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Collisionless relaxation as the origin of the anisotropic, non-thermal, and multi-temperature momentum distributions observed in space plasmas

Torsten Enßlin, Christoph Pfrommer

TL;DR

This paper addresses how collisionless space plasmas relax after anisotropic compression or expansion. By enforcing Liouville's theorem and the conservation of energy, momentum, particle number, and phase-space density, the authors show that isotropization cannot be achieved without collisions, and the initial anisotropy is retained, particularly in high-momentum shells. For electron–positron plasmas, the relaxed state remains anisotropic with a distribution linked by $g_{1}(p)=g_{0}(p/ oot 3 o r)$; for electron–ion plasmas, a two-temperature outcome is possible and governed by a global factor $t$ with $r_i=rt$ and $r_e=r t^{-1/Z_i}$, including asymptotic behavior $t^{ ext{±1}}=(3/4)^{3/2} r^{5/2}$. The work argues that anisotropy is naturally imprinted on outer momentum shells, potentially explaining non-thermal, kappa-like tails observed in the solar wind and other collisionless plasmas, and highlights the need for kinetic simulations to validate these predictions and extend them to shocks and intracluster turbulence.

Abstract

Anisotropic, non-thermal, and multi-temperature distributed particle momenta are commonly observed in collisionless space plasmas, such as the solar wind. Using Liouville's theorem, we argue that anisotropic compression or expansion of the plasma, followed by a relaxation of the resulting anisotropic stress must lead to non-equilibrium states that are either anisotropic, non-thermal distribution functions, different electron and ion temperatures, or a combination of these effects. We present arguments showing that a plasma in thermal equilibrium undergoing anisotropic compression or expansion cannot return to thermal equilibrium in the absence of particle collisions. Since most astrophysical plasmas are practically collisionless and experience significant anisotropic compression or expansion, we expect anisotropic, non-thermal, and multi-temperature particle distributions to be ubiquitous, in agreement with solar wind measurements.

Collisionless relaxation as the origin of the anisotropic, non-thermal, and multi-temperature momentum distributions observed in space plasmas

TL;DR

This paper addresses how collisionless space plasmas relax after anisotropic compression or expansion. By enforcing Liouville's theorem and the conservation of energy, momentum, particle number, and phase-space density, the authors show that isotropization cannot be achieved without collisions, and the initial anisotropy is retained, particularly in high-momentum shells. For electron–positron plasmas, the relaxed state remains anisotropic with a distribution linked by ; for electron–ion plasmas, a two-temperature outcome is possible and governed by a global factor with and , including asymptotic behavior . The work argues that anisotropy is naturally imprinted on outer momentum shells, potentially explaining non-thermal, kappa-like tails observed in the solar wind and other collisionless plasmas, and highlights the need for kinetic simulations to validate these predictions and extend them to shocks and intracluster turbulence.

Abstract

Anisotropic, non-thermal, and multi-temperature distributed particle momenta are commonly observed in collisionless space plasmas, such as the solar wind. Using Liouville's theorem, we argue that anisotropic compression or expansion of the plasma, followed by a relaxation of the resulting anisotropic stress must lead to non-equilibrium states that are either anisotropic, non-thermal distribution functions, different electron and ion temperatures, or a combination of these effects. We present arguments showing that a plasma in thermal equilibrium undergoing anisotropic compression or expansion cannot return to thermal equilibrium in the absence of particle collisions. Since most astrophysical plasmas are practically collisionless and experience significant anisotropic compression or expansion, we expect anisotropic, non-thermal, and multi-temperature particle distributions to be ubiquitous, in agreement with solar wind measurements.
Paper Structure (9 sections, 29 equations, 1 figure)

This paper contains 9 sections, 29 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Overview
  3. Related works
  4. Anisotropic forcing and relaxation into an equilibrium state
  5. Notation and conventions
  6. Electron--positron plasma
  7. Electron--ion plasma
  8. Anisotropy in momentum shells
  9. Conclusions and outlook

Figures (1)

  • Figure 1: Ratio of the momentum space compression ratio (left axis) or temperature ratio (right axis) for an initially isothermal non-relativistic hydrogen plasma after expansion by a factor $r^{-1}$ along the magnetic field direction in case this manages to completely accommodate the initial anisotropy in an asymmetry of isotropic electron and proton distribution functions.