Modeling the Transport of Nonthermal Particles in Flares Using Fokker-Planck Kinetic Theory

We describe a new approach for modeling the transport of high energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically solves the Fokker-Planck equation and includes forces corresponding to Coulomb collisions in a flux loop with nonuniform ionization, synchrotron emission reaction, magnetic mirroring and a return current electric field. Our solution to the Fokker-Planck equation includes second-order pitch angle and momentum diffusion. It is applicable to particles of arbitrary mass and charge. By tracking the collisions, we predict the bremsstrahlung produced as these particles interact with the ambient stellar atmosphere. This can be compared directly with observations and used to constrain the accelerated particle energy distribution. We have named our numerical code FP and have distributed it for general use. We demonstrate its effectiveness in several test cases.
Comment: Accepted for publication in the Astrophysical Journal, 19 pages, 7 figures