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We study frequency variation of a coherent whistler-mode wave in a homogeneous magnetic field by a self- consistent simulation model. Simulation results show that an injected whistler-mode wave packet grows due to an instability driven by temperature anisotropy and the amplified wave packet triggers emissions with frequency shift during its propagation. We clarify that the resonant currents JE and JB due to the nonlinear wave-particle interaction play significant roles in both wave growth and frequency variation. Based on the simulation results, we show that the range of the frequency shift in a homogeneous system is quantitatively estimated by the trapping frequency VT of trapped electrons; in a case that the original frequency of the wave packet is 0.62 e and VT = 4.05 × 10−2c, the lower and upper frequencies are estimated to be 0.565 e and 0.685 e, respectively. The results of the present study reveal that the role of nonlinear trapping is significant in the elementary process of VLF triggered emissions in the equatorial region of the magnetosphere.

Simulation study on nonlinear frequency shift of narrow band whistler-mode waves in a homogeneous magnetic field