The stability of electron beams in the flaring solar corona

Abstract

The conditions required for the stability of a steady-state electron beam propagating in the solar corona are determined using the quasi-linear theory. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution function being given by an analytic solution of the linearized Fokker-Planck equation. It is shown that, when the gyrofrequency is less than the plasma frequency, the instability has a narrow angular range, with the maximum growth rate occuring along the magnetic field. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of the results for alternative models of hard X-ray bursts are discussed and it is argued that Langmuir instability will not occur on either the trap model or the thermal model. Such models would, therefore, be refuted by the detection of a large flux of plasma microwave radiation associated with hard X-ray emission.