Electrostatic stability of electron-positron plasmas in dipole geometry

TL;DR

This paper analyzes the electrostatic stability of electron-positron plasmas in dipole geometries, deriving a kinetic dispersion relation and showing how finite Debye length influences stability and instability mechanisms.

Contribution

It introduces a comprehensive stability analysis in dipole geometry, highlighting the role of Debye length and temperature/density gradients in plasma stability.

Findings

Finite Debye length resolves singular stability behavior.

Temperature and density gradients can drive plasma instability.

Landau damping suppresses instability at small scales.

Abstract

The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the zero-Debye-length case, the stability diagram is found to exhibit singular behavior. However, when the Debye length is non-zero, a fluid mode appears, which resolves the observed singularity, and also demonstrates that both the temperature and density gradients can drive instability. It is concluded that a finite Debye length is necessary to determine the stability boundaries in parameter space. Landau damping is investigated at scales sufficiently smaller than the Debye length, where instability is absent.