The instability of the electromagnetic ordinary modes in counterstreaming and counterrotating plasmas

The instability of a linearly-polarised electromagnetic ordinary mode in counterrotating plasmas and propagating perpendicular to a uniform magnetic field caused by a counterstreaming of electrons along the latter is studied using a cold-plasma model. It is found that: (i) In the presence of either a streaming or a rotation or both, the ordinary-wave propagation is possible even for frequencies less than the plasma frequency; (ii) the Coriolis forces like the applied magnetic field stabilise the ordinary modes.     

Filamentation Instability of Nonlinear Alfvén Waves and Plasma Heating associated with Recombination Effect

We investigate plasma heating associated with the effect of recombination and the filamentation instability of Alfvén waves propagating along homogeneous magnetic field in low-beta plasmas, by using an MHD simulation code. The linear instability of Alfvén waves leading to the filamentation is investigated by imposing small density perturbations across a magnetic field. We show results of the nonlinear stage of the above filamentation instability and the plasma heating through a two-dimensional simulation. It is shown that the plasma heating is caused by localized heating and whole heating, which are associated with the filamentation instability and the effect of recombination, respectively. We discuss the implication of these results for plasma heating processes observed in the chromosphere of the Sun.     

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.     

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.     

Microscopic filamentation due to electrothermal instability and plasma heating in time-dependent solar transition layer

We have investigated nonlinear equilibrium states of a microscopic current filamentation (electrothermal instability) in solar atmosphere. The microscopic filamentation instability will develop for transition zone ion temperature plasmas, provided T _e/T_i > 1, where T _e and T _i are the electron and ion temperatures, respectively. Since the temperature radio for a steady-state solar atmosphere is approximately unity, the electrothermal instability will develop only in a time-dependent solar atmosphere. Indeed, such a condition is provided by time-dependent currents, which seem to exist in many magnetic loops as recent analysis by Porter et al. (1987) indicates. When the onset condition for the electrothermal instability is satisfied, the instability drives a current filamentation to a nonlinear equilibrium state with a spatially periodic electron temperature variation with the wavelength comparable to several ion-Larmor radii. The amplitude of the periodic temperature variation may be so large that the transition layer temperature and coronal temperature plasmas may exist within several Larmor radii — coexistence of the transition zone and corona within the same macro-volume.     

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.     

Radiative stability of interstellar masers — A variational technique

This paper gives a generalised theory of hydromagnetic stability of the interface between two infinitely-conducting, compressible plasmas with the latter accelerated perpendicular to the interface and streaming parallel to the interface and subjected to a constant magnetic field parallel to the streaming direction. The method used is adapted from the one given by Plesset and Hsieh (1964) for the hydrodynamical case and the general dispersion relation is found to involve Whittaker's functions and their first derivatives. The familiar Rayleigh-Taylor and Kelvin-Helmholtz instability problems are recovered from the general dispersion relation in the appropriate special cases.     

A hybrid simulation study of magnetic reconnection in anisotropic plasmas

The process of magnetic reconnection in anisotropic plasmas is studied numerically using a 2-dimensional, 3-component hybrid simulation. The results of the calculation show that, when the plasma pressure in the direction perpendicular to magnetic field is larger than that in the parallel direction (e.g. P/P = 1.5), instability may greatly increase, speeding up the rate of reconnection. When P is smaller than P, (e.g., when P/P = 0.6), fire hose instability appears, which will restrain the tearing mode instability and the process of magnetic reconnection.     

Loop heating by D.C. electric current and electromagnetic wave emissions simulated by 3-D EM particle code

We have shown that a current-carrying plasma loop can be heated by magnetic pinch driven by the pressure imbalance between inside and outside the loop, using a 3-dimensional electromagnetic (EM) particle code. Both electrons and ions in the loop can be heated in the direction perpendicular to the ambient magnetic field, therefore the perpendicular temperature can be increased about 10 times compared with the parallel temperature. This temperature anisotropy produced by the magnetic pinch heating can induce a plasma instability, by which high-frequency electromagnetic waves can be excited. The plasma current which is enhanced by the magnetic pinch can also excite a kinetic kink instability, which can heat ions perpendicular to the magnetic field. The heating mechanism of ions as well as the electromagnetic emission could be important for an understanding of the coronal loop heating and the electromagnetic wave emissions from active coronal regions.     

EMEC instability based on kappa-Maxwellian distributed trapped electrons in auroral plasma

In space plasmas, particle distributions are often observed having high energy tails and are well fitted by kappa distribution function. However, in auroral region electrons are expected to be accelerated mainly along the magnetic field lines and one may expect Maxwellian behaviour in perpendicular direction. Therefore, in the present study propagation characteristics of electromagnetic electron cyclotron (EMEC) waves is studied by employing kappa-Maxwellian distribution function for energetic trapped electrons in auroral region. Real frequency and the growth rate expressions have been solved numerically for kappa-Maxwellian plasma and then analyzed by considering the effect of different plasma parameters for wide range of auroral altitudes. The numerical results obtained show that growth rate increases with the increase in ratio \({\omega_{pe}} / {\varOmega_{e}}\), plasma beta, temperature anisotropy \({T_{\bot}} / {T_{\parallel}}\) and trapped electron drift speed but decreases when superthermal electron population increases.     

Simulation studies of electron acceleration by ion ring distributions in solar flares

Using a 2 1/2-D fully relativistic electromagnetic particle-in-cell code (PIC) we have investigated a potential electron acceleration mechanism in solar flares. The free energy is provided by ions which have a ring velocity distribution about the magnetic field direction. Ion rings may be produced by perpendicular shocks, which could in turn be generated by the super-Alfvénic motion of magnetic flux tubes emerging from the photosphere or by coronal mass ejections (CMEs). Such ion distributions are known to be unstable to the generation of lower hybrid waves, which have phase velocities in excess of the electron thermal speed parallel to the field and can, therefore, resonantly accelerate electrons in that direction. The simulations show the transfer of perpendicular ion energy to energetic electrons via lower hybrid wave turbulence. With plausible ion ring velocities, the process can account for the observationally inferred fluxes and energies of non-thermal electrons during the impulsive phase of flares. Our results also show electrostatic wave generation close to the plasma frequency: we suggest that this is due to a bump-in-tail instability of the electron distribution.     

Cross-scale coupling at a perpendicular collisionless shock

A full particle simulation study is carried out on a perpendicular collisionless shock with a relatively low Alfven Mach number (M_A = 5). Recent self-consistent hybrid and full particle simulations have demonstrated ion kinetics are essential for the non-stationarity of perpendicular collisionless shocks, which means that physical processes due to ion kinetics modify the shock jump condition for fluid plasmas. This is a cross-scale coupling between fluid dynamics and ion kinetics. On the other hand, it is not easy to study cross-scale coupling of electron kinetics with ion kinetics or fluid dynamics, because it is a heavy task to conduct large-scale full particle simulations of collisionless shocks. In the present study, we have performed a two-dimensional (2D) electromagnetic full particle simulation with a “shock-rest-frame model”. The simulation domain is taken to be larger than the ion inertial length in order to include full kinetics of both electrons and ions. The present simulation result has confirmed the transition of shock structures from the cyclic self-reformation to the quasi-stationary shock front. During the transition, electrons and ions are thermalized in the direction parallel to the shock magnetic field. Ions are thermalized by low-frequency electromagnetic waves (or rippled structures) excited by strong ion temperature anisotropy at the shock foot, while electrons are thermalized by high-frequency electromagnetic waves (or whistler mode waves) excited by electron temperature anisotropy at the shock overshoot. Ion acoustic waves are also excited at the shock overshoot where the electron parallel temperature becomes higher than the ion parallel temperature. We expect that ion acoustic waves are responsible for parallel diffusion of both electrons and ions, and that a cross-scale coupling between an ion-scale mesoscopic instability and an electron-scale microscopic instability is important for structures and dynamics of a collisionless perpendicular shock.     

Resonant behaviour of MHD waves on magnetic flux tubes

The resonances that appear in the linear compressible MHD formulation of waves are studied for equilibrium states with flow. The conservation laws and the jump conditions across the resonance point are determined for 1D cylindrical plasmas. For equilibrium states with straight magnetic field lines and flow along the field lines the conserved quantity is the Eulerian perturbation of total pressure. Curvature of the magnetic field lines and/or velocity field lines leads to more complicated conservation laws. Rewritten in terms of the displacement components in the magnetic surfaces parallel and perpendicular to the magnetic field lines, the conservation laws simply state that the waves are dominated by the parallel motions for the modified slow resonance and by the perpendicular motions for the modified Alfvén resonance.The conservation laws and the jump conditions are then used for studying surface waves in cylindrical plasmas. These waves are characterized by resonances and have complex eigenfrequencies when the classic true discontinuity is replaced by a nonuniform layer. A thin non-uniform layer is considered here in an attempt to obtain analytical results. An important result related to earlier work by Hollweg et al. (1990) for incompressible planar plasmas is found for equilibrium states with straight magnetic field lines and straight velocity field lines. For these equilibrium states the incompressible and compressible surface waves have the same frequencies at least in the long wavelength limit and there is an exact correspondence with the planar case. As a consequence, the conclusions formulated by Hollweg et al. still hold for the straight cylindrical case. The effects of curvature are subsequently considered.     

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.     

Oblique solitary Alfvén modes in relativistic electron-positron plasmas

In electron-positron plasmas the charge-to-mass ratio is the same for both species. This leads for different waves to the vanishing of certain coefficients in the dispersion laws and nonlinear evolution equations, and also to the decoupling of some of the plasma modes. In particular, there is a low-frequency mode which exists at all angles of propagation with respect to the static magnetic field, corresponding at parallel propagation to a degenerate case of circularly polarized waves, and at perpendicular propagation to part of the extraordinary mode. The nonlinear evolution of this generalizedX-mode is governed by a Korteweg-de Vries equation, valid at all angles of propagation except strictly parallel propagation, for which a different approach had been given already. The nonlinearity is strongest at perpendicular propagation.     

Electrostatic wave noise in the neutral sheet in the earth's geomagnetic tail

Numerical solutions are obtained from analytic dispersion relations for electrostatic waves in a self-consistent, one-dimensional magnetic neutral sheet. The dispersion relations are solved in the real wave number and complex frequency domain. The properties of wave modes will be described, with special emphasis on instability. Several regimes of instability are identified which may generally be divided into two classes. Wave growth is associated firstly with counterstreaming between ions and electrons, giving rise to low frequency waves similar to the usual electrostatic two-stream mode. In addition, high frequency growing waves occur, associated with harmonics of the electron oscillation frequency across the neutral plane.     

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.     

Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares

A low-frequency wave is treated as a local oscillation to modulate the guiding center of electrons beam, which is considered as free energy to excite Alfvén waves by a kinetic plasma instability under low-frequency approximation. The nonlinearity of the model is shown by a critical value of the amplitude of the low-frequency wave, and Alfvén waves are growing in a broad turbulent spectrum with fractional harmonics, which strongly depend on the criterion. The instability is limited in the direction nearly perpendicular to the ambient magnetic field. The growth rates are very sensitive to the beam speed that perpendicular to the magnetic field, the propagational angle, and the magnetic field strength, but not sensitive to the beam speed parallel to the magnetic field. This model is used to explain the modulations with multiple timescales in the flare light curves at radio, hard X-ray and H-alpha bands.