Interplay of Boltzmann equation and continuity equation for accelerated electrons in solar flares
Abstract
During solar flares a large amount of electrons are accelerated within the plasma present in the solar atmosphere. Accurate measurements of the motion of these electrons start becoming available from the analysis of hard Xray imagingspectroscopy observations. In this paper, we discuss the linearized perturbations of the Boltzmann kinetic equation describing an ensemble of electrons accelerated by the energy release occurring during solar flares. Either in the limit of high energy or at vanishing background temperature such an equation reduces to a continuity equation equipped with an extra force of stochastic nature. This stochastic force is actually described by the well known energy loss rate due to Coulomb collision with ambient particles, but, in order to match the collision kernel in the linearized Boltzmann equation it needs to be treated in a very specific manner. In the second part of the paper the derived continuity equation is solved with some hyperbolic techniques, and the obtained solution is written in a form suitable to be compared with data gathered by hard Xray imagingspectroscopy telescopes. Finally, a first validation of the model with NASA Reuven Ramaty High Energy Solar Spectroscopic Imager spectrometer measurements is provided.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 arXiv:
 arXiv:1502.04534
 Bibcode:
 2015arXiv150204534C
 Keywords:

 Astrophysics  Solar and Stellar Astrophysics;
 76P05;
 82D10;
 85A25
 EPrint:
 submitted to SIAM/ASA Journal on Uncertainty Quantification