Upstream Shift of Generation Region of Whistler-Mode Rising-Tone Emissions in the Magnetosphere

We have performed a series of simulation runs for whistler-mode wave-particle interaction in a parabolic magnetic field with 12 different frequencies of triggering waves and 3 different plasma frequencies specifying cold plasma densities. Under a given plasma condition, a specific frequency range of the triggering wave exists that can generate rising-tone emissions. The generation region of rising-tone emission shifts upstream. The velocity of the wave generation region is dependent on duration of the subpacket, which is controlled by the formation of the resonant current in the generation region. When the source velocity, which is a sum of the resonance and group velocities, is approximately the same as the velocity of the wave generation region, a long-sustaining rising-tone emission is generated. When the spatial and temporal gap between subpackets exists due to damping phase of short subpacket generation, resonant electrons in the gap of the subpackets are carried at the resonance velocity to the upstream region, and the velocity of the wave generation region becomes large in magnitude. When formation of resonant currents is delayed, the velocity of the generation region becomes smaller than the source velocity in magnitude. Below one quarter of the cyclotron frequency, coalescence of subpackets takes place, suppressing formation of the resonant current in the generation region. Since gradual upstream shift of the generation region is necessary for the wave to grow locally, the source velocity should be a small negative value.