Statistical analysis on the validity of the cold plasma approximation for chorus waves based on Van Allen Probe observations and their effects on radiation belt electrons

Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons. Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption. However, the applicability of the cold plasma assumption is doubtful, especially during geomagnetic disturbances. We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018. The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density. The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases. In addition, the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves. Compared with usage of the cold plasma dispersion relation, usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below. Furthermore, these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.