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 of energetic-ion injection, we study the harmonic structure of lower hybrid waves (LHWs) driven by energetic ions under the condition where the electron plasma frequency (ω_{pe}) is smaller than the electron cyclotron frequency (Ω_{e}). It is found that after the LHWs are excited with the wave number and frequency of (k_{1},ω_{1}), many harmonic LHWs are generated at (mk_{1},nω_{1}) where m and n are integers, up to far beyond the lower hybrid resonance frequency, m and n∼10. We show that the harmonic LHWs are generated by nonlinear wave-wave coupling between the LHWs directly excited by the energetic ions and the energetic-ion cyclotron waves above the lower hybrid resonance frequency. We also find that the harmonic LHWs can exist even after the energetic ions are artificially removed because they can be coupled with ion Bernstein waves due to bulk ions. The effect of the energetic-ion injection and the dependence of ω_{pe}/Ω_{e} on the development of the harmonic LHWs are investigated to compare the simulation results with an observation in Earth's magnetosphere.