A general kinetic mirror instability criterion for space applications

Abstract

Abstract. Suprathermal particle populations and loss-cone structures are the most common characteristics of ion and electron velocity distributions observed in space plasmas. We introduce a significant generalization of the family of kappa distributions to a suprathermal loss-cone distribution, applicable to a variety of space plasma modeling. On the basis of this concept a general mirror instability threshold criterion is derived from an energy principle for collisionless plasmas, covering the full range from two-temperature Maxwellians to complex loss-cone conditions occupied by high-energy ion species. We demonstrate that nonthermal plasma characteristics are the source of significant mirror instability threshold reduction where the specific structure of the velocity-space distribution dominates as a regulating mechanism for wave mode excitation.

Consequences of entropy bifurcation in non-Maxwellian astrophysical environments

“…A variety of subsequent analyses were devoted to clarify the mathematical and physical consequences of pseudo-additivity (Plastino et al, 1994;Tsallis, 1995;Silva et al, 1998;Almeida, 2001) where a deterministic connection between the generalized entropy and the resulting power-law functionals (Andrade et al, 2002), as well as the duality of nonextensive statistics were recognized (Karlin et al, 2002). Derived within the context of nonextensive statistics, power-law distributions provided also the missing justification for the use of the hitherto empirical, but ubiquitously observed, κ-distribution family favored in space plasma modeling from fundamental physics (Leubner, 2000;Leubner and Schupfer, 2001;Leubner, 2004a,b). The corresponding entropic index κ, as measure of the degree of long-range interactions or correlations, is not restricted to positive values and thus manifests the duality of nonextensive statistics.…”

“…Those include the thermo-statistical properties of the interplanetary medium where the electron, proton and even heavy ion velocity space distributions show ubiquitously suprathermal halo patterns (see Mendis and Rosenberg (1994) for a general review, or Leubner (2000); Leubner and Schupfer (2001) and references therein), well described by the empirical family of κ-distributions, a power law in particle speed and first recognized by Vasyliunas (1968). In continuation, significant progress was provided by Treumann (1999a,b) who developed a kinetic theory, demonstrating that power-law velocity distributions are a particular thermodynamic equilibrium state.…”

Nonextensive Theory of Dark Matter and Gas Density Profiles

“…In this situation, a single parameter, k, characterizes the degree of nonextensivity or coupling within the system. The corresponding derived power-law distributions constitute a particular thermodynamic equilibrium state (Treumann 1999), commonly applied in astrophysical plasma modeling (Leubner & Schupfer 2001;Leubner 2002).…”

A universal mirror wave-mode threshold condition for non-thermal space plasma environments

“…Let us study threshold situations not available from Leubner and Schupfer (2001), but of significance for a variety of magnetospheric and solar wind conditions. Equating (8) to zero and solving for the temperature anisotropy, Fig.…”

“…Hence, the velocity space distribution (2) is of considerable generality and importance, since it represents an analytical model applicable for most or, at least, a significantly large variety of space plasma environments observed. Following Leubner and Schupfer (2001), the general case of a suprathermal particle population (κ) embedded in a losscone structure (j ) is analyzed with respect to kinetic modifications of the mirror mode instability thresholds. Inserting the distribution function (2) into the kinetic instability criterion (1) and performing the integration in parallel and perpendicular velocity space, a solution I (κ, j ) for the integral on the left-hand side of Eq.…”