LAUSR

Although magnetosonic waves in the Earth’s magnetosphere have been well understood by the linear theory, low harmonic magnetosonic waves, which often lack of free energy, can be unusually present. By employing a 1-D particle-in-cell simulation model, we have investigated the generation of those unusual lower harmonic magnetosonic waves in a plasma containing a proton ring distribution. In our simulation, the higher harmonic magnetosonic waves (from~9Ωh to ~12Ωh) are firstly excited due to the unstable proton ring, which can be well explained by the linear theory. Several lower harmonic magnetosonic waves (below 5Ωh), which well separates away from the higher harmonics, soon appear in the system. Those lower harmonics, which do not have any positive linear growth rates, can be generated by a nonlinear mechanism. The bicoherence analysis demonstrates that there is a strong phase coupling among the unusual lower harmonic magnetosonic waves and the magnetosonic waves generated due to the proton ring, supporting the idea that the lower harmonic waves could be driven by the wave-wave couplings of the generated magnetosonic waves. This wave-wave coupling generation mechanism is further confirmed by another two simulations, where two or three pump magnetosonic waves are initially injected. The lower-frequency waves, that is, the fundamental wave and its second harmonic, are also successfully reproduced due to the nonlinear coupling of pumpmagnetosonic waves. Our simulations not only propose a potential generation mechanism of unusual lower harmonic magnetosonic waves in the Earth’s magnetosphere, but also give some new insights on the evolution of magnetosonic spectra. Plain Language Summary Over the past decades, the linear or quasi-linear theory has been successfully employed in describing the plasma waves and their interactions with charged particles in the space plasma. However, the unprecedented high-resolution satellite data (THEMIS, VAP, MMS, etc.) have discovered many intriguing phenomena in the Earth’s magnetosphere, which are not expected in the linear frame. This is why researchers begin to pay increasing attention to the nonlinear wave-particle and wave-wave interactions in space plasma. Many nonlinear processes related to whistler waves in the Earth’s magnetosphere have already been reported and studied. However, there are quite few works about nonlinear physics related to magnetosonic waves. Meanwhile, several lower harmonic magnetosonic waves, with lack of support from the linear instability, are observed in both satellite data and simulations. In this paper, we propose a new idea that the lower harmonic waves could be driven by the wave-wave couplings of the generated magnetosonic waves, which is supported by PIC simulations. This result suggests that the spectrum of magnetosonic waves in the Earth’s magnetosphere could be reshaped through nonlinear wave-wave interactions, which ultimately affects the electron dynamics in the Van Allen radiation belt.