Since the discovery of the radiation belt in the late 1950s, studies on the production, transportation, and loss processes of high-energy particles have been discussed by many researchers. Recently, many satellites for radiation belt plasma measurement, such as Van Allen Probes, Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX), and Arase have been observing plasmas at various spatial and time scales (Baker et al., 1993; Mauk et al., 2012; Miyoshi et al., 2018). In addition, the theoretical and empirical models based on these observations have been developed. In terms of the dynamics of radiation belt plasmas, the penetration of energetic particles deep into the inner magnetosphere as a transient response to solar energetic proton events has been studied through both observations and models (for example,