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

Abstract

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 density nheq/nc0 and temperature anisotropy AT 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 of nheq/nc0 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 increasing nheq/nc0. As for AT, the frequency chirping rate of the generated rising‐tone chorus is increasing with the increase of AT 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.

One‐Dimensional gcPIC‐δf Simulation of Hooked Chorus Waves in the Earth’s Inner Magnetosphere

“…The generation mechanism of chorus frequency chirping has been widely investigated in previous studies (Katoh & Omura, 2011;Ke et al, 2020;Nunn, 1974;Omura et al, 2008;Q. Lu et al, 2019;Tao, 2014).…”

“…Numerous particle‐in‐cell (PIC) and Vlasov simulations have been dedicated to studying chorus waves in the Earth’s inner magnetosphere (Hikishima et al., 2009; Katoh & Omura, 2011; Ke et al., 2017, 2020; Nunn et al., 1997; Nunn & Omura, 2012; Q. Lu et al., 2019, 2021; Tao, 2014, 2017). Chorus waves with rising, falling, and hooked tones have been reproduced in one‐dimensional (1‐D) Vlasov simulations with the ambient magnetic field close to being a parabolic function of the distance from the equator, where the monochromatic whistler‐mode wave is injected into the system as a pump wave (Nunn & Omura, 2012; Nunn et al., 1997).…”

“…Numerous particle-in-cell (PIC) and Vlasov simulations have been dedicated to studying chorus waves in the Earth's inner magnetosphere (Hikishima et al, 2009;Katoh & Omura, 2011;Ke et al, 2017Ke et al, , 2020Nunn et al, 1997;Nunn & Omura, 2012;Q. Lu et al, 2019Tao, 2014Tao, , 2017.…”

Gap Formation Around 0.5Ωe in the Whistler‐Mode Waves Due To the Plateau‐Like Shape in the Parallel Electron Distribution: 2D PIC Simulations

“…Our study provides an important clue that the plateau electron component may be the key to solving this long-standing mystery. During the propagation from the source region toward higher latitudes, the whistler-mode waves have frequency chirping due to the inhomogeneous field, leading to the generation of chorus waves (Katoh & Omura, 2006, 2007Ke et al, 2020;Lu et al, 2019). Since our simulations are performed in a homogeneous environment, the "spectrum bite" mechanism is only limited to broad-band whistler-mode waves.…”

“…They can not only efficiently scatter low‐energy (0.1–30 keV) electrons into the loss cone and cause diffuse aurora in the upper atmosphere (Kasahara et al., 2018; Ni et al., 2008), but also accelerate seed electrons (∼100 keV) to relativistic energies (∼MeV), refilling the outer radiation belt during geoactive storms (Horne et al., 2003; Summers et al., 1998; Thorne et al., 2013). Besides the typical exhibition of the frequency chirping (Burtis & Helliwell, 1969; H. Chen et al., 2022; X. L. Gao et al., 2014; Ke et al., 2017, 2020; Lu et al., 2019; Omura et al., 2009; Tsurutani & Smith, 1974, 1977) and repetitive emissions (H. Chen et al., 2022; Hikishima et al., 2010; Lu et al., 2021; Tsurutani et al., 2013), another notable characteristic of whistler‐mode waves in the Earth's magnetosphere is the power gap around 0.5Ω e (where Ω e is the equatorial electron gyrofrequency), which visually separates the spectrum into a lower band (0.1–0.5Ω e ) and an upper band (0.5–0.8Ω e ) (Fu et al., 2014; X. Gao et al., 2019; W. Li et al., 2011; Tsurutani & Smith, 1974).…”