Observational evidence of the nonlinear wave growth theory of plasmaspheric hiss

We test the recently developed nonlinear wave growth theory of plasmaspheric hiss against discrete rising tone elements of hiss emissions observed by the Van Allen Probes. From the phase variation of the waveforms processed by bandpass filters, we calculate the instantaneous frequencies and wave amplitudes. We obtain the theoretical relation between the wave amplitude and frequency sweep rates at the observation point by applying the convective growth rates and dispersion factors to the known relation at the equator. By plotting the theoretical relation over scatterplots of the wave amplitudes and the frequency sweep rates for rising tone elements, we find good agreement between the hiss observations and the nonlinear theory. We also find that the duration periods of the hiss elements are in good agreement with the nonlinear transition time necessary for the formation of a resonant current through coherent nonlinear wave-particle interactions.