Beam‐generated Plasma Turbulence during Solar Flares

Abstract

We develop a simple theoretical model to analyze the harmonic plasma radiation produced by an electron beam injected in a flaring loop and traveling along its magnetic field lines. For a given atmospheric model, we consistently consider collisional effects and the generation of Langmuir waves as a function of the atmospheric depth. Langmuir wave generation is assumed to saturate by quasilinear relaxation, which in turn causes the electron distribution function to develop a plateau at its low-energy end. We formulate an iterative procedure to integrate the coupled equations for the electron distribution function and the wave energy density, taking advantage of the fact that quasilinear relaxation occurs on times much shorter than the collisional timescale. From the wave energy density as a function of depth, we computed the microwave flux generated by second harmonic radiation, taking into account the optical thickness due to the reverse process. Previous studies yield microwave fluxes much larger than those derived from observations. The smaller levels of turbulence obtained from this model, and the lower emissivity due to the relaxation of the head-on approximation, contribute to reduce significantly the predicted microwave emission. We suggest that the simplicity of the present model makes it suitable for the quantitative analysis of spatially resolved radio observations in the GHz range.