Second Harmonic Emision During Solar Flares

Abstract

Type III (type U) radio bursts are signatures of energetic electrons generated during solar flares, traveling along open (closed) magnetic coronal field lines. The burst photons correspond to the second harmonic of the plasma frequency and are generated by the coalescence of two Langmuir waves excited by the beam. In the present paper we derive expressions for the emissivity and absorption in the second harmonic of the plasma frequency without assuming the so-called head-on approximation. Only plasma wave isotropy is assumed. The resulting expressions yield important reductions in the emissivity when compared to the head-on results, as well as to lower absorption coefficients. We calculate second harmonic emissivities for several electron beam intensities. The spectrum of Langmuir turbulence used to compute second harmonic emissivity is consistently derived from a model that includes collisional effects and quasilinear relaxation. We speculate that further reductions in the emissivity, down to levels compatible with observations, would be obtained if nonlinear scattering of Langmuir waves with ion-acoustic turbulence and background density inhomogeneities are considered.