Simulation on the Mechanism of Harmonic Maser Emission through the Wave Coalescence Process

Electron Cyclotron Maser Emission (ECME) driven by electrons with loss-cone distribution is the main mechanism for explaining solar radio spikes. However, in strongly magnetized plasmas, the losscone-driven ECME mainly generates fundamental X mode emissions, which can be efficiently absorbed when escaping through the second-harmonic layer in the solar corona. To solve the "escaping difficulty", recent studies suggested a new mechanism of harmonic maser emission (X2) involving nonlinear wave coupling process of Z-mode and fundamental X-mode (X1) waves (Z+Z$\to$X2, Z+X1$\to$X2). It is necessary to verify the nonlinear wave coalescence process with theoretical analyses and numerical simulations. Here, the possibility of a nonlinear wave coupling process is examined via solving the matching conditions for three-wave resonant interaction based on the dispersion relation of cold plasma in magneto-ionic theory. The matching conditions for the Z and/or X1 waves were found to be satisfied over a wide range of parameters, leading to the production of X2 emissions that propagate perpendicularly and obliquely relative to the direction of the background magnetic field. Based on the solutions obtained in the matching condition analysis, we selected four sets of solutions of Z+Z and Z+X1 to perform particle-in-cell simulations using wave pumping method, to verify the nonlinear process of wave coalescence generating second harmonic X-mode emissions. With X1 and/or Z modes correctly pumped in the simulation domain, efficient generation of X2 emissions was observed, with saturation achieved within 400 ${\Omega }_{\text{ce}}^{-1}$. The conversion rate of energies of X2 emissions to Z mode waves varies from 2% to 8%. The study presents strong evidence to support the new mechanism of harmonic maser emission, which can be widely applied to explain the solar and space radio emissions.