Parametric Dependence of Linear and Nonlinear Growth of Whistler-Mode Chorus Waves

We calculated the linear and nonlinear growth rates of whistler-mode chorus waves with relativistic treatment across different wave frequencies and investigated their dependence on the associated parameters, including background magnetic field strength, cold electron density, and energetic electron temperature. The linear and nonlinear growth rates, with respect to any of the three parameters in the range investigated, are confirmed to often exhibit a peak, at least, in the lower band (i.e., <0.5 f_ce, electron cyclotron frequency). For a given energetic electron temperature between 0.5 and 500 keV, both linear and nonlinear growth rates at low frequencies can be positive in a specific range of background magnetic field strength and cold electron density, with an optimum growth rate occurring when either parameter is fixed. However, as the electron temperature increases within this range, linear damping becomes more pronounced, resulting in a suppression of linear growth at high frequencies. On the other hand, as the strength of the magnetic field increases, a higher energetic electron temperature is required to sustain wave growth. Notably, nonlinear growth can still occur even when the linear growth rate is negative as previous studies have demonstrated. Parameters leading to such conditions are also demonstrated. Comparisons with previous chorus wave observations confirm the dependence on the parameters and explain the existence of an optimum wave growth condition and overlapping parameter ranges for both linear and nonlinear wave growth.