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Abstract Radiation belt electrons can be accelerated and scattered by magnetosonic waves in the Earth's magnetosphere, and the scattering rate of electrons is sensitive to the wave normal angle. However, observationally it is difficult to identify the wave normal angle within a few degrees. In this study, using 2‐D particle‐in‐cell (PIC) simulations, we investigate the wave normal angle distribution of magnetosonic waves excited by ring distribution protons. Both the linear theory and simulations have shown that the wave normal angles are distributed over a narrow range (82°–89°) with a major peak at about 85° during the linear growth stage when the proton ring velocity is close to the Alfven speed. In addition, 2‐D PIC simulations further demonstrated that the waves tend to have larger wave normal angles (84°–89°) during the saturation stage since the waves with smaller wave normal angles are dissipated faster. It is also found that wave normal angles decrease with the increase of wave frequency. With the increase of the ring velocity of the proton ring distribution, the perpendicular wavenumber of excited magnetosonic waves decreases, which leads to the decrease of the wave normal angle. The simulation results provide a valuable insight to understand the property of magnetosonic waves, and the findings are useful for the global simulations of radiation belt dynamics. 

Abstract Recent observations have reported that magnetosonic waves can exhibit rising‐tone structures in the frequency‐time spectrogram. However, the generation mechanism has not been identified yet. In this paper, we investigate the generation of rising‐tone magnetosonic waves in the terrestrial magnetosphere using 1‐D particle‐in‐cell (PIC) simulations, in which the plasma consists of three components: cool electrons, cool protons and ring distribution protons. We find that the magnetosonic waves excited by the ring distribution protons can form a rising‐tone structure with frequency of the structure ranging from about0.5Ω_lhto nearlyΩ_lh, whereΩ_lhis the lower hybrid frequency. It is further demonstrated that the rising frequency of magnetosonic waves can be accounted for by the scattering of ring distribution protons. Moreover, the rising‐tone timescale obtained by PIC simulation is compared with the satellite observation. Our findings provide some new insights to understand the nonlinear evolution of plasma waves in the Earth's magnetosphere.