Third and Fourth Harmonics of Electromagnetic Emissions by a Weak Beam in a Solar Wind Plasma with Random Density Fluctuations

Electromagnetic emissions ${{ \mathcal H }}_{3}$ and ${{ \mathcal H }}_{4}$ at the third and fourth harmonics of the plasma frequency ωp were observed during the occurrence of type II and type III solar radio bursts. Two-dimensional particle-in-cell simulations are performed using a weak beam, high space and time resolutions, and a plasma with density fluctuations of a few percent, for parameters relevant to regions of type III bursts. For the first time, a detailed study of the different wave coalescence processes involved in the generation of ${{ \mathcal H }}_{3}$ and ${{ \mathcal H }}_{4}$ waves is presented and the impact of density fluctuations on the wave interaction mechanisms is demonstrated. Energy ratios between the second, third, and fourth harmonics ${{ \mathcal H }}_{2}$, ${{ \mathcal H }}_{3}$, and ${{ \mathcal H }}_{4}$ are consistent with space observations. It is shown that, in both homogeneous and inhomogeneous plasmas, the dominant processes generating ${{ \mathcal H }}_{3}$ (${{ \mathcal H }}_{4}$) are the coalescence of ${{ \mathcal H }}_{2}$ (${{ \mathcal H }}_{3}$) with a Langmuir wave, in spite of the random density fluctuations modifying the waves' resonance conditions by energy transport in the wavevector space and of the damping of Langmuir waves. The role of the backscattered (forward-propagating) Langmuir waves coming from the first (second) cascade of the electrostatic decay of beam-driven Langmuir waves is determinant in these processes. Understanding such wave coalescence mechanisms can provide indirect information on Langmuir and ion acoustic wave turbulence, the average level of density inhomogeneities, and suprathermal electron fluxes generated in solar wind regions where the harmonics manifest. Causes for the rarity of their observations are discussed.