Stochastic Acceleration of Electrons by Fast Magnetosonic Waves in Solar Flares: the Effects of Anisotropy in Velocity andWavenumber Space

TL;DR

This paper presents a two-dimensional, anisotropic model for electron acceleration in solar flares driven by fast magnetosonic waves, incorporating wave-particle interactions, collisions, and electric fields, and compares results with observations.

Contribution

It introduces a novel 2D anisotropic model for stochastic electron acceleration in solar flares, extending previous isotropic models and providing analytic expressions for energy bounds.

Findings

Electron distribution develops a power-law tail within a specific energy range.

Electron spectra are softer and closer to observations than in isotropic models.

Model results agree qualitatively with observed hard-x-ray spectra from solar flares.

Abstract

We develop a model for stochastic acceleration of electrons in solar flares. As in several previous models, the electrons are accelerated by turbulent fast magnetosonic waves ("fast waves") via transit-time-damping (TTD) interactions. (In TTD interactions, fast waves act like moving magnetic mirrors that push the electrons parallel or anti-parallel to the magnetic field). We also include the effects of Coulomb collisions and the waves' parallel electric fields. Unlike previous models, our model is two-dimensional in both momentum space and wavenumber space and takes into account the anisotropy of the wave power spectrum $F_k$ and electron distribution function $f_{\rm e}$. We use weak turbulence theory and quasilinear theory to obtain a set of equations that describes the coupled evolution of $F_k$ and $f_{\rm e}$. We solve these equations numerically and find that the electron distribution function develops a power-law-like non-thermal tail within a restricted range of energies $E\in (E_{\rm nt}, E_{\rm max})$. We obtain approximate analytic expressions for $E_{\rm nt}$ and $E_{\rm max}$, which describe how these minimum and maximum energies depend upon parameters such as the electron number density and the rate at which fast-wave energy is injected into the acceleration region at large scales. We contrast our results with previous studies that assume that $F_k$ and $f_{\rm e}$ are isotropic, and we compare one of our numerical calculations with the time-dependent hard-x-ray spectrum observed during the June 27, 1980 flare. In our numerical calculations, the electron energy spectra are softer (steeper) than in models with isotropic $F_k$ and $f_{\rm e}$ and closer to the values inferred from observations of solar flares.