Effects of Heavy Ions on the Second-Harmonic Generation of EMIC Waves in the Inner Magnetosphere

Recent studies have reported electromagnetic ion cyclotron (EMIC) waves with nonlinear second harmonics (SHs) whose frequency and wave number are twice those of the fundamental waves (FWs). In this paper, we provide detailed analyses of the cross-band SH generation of EMIC waves in a multi-ion plasma. In the presence of heavy ions, EMIC wave modes can be divided into distinct wave bands according to heavy ion gyrofrequencies, and the SH can exist in a wave band different from that of the FW. The SH can be generated around or even exactly on the normal modes of the plasma system, leading to a more efficient energy transfer than that in H+-only plasmas. The detailed parametric analysis also manifests the vital role of heavy ions in promoting SH's amplitude. Further, multiple 1-D hybrid simulations are performed to investigate the cross-band SH generation and validate the theoretical results. The SHs are well reproduced in simulations and the quantitative relation of frequency and wave number between the FW and the SH is well satisfied. The variations of the amplitude ratios (the SH to the FW) with fundamental frequencies are well consistent with those obtained from theoretical calculations in magnitude. Therefore, our results demonstrate the significant roles of heavy ions in the SH generation.