Full Particle Simulation of Whistler-Mode Triggered Falling-Tone Emissions in the Magnetosphere

We perform a one-dimensional electromagnetic full particle simulation for triggered falling-tone emissions in the Earth's magnetosphere. The equatorial region of the magnetosphere is modeled with a parabolic magnetic field approximation. The short whistler-mode waves with a large amplitude are excited and propagate poleward from an artificial current oscillating with a constant frequency and amplitude. Following the excited waves, clear emissions are triggered with a falling frequency. Without the inhomogeneity of the background magnetic field, no triggered emission appears. The falling tone has several subpackets of amplitude and decreases the frequency in a stepwise manner. The positive resonant current formed by resonant electrons in the direction of the wave magnetic field clearly shows that an electron hill is formed in the phase space and causes the frequency decrease. The entrapping of the resonant electrons at the front of the packets and the decrease of the amplitude at the end of packets are essential for the generation of falling-tone emissions. Each wavefront of the emission has a strongly negative resonant current -J(E), which results in the wave growth. In the formation process of the resonant currents, we investigate the inhomogeneous factor S, which controls the nonlinear motion of the resonant electrons interacting with waves. The factor S consists of two terms, a frequency sweep rate and a gradient of the background magnetic field. The resonant current J(E) in the wave packet changes its sign from negative to positive as the packet moves away from the equator, terminating the wave growth.