Towards a theory for type III solar radio bursts

The mechanisms for the transformation of plasma waves into radiation near the fundamental and second harmonic of the plasma frequency are reviewed and equations are given for both the emission and absorption coefficients for these mechanisms. Near the fundamental the process is the scattering of plasma waves on the polarization clouds of ions and the absorption coefficient can be negative, i.e. the radiation can be amplified. Near the second harmonic the process is the combination of two excited plasma waves for which the absorption coefficient can only be positive. These results are applied to construct models of the radiation source for type III solar radio bursts both at high frequencies where the fundamental is dominant and at low frequencies where the second harmonic is dominant using two model plasma wave spectra, one being one-dimensional, the other isotropic. At high frequencies second harmonic radiation is used to determine the source area for a given energy density in plasma waves W _p . The source size and W _p are detrmined uniquely for a given plasma wave spectrum by tracing rays in a model source taking into account amplification of the fundamental. The results for a strong source at the 80 MHz plasma level with a ratio of emissivities of the fundamental to second harmonic P(ω _p )/P(2ω _p ) ≈ 10 are that the source with a one-dimensional plasma wave spectrum is about 14000 km in diameter and W _p = 10^?6.52 erg cm^?3, and the source with an isotropic distribution of plasma waves is about 200 km in diameter and W _p = 10^?6.3 erg cm^?3. It is shown that at low frequencies, where amplification of the fundamental is no longer possible, second harmonic radiation must be dominant and thus very little information about the source can obtained from the radiation.