Modeling complex plasma instabilities in space plasmas

Three-component electron formalism of heat-flux instabilities

¹ Institute for Theoretical Physics IV, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
² Centre for mathematical Plasma-Astrophysics, KU Leuven, 3001 Leuven, Belgium
³ Research Center in the intersection of Plasma Physics, Matter, and Complexity ( P 2 mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
⁴ Departamento de Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212 Santiago 8370136, Chile
⁵ Institute of Physics, University of Maria Curie-Skłodowska, ul. Radziszewskiego 10, 20-031 Lublin, Poland

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 23 December 2025
Accepted: 16 March 2026

Abstract

Context. Despite the fact that electrons observed in situ in space plasmas have three major components – the quasi-thermal core, suprathermal halo, and strahl – the analysis of instabilities triggered by kinetic, velocity-space anisotropies (such as relative drifts and temperature anisotropy) generally considers only two of these components.

Aims. We aim to demonstrate that a realistic modeling with all three components is achievable in the present analysis focusing on heat-flux instabilities. In the absence of particle–particle collisions, these instabilities are responsible for the regulation of the heat flux carried mainly by suprathermal electrons.

Methods. The velocity distributions of the electron populations were modeled according to in situ observations, with a Maxwellian core and Kappa-distributed halo and strahl components. We exploited new advanced numerical codes capable of solving the linear dispersion and stability properties of any plasma system with Maxwellian- and Kappa-distributed populations.

Results. The unstable solutions differ significantly from those obtained with simplified models with only two components (such as core-strahl or core-beam models). The growth rates predict the systematic excitation and interplay of two unstable modes, whistler heat-flux and/or fire-hose heat-flux instabilities. The numerical solver “ALPS” was successfully applied to systems with regularized Kappa distributions, for which the analytical derivation of dispersion relations is not straightforward.

Conclusions. The two instabilities are triggered by the two relative drifts, core-strahl and halo-strahl, and may have new consequences concerning the regulation of the heat flux. Particularly important are the cases when the core-strahl instability known from previous studies is in competition with the new instability driven by the halo-strahl drift, as well as when the two instabilities have the same nature and can accumulate. Future studies are thus motivated to confirm these predictions in quasilinear theories and numerical simulations.