Nonlinear Evolution of Counter‐Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1‐D PIC Simulations

Abstract

Nonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1‐D particle‐in‐cell simulation model, we have investigated the nonlinear evolution of parallel counter‐propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter‐propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high‐k modes in this plasma system. Compared with excited whistler mode waves, these high‐k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

Whistler Mode Waves Excited by Anisotropic Hot Electrons With a Drift Velocity in Earth's Magnetosphere: Linear Theory

“…In previous studies, this energy source is often modeled as a single bi‐Maxwellian distribution in velocity space without the bulk velocity. In this scenario, whistler mode waves with parallel and antiparallel propagating directions are simultaneously excited in the source region and have the same amplitude, which has been supported by both the linear theory and particle‐in‐cell simulations (An et al, 2017; H. Y. Chen et al, 2018; Fan et al, 2019; Gary et al, 2011). As a result, the presence of mixed Poynting flux directions of whistler mode chorus waves becomes a common method to determine their source region from satellite observations (LeDocq et al, 1998; Santolik et al, 2003).…”

“…The WHAMP (Waves in Homogeneous Anisotropic Magnetized Plasma) model (Ronnmark, 1982), which can be easily accessed on the website (https://github.com/irfu/whamp), is utilized to calculate the dispersion relation of whistler mode waves and associated linear growth rates. This code has been widely used in previous works (H. Y. Chen et al, 2018; Denton, 2018; Fan et al, 2019; Sun et al, 2019; Xiao et al, 2007).…”

Electron Diffusion and Advection During Nonlinear Interactions With Whistler‐Mode Waves

“…Once the thermal instability saturates (at roughly t ≈ 0.08s for Run VIII), we see that the wave spectrum stops widening in frequency space, and slowly begins to become more narrow (in a manner somewhat similar to that in Tao et al [2017], H. Chen et al [2017Chen et al [ , 2018, and Kuzichev et al [2019]). This narrowing occurs as the instability saturates and the anisotropy decreases, reducing the maximum frequency with positive growth rate (i.e., the condition on marginal instability is satisfied in a smaller ranger of frequencies) (Kennel & Petschek, 1966;Ossakow et al, 1972;Tao et al, 2017).…”

“…As is a very common approach in such numerical experiments (e.g., see Allanson et al., 2019, 2020; Camporeale, 2015; Camporeale & Zimbardo, 2015; H. Chen et al., 2017, 2018; Gao et al., 2017; Kuzichev et al., 2019; Liu et al., 2010, 2012; Tao et al., 2011, 2017), we consider one field‐aligned dimension (x), which is a reasonable approximation near the magnetic equator (i.e., uniform fields and field‐aligned wave propagation) (Tsurutani & Smith, 1977), i.e., the region that is most important for whistler‐mode wave generation (Gao et al., 2014; W. Li et al., 2010, 2012; Teng et al., 2018). We therefore use the one‐dimensional version of the EPOCH code, such that all quantities have spatial gradients in the x ‐direction only.…”

Particle‐in‐cell Experiments Examine Electron Diffusion by Whistler‐mode Waves: 1. Benchmarking With a Cold Plasma

“…Under these circumstances, wave‐particle resonance occurs for a given wave frequency, ω , for pitch angles and energies defined by for ε = E /( m 0 e c 2 ), and kc / ω given by equation . This equation implies that for a given pitch angle, lower frequency waves resonate with higher energies (Camporeale, ; Chen et al, ). Furthermore, for a given wave frequency, the values of particle energy that can resonate are a monotonically increasing function of pitch angle.…”