We quantify the electron scattering effects of simultaneous plasmaspheric hiss and magnetosonic waves that occurred in two neighboring time intervals but with distinct wave intensity profiles on 21 August 2013. Their combined scattering is found capable of causing electron distribution variations largely distinguishable from the consequences of individual waves. The net effect of electron diffusion relies strongly on the relative dominance of the two wave intensities, which also controls the relative contribution of each wave mode. In combination, MS waves slow down the hiss‐induced loss of ~100 keV electrons, and hiss efficiently inhibits the electron butterfly distribution caused by MS waves to produce a gradual acceleration process. Our results strongly suggest that comprehensive simulations of the radiation belt electron dynamics should carefully incorporate the combined scattering and complex competition resulting from simultaneous occurrences of various magnetospheric emissions, including, but not limited to, plamaspheric hiss and magnetosonic waves.

We develop a full relativistic test particle code to model the combined electron scattering effect of Landau and bounce resonances with magnetosonic waves. Test particle simulations of magnetosonic wave‐electron interactions indicate that the two resonances coexist to affect radiation belt electrons at different energies and pitch angles, and the resultant combined pitch angle scattering and energy diffusion can reach the rates of ~10−4 and ~10‐5 s, respectively, for electrons ~40–500 keV at pitch angles ~   70 ° –   80° for the given wave model (~200 pT) inside the plasmapause at L = 4.5. Comparisons with the quasi‐linear theory results show that the test particle combined scattering rates are generally an order of magnitude weaker, possibly because the electrons are moved out of the Landau resonance by the advective effect of the bounce resonance. Our investigation demonstrates that the Landau and bounce resonances with magnetosonic waves cannot be treated independently or additively in terms of quasi‐linear theory to simulate the associated radiation belt electron dynamics.

Low‐frequency hiss is known to play an important role in the precipitation of radiation belt electrons by cyclotron, Landau, and bounce resonances. To investigate the potential combined scattering effect caused by these resonant processes, we analyze the resonant conditions and develop a full relativistic test particle code to quantify the net pitch angle scattering efficiency. It is indicated that the three resonance processes can coexist to scatter electrons at different energies and pitch angles, with the net pitch angle scattering rates up to ~10−3 s−1 for low‐frequency hiss ~175 pT at L = 4.5. Comparisons with the quasi‐linear theory results demonstrate that the cyclotron resonance is mainly responsible for the pitch angle scattering of electrons < ~ 80°, while both Landau and bounce resonances can affect the scattering of near‐equatorially mirroring electrons and their combined diffusion produces smaller scattering coefficients compared to quasi‐linear theory calculations.

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Using the full relativistic test particle (TP) simulation code, we investigate the parametric dependence of electron scattering and phase space density evolution driven by magnetosonic (MS) waves at L = 4.5 both inside and outside the plasmapause. The scattering effects caused by Landau resonance, bounce resonance, and the transit-time effect are all involved in the study. The net scattering effects are evaluated in the form of diffusion coefficients with different combinations of MS wave parameters, such as frequency bandwidth and wave normal angle, and ambient plasma density. The results demonstrate that (1) Landau resonance and the transit-time effect dominate the electron scattering inside and outside the plasmapause, respectively, while both are modulated by bounce resonant scattering; (2) bounce resonant scattering becomes more important with narrowband MS waves; (3) electron scattering induced by MS waves is highly sensitive to wave normal angle. The temporal phase space density (PSD) evolution obtained from 2-D kinetic Fokker-Planck simulations shows that MS waves with larger wave normal angles are more likely to generate electron butterfly pitch angle distributions (PADs) for hundreds of keV electrons outside the plasmapause. Our study suggests that the electron butterfly distribution has important implications for revealing the combined scattering of MS wave-particle interactions, and the combination of the multiple scattering mechanisms should be carefully incorporated in future global modeling of radiation belt dynamics.