Saturation Characteristics of Multi‐Band EMIC Waves in the Inner Magnetosphere and Observational Evidence for the Second Saturation Process

The wave amplitude is vital for quantifying the impact of electromagnetic ion cyclotron (EMIC) waves on inner magnetospheric dynamics. Previous numerical studies mainly focused on the evolution of total wave energy/amplitude, whose maximum is usually modeled as a function of initial conditions. Recent quasilinear theory analysis shows existence of a second saturation of multi‐band EMIC waves which exhibits a dip of the total amplitude, emphasizing the need for more precise band‐specific models. Through one‐dimensional hybrid simulations, we reproduce the second saturation phenomenon and separately model wave characteristics for H+‐ and He+‐bands waves, including the maximum amplitudes and the time to maximum as a function of the initial maximum growth rate. Moreover, new parameters for the anisotropy‐beta inverse correlation of hot protons are obtained at the second saturation stage. We further present an in situ observation that first demonstrates the existence of the second saturation. Plain Language Summary Electromagnetic ion cyclotron (EMIC) waves can be naturally generated by hot protons with frequencies below the proton gyrofrequency. In the inner magnetosphere, the presence of heavy ions, such as helium and oxygen ions, leads to the classification of EMIC waves into distinct bands separated by the heavy ion gyrofrequencies. The wave properties and evolution characteristics can vary significantly across different bands, influencing their role in plasma dynamics. This study employs one‐dimensional hybrid simulations to separately model the wave characteristics across different bands, which has seldom been done yet. The maximum amplitude and the time to maximum are well modeled by simple two‐parameter power law functions of the initial maximum growth rate through the optimal fitting. Furthermore, the simulations capture the phenomenon of “second saturation” where a new saturation stage occurs after the usual first saturation. We also identify an anisotropy‐beta inverse correlation for hot protons at the second saturation stage. Importantly, we provide the first direct observational evidence of the second saturation, demonstrating strong agreement between observational data and simulation results. Key Points A series of one‐dimensional hybrid simulations are conducted to investigate the saturation process of parallel H+‐ and He+‐band EMIC waves Wave characteristics in H+‐ and He+‐ bands are separately parameterized as a function of the initial maximum