The role of diffusion in the transport of energetic electrons during solar flares

Abstract

The transport of the energy contained in suprathermal electrons in solar flares plays a key role in our understanding of many aspects of flare physics, from the spatial distributions of hard X-ray emission and energy deposition in the ambient atmosphere to global energetics. Historically the transport of these particles has been largely treated through a deterministic approach, in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or even neglected. We here critically analyze this approach, and we show that spatial diffusion through pitch-angle scattering necessarily plays a very significant role in the transport of electrons. We further show that a satisfactory treatment of the diffusion process requires consideration of non-local effects, so that the electron flux depends not just on the local gradient of the electron distribution function but on the value of this gradient within an extended region encompassing a significant fraction of a mean free path. Our analysis applies generally to pitch-angle scattering by a variety of mechanisms, from Coulomb collisions to turbulent scattering. We further show that the spatial transport of electrons along the magnetic field of a flaring loop can be modeled rather effectively as a Continuous Time Random Walk with velocity-dependent probability distribution functions of jump sizes and occurrences, both of which can be expressed in terms of the scattering mean free path.

arXiv comment11 pages, to be published in Astrophysical Journal

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• Si IV Resonance Line Emission During Solar Flares: Non-LTE, Non-equilibrium, Radiation Transfer Simulations
• Particle Acceleration and Fractional Transport in Turbulent Reconnection
• Determination of the total accelerated electron rate and power using solar flare hard X-ray spectra
• Numerical Modeling of Energetic Electron Acceleration, Transport, and Emission in Solar Flares: Connecting Loop-top and Footpoint Hard X-Ray Sources
• Heating and cooling of coronal loops with turbulent suppression of parallel heat conduction
• A Fokker-Planck Framework for Studying the Diffusion of Radio Burst Waves in the Solar Corona
• Coronal Loop Scaling Laws for Various Forms of Parallel Heat Conduction
• Synergy of stochastic and systematic energization of plasmas during turbulent reconnection
• Energy Deposition by Energetic Electrons in a Diffusive Collisional Transport Model
• Particle acceleration with anomalous pitch angle scattering in 2D MHD reconnection simulations
• The invariance of the diffusion coefficient with the iterative operations of charged particles' transport equation
• Study of momentum diffusion with the effect of adiabatic focusing