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Stationary and impulsive injection of electron beams in converging magnetic field

In this work 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. The time dependent Fokker-Planck equation for electron distribution in depth, energy and pitch angle was solved numerically by using the summary approximation method. It was found that steady state injection is established for beam electrons at 0.07-0.2 seconds 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 less 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 a magnetic convergence. Short beam impulses are shown to produce sharp asymmetric hard X-ray bursts within a millisecond timescale often observed in solar flares.