A Quasi-Linear Diffusion Model for Resonant Wave-Particle Instability in Homogeneous Plasma

TL;DR

This paper introduces a quasi-linear diffusion model for wave-particle instability in homogeneous plasma, combining analytical Gaussian wave packet representation with numerical Crank-Nicolson solutions, applied to solar wind electron scattering.

Contribution

It develops a novel quasi-linear diffusion model using Gaussian wave packets and a numerical Crank-Nicolson scheme for plasma wave-particle interactions.

Findings

The model accurately describes the velocity-space evolution of particles.

Numerical results agree with theoretical predictions.

Application to solar wind electrons demonstrates the model's relevance.

Abstract

In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a Gaussian wave packet, allowing for an arbitrary direction of propagation with respect to the background magnetic field. We show that the localized energy density of the Gaussian wave packet determines the velocity-space range in which the dominant wave-particle instability and counter-acting damping contributions are effective. Moreover, we derive a relation describing the diffusive trajectories of resonant particles in velocity space under the action of such an interplay between the wave-particle instability and damping. For the numerical computation of our theoretical model, we develop a mathematical approach based on the Crank-Nicolson scheme to solve the full quasi-linear diffusion equation. Our numerical analysis solves the time evolution of the velocity distribution function under the action of a dominant wave-particle instability and counteracting damping and shows a good agreement with our theoretical description. As an application, we use our model to study the oblique fast-magnetosonic/whistler instability, which is proposed as a scattering mechanism for strahl electrons in the solar wind. In addition, we numerically solve the full Fokker-Planck equation to compute the time evolution of the electron-strahl distribution function under the action of Coulomb collisions with core electrons and protons after the collisionless action of the oblique fast-magnetosonic/whistler instability.