Mirror-Mode Instability versus L-Mode Electromagnetic Ion Cyclotron Instability: Comparison of 2-D and 3-D Simulations

Spacecraft observations show that the mirror instability dominates over the L-mode electromagnetic ion cyclotron (EMIC) instability in the terrestrial magnetosheath, although the theoretical linear growth rate of the L-mode EMIC wave is higher than that of the mirror mode waves. This has been a long-standing puzzle. To analyze the competing processes between the L-mode instability and the mirror instability, we have performed multi-dimensional hybrid simulations, assuming anisotropic energetic ions. In the 2D model, the energy of the L-mode wave is higher at the initial stage in a good agreement with the linear theory. However, in the 3D simulation, the mirror mode wave can gain much higher amplitude than the L-mode EMIC wave in both linear and nonlinear stages. Results issued from the 3D model evidence a torus-shape emission in the energy spectra (not accessible in the 2D model). The growth of the L-mode EMIC waves declines earlier in the 3D model than that in the 2D model, due to efficient proton scattering by the mirror mode waves. To understand the nonlinear processes, we have performed 2D and 3D hybrid simulations with higher spatial resolutions. The L-mode EMIC waves are subject to inverse-cascade in the 2D model, while this is not the case in the 3D model, so hence it vanishes. We analyzed the inverse-cascade of the L-mode EMIC waves. We also find that the nonlinear evolution of the mirror waves in the 3D model is significantly different from that in the 2D model. Although coalescence of the mirror mode structures takes place in both models, coalescence in the 3D case is much more rapid than 2D. The transfer of energy between electromagnetic fields and ions (heating) is analyzed both in linear and nonlinear stages.