Generation of Harmonic Emission of Type III Radio Bursts in Strongly Inhomogeneous Plasma

Harmonic emission from plasma is a well-known feature of solar type III radio bursts. It commonly dominates closer to the Sun, i.e. on higher frequencies, while fundamental emission dominates on larger distances. Often harmonic emission reveals interesting properties, for instance, it can be brighter than fundamental within certain frequency range. Disregarding big observational base and strong research interest, there still remain long-standing problems concerning type III harmonic emission. Some of them, like anomalous harmonic-to-fundamental ratio, long decay time of radiation etc. are supposed to be strongly associated with density fluctuations in solar wind. It indicates, that inhomogeneity may play a significant role in observed properties of type III radio emission. Numerous observations prove the existence of density fluctuations with a wide spectrum of scales within solar wind and corona. Here we are interested in how scattering of Langmuir waves on density fluctuations can produce harmonic electromagnetic emission by coalescence of incident and reflected wave in the vicinity of the reflection region. In present work we derive analytical expressions for scattering of Langmuir waves in inhomogeneous plasma. Density gradient of fluctuations is presented in a form of a linear profile. We perform a statistical averaging of energy transformation coefficient over density fluctuation amplitudes and scales. After we compare the efficiency of this process with the conventional wave-wave interaction in homogeneous plasma. So far, our results can be utilized to evaluate the efficiency of energy conversion from electrostatic to electromagnetic waves for fundamental and harmonic emission in presence of density fluctuations.