upcoming new generation of radio telescopes (like Expanded Very Large Array, Low Wavelength Array, Low Frequency Array and Square Kilometer Array), a huge effort is being made to learn more about cosmological magnetic fields from the observational perspective. Here we present the implementation of magnetohydrodynamics (MHD) in the cosmological smoothed particle hydrodynamics (SPH) code gadget . We discuss the details of the implementation and various schemes to suppress numerical instabilities as well as regularization schemes, in the context of cosmological simulations. The performance of the SPH–MHD code is demonstrated in various one- and two-dimensional test problems, which we performed with a fully, three-dimensional set-up to test the code under realistic circumstances. Comparing solutions obtained using athena , we find excellent agreement with our SPH–MHD implementation. Finally, we apply our SPH–MHD implementation to galaxy cluster formation within a large, cosmological box. Performing a resolution study we demonstrate the robustness of the predicted shape of the magnetic field profiles in galaxy clusters, which is in good agreement with previous studies.     

Local potential analysis of MHD instability

In many astrophysical problems, the study of the stability of an atmosphere in the presence of a magnetic field is of importance. In most cases the MHD instabilities of atmospheres are studied by energy principle of Bernsteinet al. (1958). In this paper, a general method for studying the stability of a system subject to MHD equations of conditions has been proposed. This is based on the local potential concept put forward by Glansdorff and Prigogine (1964). The scheme for securing stability criteria has been demonstrated in two particular cases.     

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.     

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.     

Drift instabilities associated with the particles in ring current and inner edge of plasma sheet

Electromagnetic waves propagating transverse to the magnetic field, containing inhomogenous and loss cone plasma, may become unstable due to the excitation of resonant proton, resonant electron and drift cyclotron instabilities. Resonant proton instability gets excited in inhomogenous plasma, irrespective of the presence of temperature anisotropy, loss cone or temperature gradient. However, the growth rate of this instability is much smaller than the other two instabilities. The maximum growth rates of resonant electron instability are enhanced with the increase of loss cone index, gradients in transverse temperature and magnetic field, and with the decrease of temperature anisotropy and gradients in density and parallel temperature. The drift cyclotron instability exists in a bounded range of wave numbers and its growth rate increases with the increase of electron temperature, density and magnetic field gradient, and with the decrease of proton temperature and temperature anisotropy. In the region of ring current for beyond plasmapause the resonant proton and resonant electron instabilities have the characterstic frequencies around 0.1Ω_p and growth rates ~10^?6Ω_p and 10^?3Ω_p, respectively. In the ring current region the drift cyclotron instability is not excited whereas in the plasma sheet region the frequency and growth rate of this instability are around Ω_p and 10^?2Ω_p, respectively. These instabilities can accelerate the ring current particles along the magnetic field lines and dump them into the auroral region.