Relaxation and bremsstrahlung of thick-target electron streams: A simple application of the Legendre expansion method

Relaxation of a stationary, axisymmetric electron stream in a homogeneous and fully ionized hydrogen plasma is considered, taking into account quasi-linear and Coulomb interactions. The technique used is based on the Legend Legendre series expansion of the 3D equations for the electronic velocity and Langmuir wave distributions. The expansions are truncated for l> or =2 and the resulting equations are solved numerically, under the assumption that the waves are everywhere locally in equilibrium with the electron velocity distribution. A Fokker-Planck system of equations is used for the electrons, which has the advantage that the distinction between background and stream electrons disappears. Thus, the problem of the low energy cut-off is eliminated.The bremsstrahlung associated with the isotropic component of the electron distribution is computed, and in this way a simple model is obtained for the radiation emerging from thick-target electron streams, e.g., in the impulsive phase of solar flares.The analysis in this paper applies only to electron streams with a broad forward directional velocity distribution (deltatheta/sub upsilon/> or approx. =1000 FWHM).The results of our work indicate that power law-like bremsstrahlung spectra such as they are often observed can be produced fairly easily