The main aim of this study is to examine whether the combined scattering effects simultaneously induced by different plasma waves can be treated as the linear superposition (LS) of independent scattering effect caused by each single wave mode or not. Accordingly, this study investigates the individual and combined scattering effects of simultaneous H + and He~+ band electromagnetic ion cyclotron (EMIC) waves as an example. Both quasi-linear theory and test particle simulations have been applied to evaluate the scattering effects in the form of diffusion rates and single particle tracing. The narrowband EMIC waves with amplitudes (1, 5, and 10 nT) and monochromatic EMIC waves with amplitudes ranging from 0.1 to 10 nT have been adopted in this study to involve both linear and nonlinear resonant scattering effects. The analysis on resonant condition indicates that H + and He~+ band EMIC waves can simultaneously scatter electrons with the same energies and pitch angles. For both narrowband and monochromatic EMIC waves, the combined diffusion rates induced by simultaneous two band waves are consistent with the LS of independent scattering rates caused by single band waves. The following single particle tracing presents two different wave-particle interaction conditions at different magnetic latitudes. In conclusion, our results suggest that the linear superposed scattering results can effectively evaluate the combined resonant scattering effects driven by two-band EMIC waves, which can easily be generalized to estimate the combined scattering effects simultaneously induced by different plasma waves for radiation belt modeling.
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