Magnetosonic Harmonic Falling and Rising Frequency Emissions Potentially Generated by Nonlinear Wave-Wave Interactions in the Van Allen Radiation Belts

Magnetosonic waves play a potentially important role in the complex evolution of the radiation belt electrons. These waves typically appear as discrete emission lines along the proton gyrofrequency harmonics, consistent with the prediction of the local Bernstein mode instability of hot proton ring distributions. Magnetosonic waves are nearly dispersionless particularly at low harmonics and therefore have the roughly unchanged frequency time structures during the propagation. On the basis of Van Allen Probes observations, we here present the first report of magnetosonic harmonic falling and rising frequency emissions. They lasted for up to 2hr and occurred primarily in the dayside plasmatrough following intense substorms. These harmonic emission lines were well spaced by the proton gyrofrequency but exhibited a clear falling (rising) frequency characteristic in a regime with the temporal increase (decrease) of the proton gyrofrequency harmonics. Such unexpected structures might be produced by the nonlinear interactions between the locally generated magnetosonic waves at the proton gyrofrequency harmonics and a constant frequency magnetosonic wave propagating away from the Earth.