Resonant Interactions Between Relativistic Electrons and EMIC Waves Modified by Partial Shell Proton Velocity Distributions

Resonant interactions of relativistic electrons with electromagnetic ion cyclotron (EMIC) waves were previously considered under the cold plasma approximation or in hot plasmas with bi-Maxwellian distributions. Here, we examine their resonant interactions in hot plasmas with partial shell distributions and find that such distributions can significantly alter the dispersion relation of EMIC waves and thus the corresponding wave-induced electron pitch angle scattering rates and loss timescales compared to those under the cold plasma assumption. Regardless of wave band and frequency, partial shell distributed hot protons tend to uplift the electron minimum resonant energy, and reduce (raise) the pitch angle scattering rates of electrons at low (high) energies and large (small) pitch angles. Correspondingly, the loss timescales lengthen for low-energy electrons but shorten for high-energy electrons. Such tendencies are generally more significant for lower-frequency EMIC waves and larger shell temperature, anisotropic degree, and concentration. Electromagnetic ion cyclotron (EMIC) waves below the proton gyrofrequency can cause pitch angle scattering loss of relativistic electrons via cyclotron resonant interactions. The dispersion relation, the relation between the wave frequency and the wave number, is crucial in calculating the pitch angle scattering rates to quantify the loss of electrons induced by EMIC waves. The cold plasma dispersion relation obtained by assuming that particles are absolutely cold is widely used but recently demonstrated to be not always applicable. Usually, the kinetic dispersion relations of EMIC waves in the hot plasmas with bi-Maxwellian distributions are adopted as an alternative. However, recent observations show that EMIC waves are often accompanied by protons with shell-type distributions, a spherical shell of protons in the velocity space, significantly deviating from bi-Maxwellian distributions. How such type of velocity distributions affects the resonant interactions of relativistic electrons with EMIC waves remains unknown. Compared to the cold plasma dispersion relation, we show that shell-type distributed hot protons can significantly modify the dispersion relation of EMIC waves and thus the corresponding wave-induced electron pitch angle scattering rates and loss timescales. These results highlight the importance of taking appropriate hot plasma distributions in quantifying the EMIC wave-induced electron pitch angle scattering efficiency and in future modeling the radiation belt dynamics. Partial shell distributed hot protons can significantly modify the resonant interactions of relativistic electrons with electromagnetic ion cyclotron (EMIC) waves The modification is highly frequency-dependent and is more pronounced for lower-frequency EMIC waves of H+ and He+ band The modification is generally more pronounced as the shell temperature, anisotropic degree, and concentration increase