Particle-in-Cell Simulations of Characteristics of Rising-Tone Chorus Waves in the Inner Magnetosphere

Whistler mode chorus waves in the Earth's inner magnetosphere are usually composed of discrete elements, and each element can be characterized by the following properties: the amplitude, the duration, the frequency span, and the frequency chirping rate. Using a one-dimensional (1-D) particle-in-cell (PIC) simulation code, we study the dependence of these properties of a rising-tone chorus on the number densityn(heq)/n(c0)and temperature anisotropyA(T)of energetic electrons at the magnetic equator. The whistler waves are first excited around the magnetic equator by anisotropic energetic electrons and then develop into a rising-tone chorus when they leave away from the equator. During the propagation toward the pole, the rising-tone chorus with nearly constant frequency span first enhances and then decays. Its frequency chirping rate declines in the early stage and then gradually increases. Meanwhile, the chorus duration is quite the opposite due to propagation effect. Over a suitable range ofn(heq)/n(c0)to generate rising-tone chorus, the frequency chirping rate of the excited rising-tone chorus first increases and then saturates, while its saturated amplitude, duration, and frequency span have a rising tendency with the increasingn(heq)/n(c0). As forA(T), the frequency chirping rate of the generated rising-tone chorus is increasing with the increase ofA(T)that is consistent with prediction of nonlinear theory, while the duration is just the opposite. Our simulation study can give a further understanding of the generation and propagation of rising-tone chorus waves.