Marian Lazar

Kappa Distributions: Theory and Applications in Space Plasmas

The plasma particle velocity distributions observed in the solar wind generally show enhanced (non-Maxwellian) suprathermal tails, decreasing as a power law of the velocity and well described by the family of Kappa distribution functions. The presence of non-thermal populations at different altitudes in space plasmas suggests a universal mechanism for their creation and important consequences concerning plasma fluctuations, the resonant and nonresonant wave – particle acceleration and plasma heating. These effects are well described by the kinetic approaches where no closure requires the distributions to be nearly Maxwellian. This paper summarizes and analyzes the various theories proposed for the Kappa distributions and their valuable applications in coronal and space plasmas.

Cosmological Effects of Weibel-Type Instabilities

New arguments are given here in favor of Weibel-type instabilities as one of the most plausible sources of the cosmological magnetic field. The Weibel instability has recently been proposed as one of the secondary mechanisms of relaxation for the large interpenetrating formations of galactic and intergalactic plasma. Here, these investigations are extended to counterstreaming plasmas which have, in addition, intrinsic temperature anisotropies, and where any form of the Weibel-type instability can be excited. This can be a simple filamentation instability due to the relative motion of counterstreaming plasmas, or a Weibel-like instability when it is generated by an excess of transverse temperature with respect to the streaming direction. But it can also be a cumulative filamentation/Weibel instability when the plasma is hotter along the streaming direction. Such plasma systems are relevant for the relative motions of filaments and sheets of galaxies, and are expected to exist at large scales and any age of our Universe. For such counterstreaming plasmas with internal temperature anisotropies, any Weibel-type instability mentioned before can become the primary wave relaxation mechanism of the plasma anisotropy, because it develops easily faster than the principal competitor, which is the two-stream electrostatic instability. The estimations made here for typical parameters of intergalactic plasmas, provide micro-Gauss levels of the magnetic field of Weibel type, which are consistent with magnetic field values, 10–7-10–5 G, derived from Faraday rotation measure of the linearly polarized emission of galactic or extragalactic sources.

Firehose instability in space plasmas with bi-kappa distributions

Context. The existence of suprathermal charged particle populations in space plasma is frequently confirmed by interplanetary missions. In general, the velocity distribution functions are anisotropic, field aligned (gyrotropic) with two temperatures, parallel (T� )a nd perpendicular (T⊥) to the ambient magnetic field B0. Aims. Here, the dispersion properties of the firehose instability, which relaxes an anisotropic electron distribution function (T� > T⊥) of bi-kappa type, are investigated for the first time. Methods. The Solar wind is generally accepted to be a collisionless plasma and, therefore, the dispersion formalism is constructed on the basis of the kinetic Vlasov-Maxwell equations. The general dispersion relations are derived in terms of the modified plasma dispersion function. Results. Simple analytical forms are obtained for the dispersion relation of the firehose instability and the instability criterion is derived. The exact numerical evaluation shows a significant departure of the dispersion curves from those obtained for a bi-Maxwellian plasma. Conclusions. While the maximum growth rate is slightly diminished, the instability extends to large wave-numbers in the presence of suprathermal particles. Thus, this instability is more likely to be found in space plasmas with an anisotropic distribution of bi-kappa type. If all other parameters are known, measuring the instability growth time enables the determination of the spectral index κ.

Cumulative effect of the Weibel-type instabilities in symmetric counterstreaming plasmas with kappa anisotropies

Counterstreaming plasma structures are widely present in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. Filamentationally unstable mode is described by assuming that each of the counterstreaming plasmas has an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growth rate can reach a maximum value markedly larger than that for a a plasma with a Maxwellian distribution function. This behaviour is opposite to what was observed for the Weibel instability growth rate in a bi-kappa plasma, which is always smaller than that obtained for a bi-Maxwellian plasma. The approach is further generalized for a counterstreaming plasma with a bi-kappa temperature anisotropy. In this case, the filamentation instability growth rate is enhanced by the Weibel effect when the plasma is hotter in the streaming direction, and the growth rate becomes even larger. These effects improve significantly the efficiency of the magnetic field generation, and provide further support for the potential role of the Weibel-type instabilities in the fast magnetization scenarios.

Proton firehose instability in bi-Kappa distributed plasmas

Context. Protons or heavier ions with anisotropic velocity distributions and non-thermal departure from Maxwellian, are frequently reported in the magnetosphere and at different altitudes in the solar wind. These observations are sustained by an extended number of mechanisms of acceleration in any direction with respect to the interplanetary magnetic field. However, the observed anisotropy is not large and most probably constrained by the kinetic instabilities. Aims. An excess of parallel kinetic energy, T� /T⊥ > 1( whereand ⊥ denote directions relative to the background magnetic field) drives a proton firehose mode to grow, limiting any further increase in the anisotropy according to the observations. The effects of suprathermal populations on the principal characteristics of the proton firehose instability are investigated. Methods. For low-collisional plasmas, the dispersion approach is based on the fundamental kinetic Vlasov-Maxwell equations. The anisotropy of plasma distributions including suprathermal populations is modeled by bi-Kappa functions, and the new dispersion relations are derived in terms of the modified plasma dispersion function (for Kappa distributions), and analytical approximations of this function. Results. Growth rates of the proton firehose solutions and threshold conditions are provided in analytical forms for different plasma regimes. The proton firehose instability needs a larger anisotropy and a larger parameter β� to occur in a Kappa-distributed plasma. A precise numerical evaluation shows that the growth rates are, in general, lower and the wave frequency is only slightly affected, but the influence of suprathermal populations is essentially dependent on both the proton and electron anisotropies. Departures from the standard dispersion of a Maxwellian plasma can eventually be used to evaluate the presence of suprathermal populations in solar flares and the magnetosphere.

Cumulative effect of the filamentation and Weibel instabilities in counterstreaming thermal plasmas

Introducing a thermal particle distribution is important for a realistic investigation of counterstreaming plasmas with finite temperatures. Such counterstreaming thermal plasmas are described by the particle distributions, which include the counterstreams and thermal distribution as well. Two nonrelativistic counterstreams are considered here, with a bi-Maxwellian thermal anisotropy for each of them. This type of distribution is often expected to be found in both laboratory or cosmic plasmas, and it is able to cumulate the effects of the filamentation and Weibel instability. Comparing with the growth rates of each of these instabilities, the cumulative effect provides larger values, if they are emitted in the same direction. If the thermal anisotropy is negative, which means that Weibel instability develops on a perpendicular direction with respect to the filamentation instability, then their cumulative effect will suppress the instability. In both of these cases, the cumulative effect of the filamentation and Weibel instabilities can modify significantly the effective growth rate of the electromagnetic unstable modes.

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.

Spontaneously growing, weakly propagating, transverse fluctuations in anisotropic magnetized thermal plasmas

A new dispersion formalism describing the weakly propagating, transverse fluctuations with wave vectors (k∥B) parallel to the uniform background magnetic field B in an anisotropic bi-Maxwellian magnetized electron-proton plasma is presented. Different transverse right-handed or left-handed polarized modes can be excited, which are the whistler Weibel-like modes and the electron and proton firehose modes. Analytic instability threshold conditions are derived in terms of the combined temperature anisotropy A=T⊥/T∥, the parallel plasma beta β∥=8πnekBT∥/B2, and the electron plasma frequency phase speed w=ωp,e/(kc).

Spontaneous electromagnetic fluctuations in unmagnetized plasmas. III. Generalized Kappa distributions

In the first two papers of this series, the general expressions for the spontaneous fluctuations spectra (electric and magnetic field, charge and current densities) from uncorrelated plasma particles are derived and illustrated for a Maxwellian (relativistic or nonrelativistic) plasma close to thermal equilibrium. In this paper, the results are illustrated for the nonideal case of a plasma out of thermal equilibrium and described by the generalized Kappa (power-law) particle distribution function in the nonrelativistic limit. The suprathermal fluctuations of weakly amplified modes and aperiodic modes are provided. Thus, it is shown for the first time the existing finite level of noncollective fluctuations, which are particularly important in the context of plasma fluctuations (collective or noncollective) as the best agent in the energy dissipation and transfer to suprathermal populations. The results obtained in the first paper for an equilibrium plasma are recovered only in the limit of a very large pow...

On the existence of Weibel instability in a magnetized plasma. II. Perpendicular wave propagation: The ordinary mode

In a magnetized plasma with a temperature anisotropy T||>T⊥ (where || and ⊥ denote directions with respect to the uniform magnetic field B0), the nonresonant Weibel instability can develop and destabilize purely growing, ordinary plasma modes (k=k⊥). This paper presents a rigorous extended analysis of this instability on the basis of a new threshold b0(k), which enables to determine the instability conditions as well as the upper limits of the growth rates. Accurate analytical forms of the threshold conditions are provided here for the first time and for the full physical range of the temperature anisotropy and the parallel plasma beta. The marginal and threshold conditions for the plasma parameters, which directly lead to an instability of the ordinary mode, are explicitly derived numerically and analytically. The new analytical tools developed here provide premises for a comprehensive investigation of the interplay of this instability with the firehose instability, as they both can develop in the same c...