Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

Two‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation. Plain Language Summary Recent studies have unveiled the generation of nonlinear second harmonics (SH) of electromagnetic ion cyclotron (EMIC) waves. The SH is nonlinearly driven by the fundamental wave (FW) and satisfies the necessary conditions: ω2 = 2ω1 and k2 = 2k1, where ω1 (ω2) and k1 (k2) are the frequency and the wave vector of the FW (SH), respectively. Previous studies have relied on one‐dimensional (1‐D) hybrid simulations to investigate the SH. However, 1‐D simulations allow waves to propagate along a single dimension and lack spatial variation of the field orthogonal to this dimension, which impedes the complete verification of the relation k2//k1. Thus, in this study, the SH generation is modeled by two‐dimensional (2‐D) hybrid codes. The simulated SH exhibits characteristics similar to typical EMIC waves with left‐hand polarization and small wave normal angle. The bicoherence index is utilized to reveal the phase coupling between the SH and FW. The necessary conditions, especially for the wave vector relation, are verified from a 2‐D perspective for the first time. Additionally, the amplitude ratios of the SH to the FW and their phase velocities are compared with theoretical results. The comprehensive analyses of this study provide substantial evidence for the SH generation mechanism. Key Points Two‐dimensional (2‐D) hybrid codes are developed to model the nonlinear second‐harmonic (SH) generation of electr