Weibel, Two-Stream, Filamentation, Oblique, Bell, Buneman... which one grows faster ?

TL;DR

This paper develops an analytical model to determine which plasma instability grows fastest in astrophysical settings, considering various parameters and providing a unified description of multiple instabilities.

Contribution

It introduces a comprehensive 3D dielectric tensor model that unifies the description of key plasma instabilities and determines their hierarchy based on system parameters.

Findings

Identifies dominant instabilities in different parameter regimes.

Shows the influence of electron-to-proton mass ratio on instability hierarchy.

Provides application insights for Solar Flares, intergalactic streams, and shocks.

Abstract

Many competing linear instabilities are likely to occur in astrophysical settings, and it is important to assess which one grows faster for a given situation. An analytical model including the main beam plasma instabilities is developed. The full 3D dielectric tensor is thus explained for a cold relativistic electron beam passing through a cold plasma, accounting for a guiding magnetic field, a return electronic current and moving protons. Considering any orientations of the wave vector allows to retrieve the most unstable mode for any parameters set. An unified description of the Filamentation (Weibel), Two-Stream, Buneman, Bell instabilities (and more) is thus provided, allowing for the exact determination of their hierarchy in terms of the system parameters. For relevance to both real situations and PIC simulations, the electron-to-proton mass ratio is treated as a parameter, and numerical calculations are conducted with two different values, namely 1/1836 and 1/100. In the system parameters phase space, the shape of the domains governed by each kind of instability is far from being trivial. For low density beams, the ultra-magnetized regime tends to be governed by either the Two-Stream or the Buneman instabilities. For beam densities equalling the plasma one, up to four kinds of modes are likely to play a role, depending of the beam Lorentz factor. In some regions of the system parameters phase space, the dominant mode may vary with the electron-to-proton mass ratio. Application is made to Solar Flares, Intergalactic Streams and Relativistic shocks physics.