Simulation for electron acceleration by DC electric field in the presence of ion sound waves and associated hard X-ray emission

Abstract

Time-dependent Fokker-Planck equation was numerically solved to demonstrate the dynamics of electrons in a uniform coronal loop with an applied axial DC electric field in the presence of ion-sound waves. This electric field is attributed to an anomalous resistivity due to the ion-sound turbulence caused by an initially given critical current density.

The electron momentum distribution becomes a steady state in the whole turbulent region in a short time for which some electrons can be accelerated to the maximum electric potential K _c. The steady energy distribution of electrons flowing out the end of the turbulent region has a very hard power-law-like spectrum with an index δ of about 0.75. The associated hard X-rays from a thick target also show a hard spectrum with a photon spectral index γ of 1.3. In order for γ to be much greater as observed in impulsive X-ray bursts, it is required that the source is a sum of many elementary loops with a power-law-like distribution in K _c with an index α = γ − δ + 2.5.