The Formation of Kappa-Distribution Accelerated Electron Populations in Solar Flares

Abstract

Driven by recent RHESSI observations of confined loop-top hard X-ray sources in solar flares, we consider stochastic acceleration of electrons in the presence of Coulomb collisions. If electron escape from the acceleration region can be neglected, the electron distribution function is determined by a balance between diffusive acceleration and collisions. Such a scenario admits a stationary solution for the electron distribution function that takes the form of a kappa distribution. We show that the evolution toward this kappa distribution involves a "wave front" propagating forwards in velocity space, so that electrons of higher energy are accelerated later; the acceleration time scales with energy according to ${\tau }_{\mathrm{acc}}\sim E^{3/2}$. At sufficiently high energies escape from the finite-length acceleration region will eventually dominate. For such energies, the electron velocity distribution function is obtained by solving a time-dependent Fokker-Planck equation in the "leaky-box" approximation. Solutions are obtained in the limit of a small escape rate from an acceleration region that can effectively be considered a thick target.

accepted to Astrophysical Journal

References in corpus (5)

• Particle acceleration mechanisms
• Stereoscopic electron spectroscopy of solar hard X-ray flares with a single spacecraft
• Kappa distribution and hard X-ray emission of solar flares
• Effect of collisions and magnetic convergence on electron acceleration and transport in reconnecting twisted solar flare loops
• On the variation of solar flare coronal x-ray source sizes with energy

Cited by in corpus (16)

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• Determination of the total accelerated electron rate and power using solar flare hard X-ray spectra
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• Imaging and Spectroscopic Observations of a Transient Coronal Loop: Evidence for the Non-Maxwellian $\kappa$-Distributions
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• Solar Flare Heating with Turbulent Suppression of Thermal Conduction