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

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 $f_{\mathrm{e}}$. We use weak turbulence theory and quasilinear theory to obtain a set of equations that describes the coupled evolution of $F_k$ and $f_{\mathrm{e}}$. 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 $E\in (E_{\mathrm{nt}},E_{\max })$. We obtain approximate analytic expressions for $E_{\mathrm{nt}}$ and $E_{\max }$, 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 $f_{\mathrm{e}}$ 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 $f_{\mathrm{e}}$ and closer to the values inferred from observations of solar flares.

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• The spectral evolution of impulsive solar X-ray flares
• RHESSI Line and Continuum Observations of Super-hot Flare Plasma
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Cited by in corpus (3)

• The Acceleration and Confinement of Energetic Electrons by a Termination Shock in a Magnetic Trap: An Explanation for Nonthermal Loop-top Sources during Solar Flares
• Turbulence and particle acceleration in a relativistic plasma
• Stochastic Electron Acceleration by Temperature Anisotropy Instabilities Under Solar Flare Plasma Conditions