Stationary and impulsive injection of electron beams in converging magnetic field

Department of Mathematics, University of Bradford, Bradford BD7 1DP, UK e-mail: taras.siversky@gmail.com

Received: 16 April 2009
Accepted: 5 June 2009

Abstract

Aims. We study time-dependent precipitation of an electron beam injected into a flaring atmosphere with a converging magnetic field by considering collisional and Ohmic losses with anisotropic scattering and pitch angle diffusion. Two injection regimes are investigated: short impulse and stationary injection. The effects of converging magnetic fields with different spatial profiles are compared and the energy deposition produced by the precipitating electrons at different depths and regimes is calculated.

Methods. The time dependent Fokker-Planck equation for electron distribution in depth, energy and pitch angle was solved numerically by using the summary approximation method.

Results. Steady state injection was found to be established for beam electrons 0.07–0.2 s after the injection onset depending on the initial beam parameters. Energy deposition by a stationary beam is strongly dependent on a self-induced electric field but more weakly dependent on a magnetic field convergence. Energy depositions by short electron impulses are found to be insensitive to the self-induced electric field but are strongly affected by magnetic convergence. Short beam impulses are shown to produce sharp asymmetric hard X-ray bursts on a timescale of the order of tens of milliseconds, often observed in solar flares.