Simulation study of the harmonic structure of lower hybrid waves driven by energetic ions

By means of one-dimensional, electromagnetic, particle-in-cell simulations considering the effects energetic-ion injection, we study harmonic structure lower hybrid waves (LHWs) driven by energetic ions under condition where electron plasma frequency (${\ensuremath{\omega}}_{pe}$) is smaller than cyclotron (${\mathrm{\ensuremath{\Omega}}}_{e}$). It found that after LHWs are excited with wave number and (${k}_{1},{\ensuremath{\omega}}_{1}$), many generated at ($m{k}_{1},n{\ensuremath{\omega}}_{1}$) $m$ $n$ integers, up to far beyond resonance frequency, $n\ensuremath{\sim}10$. We show nonlinear wave-wave coupling between directly above frequency. also find can exist even artificially removed because they be coupled ion Bernstein due bulk ions. The effect injection dependence ${\ensuremath{\omega}}_{pe}/{\mathrm{\ensuremath{\Omega}}}_{e}$ on development investigated compare simulation results an observation in Earth's magnetosphere.