[1] We develop a nonlinear wave growth theory of magnetospheric chorus emissions, taking into account the spatial inhomogeneity of the static magnetic field and the plasma density variation along the magnetic field line. We derive theoretical expressions for the nonlinear growth rate and the amplitude threshold for the generation of self-sustaining chorus emissions. We assume that nonlinear growth of a whistler mode wave is initiated at the magnetic equator where the linear growth rate maximizes. Self-sustaining emissions become possible when the wave propagates away from the equator during which process the increasing gradients of the static magnetic field and electron density provide the conditions for nonlinear growth. The amplitude threshold is tested against both observational data and self-consistent particle simulations of the chorus emissions. The self-sustaining mechanism can result in a rising tone emission covering the frequency range of 0.1-0.7 W e0 , where W e0 is the equatorial electron gyrofrequency. During propagation, higher frequencies are subject to stronger dispersion effects that can destroy the self-sustaining mechanism. We obtain a pair of coupled differential equations for the wave amplitude and frequency. Solving the equations numerically, we reproduce a rising tone of VLF whistler mode emissions that is continuous in frequency. Chorus emissions, however, characteristically occur in two distinct frequency ranges, a lower band and an upper band, separated at half the electron gyrofrequency. We explain the gap by means of the nonlinear damping of the longitudinal component of a slightly oblique whistler mode wave packet propagating along the inhomogeneous static magnetic field.
The Exploration of energization and Radiation in Geospace (ERG) project aims to study acceleration and loss mechanisms of relativistic electrons around the Earth. The Arase (ERG) satellite was launched on December 20, 2016, to explore in the heart of the Earth's radiation belt. In the present paper, we introduce the specifications of the Plasma Wave Experiment (PWE) on board the Arase satellite. In the inner magnetosphere, plasma waves, such as the whistlermode chorus, electromagnetic ion cyclotron wave, and magnetosonic wave, are expected to interact with particles over a wide energy range and contribute to high-energy particle loss and/or acceleration processes. Thermal plasma density is another key parameter because it controls the dispersion relation of plasma waves, which affects wave-particle interaction conditions and wave propagation characteristics. The DC electric field also plays an important role in controlling the global dynamics of the inner magnetosphere. The PWE, which consists of an orthogonal electric field sensor (WPT; wire probe antenna), a triaxial magnetic sensor (MSC; magnetic search coil), and receivers named electric field detector (EFD), waveform capture and onboard frequency analyzer (WFC/OFA), and high-frequency analyzer (HFA), was developed to measure the DC electric field and plasma waves in the inner magnetosphere. Using these sensors and receivers, the PWE covers a wide frequency range from DC to 10 MHz for electric fields and from a few Hz to 100 kHz for magnetic fields. We produce continuous ELF/VLF/HF range wave spectra and ELF range waveforms for 24 h each day. We also produce spectral matrices as continuous data for wave direction finding. In addition, we intermittently produce two types of waveform burst data, "chorus burst" and "EMIC burst. " We also input raw waveform data into the software-type wave-particle interaction analyzer (S-WPIA), which derives direct correlation between waves and particles. Finally, we introduce our PWE observation strategy and provide some initial results. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
[1] We perform an electromagnetic full particle simulation to study the generation mechanism of VLF whistler-mode chorus emissions in the equatorial region of the magnetosphere. Parabolic variation of the static magnetic field is assumed as a model for the dipole magnetic field in the vicinity of the equator. We have cold thermal electrons and relatively low anisotropic hot electrons as plasma particles. In the initial phase, the amplitude growth of the incoherent whistler-mode waves is determined by the linear growth rate. When the wave amplitude reaches a certain level, it begins to grow more rapidly with a series of rising tone emissions consisting of coherent phase structures in the vicinity of the magnetic equator, and their wave packets propagate away form the magnetic equator. The frequency sweep rates of the excited rising tone elements decrease gradually. We find a distinct threshold for such a nonlinear wave growth generating the rising chorus-like elements. The relation between the wave amplitude and the frequency sweep rate of each element found in the simulation fully supports the nonlinear wave growth theory of chorus emissions.
We perform test particle simulations of energetic electrons interacting with whistler mode chorus emissions. We compute trajectories of a large number of electrons forming a delta function with the same energy and equatorial pitch angle. The electrons are launched at different locations along the magnetic field line and different timings with respect to a pair of chorus emissions generated at the magnetic equator. We follow the evolution of the delta function and obtain a distribution function in energy and equatorial pitch angle, which is a numerical Green's function for one cycle of chorus wave‐particle interaction. We obtain the Green's functions for the energy range 10 keV–6 MeV and all pitch angles greater than the loss cone angle. By taking the convolution integral of the Green's functions with the distribution function of the injected electrons repeatedly, we follow a long‐time evolution of the distribution function. We find that the energetic electrons are accelerated effectively by relativistic turning acceleration and ultrarelativistic acceleration through nonlinear trapping by chorus emissions. Further, these processes result in the rapid formation of a dumbbell distribution of highly relativistic electrons within a few minutes after the onset of the continuous injection of 10–30 keV electrons.
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