Oblique shock dynamics in nonextensive magnetized plasma

The detailed properties of the classical electromagnetic Weibel instability in a semi-relativistic anisotropic plasma are investigated for Maxwellian distribution. In this article, the effects of one particular factor affecting the growth rate of Weibel instability, Coulomb collision effect of electrons and ions, is studied and discussed based on the equilibrium semi-relativistic Maxwellian distribution function, in a dense and unmagnetized anisotropic plasma. An analytical expression is derived for the growth rate of the Weibel instability. The two limiting cases ( $\left| \xi\right| \ll1$ and $\left| \xi\right| \gg1$ ) are considered. It is shown that in the limit $\left| \xi\right| \ll 1$ , the quantity η, which is due to the collision term, will appear in the growth and in the conditions of the rate of the Weibel instability. The quantity χ symbolizes the contribution from relativistic terms which becomes unity as we approach the non-relativistic Maxwellian case, leading to the standard Weibel instability scenario. The increasing of η leads to decreasing of the growth rate, and with the decreasing of η the growth rate will increase.     

Weibel Turbulence in Laboratory Experiments and GRB/SN Shocks

It has recently been realized that the Weibel instability plays a major role in the formation and dynamics of astrophysical shocks of gamma-ray bursts and supernovae. Thanks to technological advances in the recent years, experimental studies of the Weibel instability are now possible in laser-plasma interaction devices. We, thus, have a unique opportunity to model and study astrophysical conditions in laboratory experiments – a key goal of the Laboratory Astrophysics program. Here we briefly review the theory of strong non-magnetized collisionless GRB and SN shocks, emphasizing the crucial role of the Weibel instability and discuss the properties of radiation emitted by (isotropic) electrons moving through the Weibel-generated magnetic fields, which is referred to as the jitter radiation. We demonstrate that the jitter radiation field is anisotropic with respect to the direction of the Weibel current filaments and that its spectral and polarization characteristics are determined by microphysical plasma parameters. We stress that the spectral analysis can be used for accurate diagnostics of the plasma conditions in laboratory experiments and in astrophysical GRB and SN shocks.     

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.     

Interstellar turbulent magnetic field generation by plasma instabilities

The maximum magnetic field strength generated by Weibel-type plasma instabilities is estimated for typical conditions in the interstellar medium. The relevant kinetic dispersion relations are evaluated by conducting a parameter study both for Maxwellian and for suprathermal particle distributions showing that micro Gauss magnetic fields can be generated. It is shown that, depending on the streaming velocity and the plasma temperatures, either the longitudinal or a transverse instability will be dominant. In the presence of an ambient magnetic field, the filamentation instability is typically suppressed while the two-stream and the classic Weibel instability are retained.     

Hydromagnetic wave propagation and the Kelvin-Helmholtz instability in an arbitrary-β collisional inhomogeneous plasma

The instability of an inhomogeneous arbitrary- plasma occurring due to the transverse velocity shear, has been studied to analyse the effects of collisional thermal transfer. The dissipation of hydromagnetic waves in such a plasma has also been discussed. It has been found that the thermal forces modify the instability criteria in several limiting cases. Numerical solutions have also been obtained to investigate the effects of various physical parameters for a non-isothermal plasma with different adiabticity of two species, viz., electrons and ions.     

Collisional instability of the drift wave in multi-component plasmas

The collisional instability of the drift wave in a multi-component plasma is investigated. It is shown that when the electron and ion density gradients are different, e.g., due to the presence of a static third component or due to neutral drag effects, the drift mode becomes unstable. The instability is caused by the simultaneous action of the electron collisions with all other plasma species and the spatial difference of the density of the plasma components. This instability may be expected as a natural consequence of the stratification of a multi-component plasma placed in an external gravity field where it can operate for any amount of charge on heavy particles. Therefore it could develop in weakly ionized cold interstellar regions for example, when the heavy particles, i.e. charged grains, are a few tens of Å in size, and carry typically ±1,±2 charge. In the solar atmosphere, it may appear in the weakly ionized photospheric layers due to the convective motion of the neutral component.     

Instability of the electromagnetic ordinary mode in counterstreaming plasmas

The instability of a linearly-polarised electromagnetic ordinary mode in a plasma and propagating perpendicular to a uniform magnetic field caused by a counterstreaming of electrons along the latter is studied using a Vlasov plasma model. The results show that (i) for weak magnetic fields, the thermal effects stabilise the ordinary mode; (ii) for strong magnetic fields, the thermal effects destabilise the ordinary mode.     

Ion‐ion charge exchange and X‐rays from the winds of hot stars

Charge exchange occurs between charged ions with enough energy to overcome Coulomb repulsion, a condition satisfied for collisions at velocities like those of the winds driven from hot stars by radiation pressure. X‐ray line ratios in some hot stars are inconsistent with those expected from thermal plasmas excited by electron impact. Ion‐ion interactions including charge exchange might be responsible instead if high‐velocity collisions between ions are enabled by the presence of a magnetic field in the wind, suggesting a possible alternative mechanism to the widely accepted instability‐driven shock model. The nature of a plasma in charge‐exchange equilibrium is yet to be determined (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal instability in slab geometry in the presence of anisotropical thermal conduction

Prominences and filaments are thought to arise as a consequence of a magnetized plasma undergoing thermal instability. Therefore, the thermal stability of a magnetized plasma is investigated under coronal conditions. The equilibrium structure of the plasma is approximated by a 1-D slab configuration. This is investigated in thermal instability taking into account optically thin plasma radiation and anisotropic thermal conduction. The thermal conduction perpendicular to the magnetic field is taken to be small but non-zero.The classic rigid wall boundary conditions which are often applied in the literature, either directly on the plasma or indirectly through some other medium, are replaced by a more physical situation in which the plasma column is placed in a low-density background stretching towards infinity. Results for a uniform equilibrium structure indicate the major effect of this change is on the eigenfunctions rather than on the growth rate. Essentially, perpendicular thermal conduction introduces field-aligned fine structure. It is also shown that in the presence of perpendicular thermal conduction, thermal instability in a slab model is only possible if the inner plasma has the shortest thermal instability time scale.Research Assistant of the National Fund for Scientific Research (Belgium).     

Magnetostatic structures in collisionless plasma and their synchrotron radiation

The properties of the magnetostatic structures in a collisionless relativistic plasma found by exactly solving the nonlinear self-consistent kinetic and Maxwell equations using the method of invariants of particle motion are analyzed. These structures include individual neutral current sheets and cylindrically symmetric filaments as well as their ensembles, admitting a wide variety of types of particle energy distribution functions. Relationships are established between the possible parameters of the current sheets and filaments—their sizes, currents and magnetic fields, and the degree of anisotropy of the particle momentum distribution. The extent to which these parameters are conditioned by the properties of the Weibel instability that can produce these structure is also discussed. The spectral peculiarities of the synchrotron radiation from the particles that form the current sheets and filaments are investigated in the special case of power-law energy distribution functions.     

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.     

Thermal instability and transport effects in comets

The localized ion density depletion region observed at comet Halley can be understood in terms of a thermal instability of the cometary plasma due to the excitation of rotational and vibrational levels of water molecules. The electron energy losses due to these processes peak near 4000 K and at higher temperatures a localized cooling leads to the thermal instability due to the increased radiation loss. The resulting increase in recombination leads to the ion density depletion and the estimates for this depletion at comet Halley agree with the observations. The transport effects at the density depletion region due to the diffusion and thermal conductivity are found have time scales larger than the instability time scale and does not affect the formation of the depletion region.     

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.     

Self-gravitational instability of rotating viscous Hall plasma with arbitrary radiative heat-loss functions and electron inertia

The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous, viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that the presence of arbitrary radiative heat-loss functions and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the curves we find that the presence of thermal conductivity, finite electrical resistivity and density-dependent heat-loss function has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability. The effect of arbitrary heat-loss functions is also studied on the growth rate of a radiative instability.     

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.     

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.     

Non-stationary pair plasma in a pulsar magnetosphere and the two-stream Instability

We test a new emission mechanism in pulsar magnetospheres, eventually responsible in part for the high level of observed radio radiation. This is carried out by comparing the efficiency of the two-stream instability of Langmuir waves in a pulsar emission region, where the stationary and non-stationary characters of pair plasma outflows produced in the gap region are characterized by two different time-scales. On the shorter time-scale, the Ruderman &38; Sutherland 'sparking' phenomenon leads to the creation of pair plasma clouds, in motion along magnetic field lines, that contain particles with a large spectrum of momenta. The overlapping of particles with different energies produced in successive clouds results in an efficient 'two stream'-like instability. This effect is a consequence of the non-stationary character of the pair plasma produced in the gap region, just above the magnetic poles of the neutron star. On a long time-scale, resulting pair plasma outflows in pulsar magnetospheres can be treated as stationary. In this case, the instability which results from interaction between existing primary beam particles and the pair plasma is negligible, whereas the instability owing to interaction between electrons and positrons of the pair plasma itself, and more precisely to their relative drift motion along curved magnetic field lines, is effective. We derive characteristic features of the triggered instability, using specific distribution functions to describe either particles in the assembly of clouds or relative drifting of electrons and positrons in these same plasma clouds. Although linear and local, our treatment suggests that non-stationary effects may compete with, or even dominate over, drifting effects in parts of pulsar emission regions.     

Effect of general loss-cone distribution function on electrostatic ion-cyclotron instability in an inhomogeneous plasma: particle aspect analysis

The electrostatic ion-cyclotron instability (EICI) in low β (ratio of plasma to magnetic pressure), anisotropic, inhomogeneous plasma is studied by investigating the trajectories of the particles using the general loss-cone distribution function (Dory-Guest-Harris type) for the plasma ions. In particular, the role of the loss-cone feature as determined by the loss-cone indices, in driving the drift-cyclotron loss-cone (DCLC) instability is analysed. It is found that for both long and short wavelength DCLC mode the loss-cone indices and the perpendicular thermal velocity affect the dispersion equation and the growth rate of the wave by virtue of their occurrence in the temperature anisotropy. The dispersion relation for the DCLC mode derived here using the particle aspect analysis approach and the general loss-cone distribution function considers the ion diamagnetic drift and also includes the effects of the parallel propagation and the ion temperature anisotropy. It is also found that the diamagnetic drift velocity due to the density gradient of the plasma ions in the presence of the general loss-cone distribution acts as a source of free energy for the wave and leads to the generation of the DCLC instability with enhanced growth rate. The particle aspect analysis approach used to study the EICI in inhomogeneous plasma gives a fairly good explanation for the particle energisation, wave emission by the wave–particle interaction and the results obtained using this particle aspect analysis approach are in agreement with the previous theoretical findings using the kinetic approach.     

Steady heat conduction in coronal loop unstable against plasma instability

The Fokker-Planck equation is numerically solved to study the electron velocity distribution under steady heat conduction with an applied axial electric current in a model coronal loop.If the loop temperature is so high that the electron mean-free path is longer than the local temperature scale height along the loop, a velocity hump appears at about the local thermal electron velocity. The hump is attributed to cooler electrons moving up the temperature gradient to compensate for the runaway electrons moving down the gradient. If the ratio between the mean free path and temperature scale height is greater than about 2, negative absorption for the plasma waves can appear (waves grow). This effect is enhanced by the presence of axial electric current in the half of the coronal loop in which the electrons carrying the current are drifting up the temperature gradient. Thus, the plasma instability may occur in the coronal elementary magnetic flux tubes. Although the present paper is limited to show the critical condition and linear growth rate of the instability, the following scenarios may be inferred.If the flux tubes change from marginally stable to unstable against the plasma instability, due to an increase in the loop temperature, anomalous resistivity may suddenly appear because of the growth of plasma waves. Then a high axial electric field is induced that may accelerate particles. This could be the onset of impulsive loop flares.For a low electric current, if the loop temperature is sufficiently high to give the negative absorption for the plasma waves in a large part of the coronal loop, steady plasma turbulence may originate. This could be a source for the type I radio noise storm.     

Rayleigh-Taylor instability of a Hall plasma with arbitrary density gradient

The Rayleigh-Taylor instability of a plasma layer in the presence of a horizontal magnetic field is investigated, taking into account the effects of Hall-currents and an arbitrarily large density gradient. It is shown for the general case that if the density decreases vertically upward, the system is thoroughly stable.For a plasma layer with exponentially varying density an approximate dispersion relation is obtained using the Galerkin's method. An analysis of the roots of the dispersion relation reveals that the Hall-currents loosen the stabilizing influence of the magnetic field and impart instability to the system. For sufficiently large values of the density gradient and the Hall currents the system is throughly destabilized for all perturbations.