Quasi-linear approach of bi-Kappa distributed electrons with dynamic $\kappa$ parameter. EMEC instability

TL;DR

This paper introduces a quasi-linear model that allows the $ppa$ parameter to vary dynamically in bi-Kappa electron distributions, revealing how wave-particle interactions influence suprathermal electron populations and temperature anisotropy in plasma instabilities.

Contribution

It develops a novel QL approach that couples $ppa$ variation with kurtosis and temperature evolution, improving understanding of plasma wave instabilities with non-equilibrium electron distributions.

Findings

$ppa$ generally decreases during instability saturation, indicating suprathermal electron energization.

In low-beta regimes with high initial $ppa$, distributions tend toward Maxwellian shapes.

Wave fluctuations partially relax temperature anisotropy but also energize suprathermal electrons.

Abstract

In recent years, significant progress has been made in the velocity-moment-based quasi-linear (QL) theory of waves and instabilities in plasmas with nonequilibrium velocity distributions (VDs) of the Kappa (or $\kappa$) type. However, the temporal variation of the parameter $\kappa$, which quantifies the presence of suprathermal particles, is not fully captured by such a QL analysis, and typically $\kappa$ remains constant during plasma dynamics. We propose a new QL modeling that goes beyond the limits of a previous approach, realistically assuming that the quasithermal core cannot evolve independently of energetic suprathermals. The case study is done on the electron-cyclotron (EMEC) instability generated by anisotropic bi-Kappa electrons with $A=T_\perp/T_\parallel > 1$ ($\parallel, \perp$ denoting directions with respect to the background magnetic field). The parameter $\kappa$ self-consistently varies through the QL equation of kurtosis (fourth-order moment) coupled with temporal variations of the temperature components, relaxing the constraint on the independence of the low-energy (core) electrons and suprathermal high-energy tails of VDs. The results refine and extend previous approaches. A clear distinction is made between regimes that lead to a decrease or an increase in the $\kappa$ parameter with saturation of the instability. What predominates is a decrease in $\kappa$, i.e., an excess of suprathermalization, which energizes suprathermal electrons due to self-generated wave fluctuations. Additionally, we found that VDs can evolve toward a quasi-Maxwellian shape (as $\kappa$ increases) primarily in regimes with low beta and initial kappa values greater than five. Instability-driven relaxation only partially resolves temperature anisotropy in bi-Kappa electron VDs, as wave fluctuations generally act to further energize suprathermal electrons.