Rising-tone chorus waves have already been successfully produced in a mirror magnetic field with the use of one-and two-dimensional particle-in-cell (PIC) simulations. However, in reality, the background magnetic field in the inner Earth's magnetosphere is a dipole magnetic field, unlike symmetric mirror fields. In this paper, with the two-dimensional (2-D) general curvilinear PIC (gcPIC) code, we investigate the generation of rising-tone chorus waves in the dipole magnetic field configuration. The plasma consists of three components: immobile ions, cold background, and hot electrons. In order to save computational resource, the topology of the magnetic field
Linear Vlasov theory and particle‐in‐cell (PIC) simulations for electromagnetic fluctuations in a homogeneous, magnetized, and collisionless plasma are used to investigate a fast magnetosonic wave event observed by the Van Allen Probes. The fluctuating magnetic field observed exhibits a series of spectral peaks at harmonics of the proton cyclotron frequency Ωp and has a dominant compressional component, which can be classified as fast magnetosonic waves. Furthermore, the simultaneously observed proton phase space density exhibits positive slopes in the perpendicular velocity space, ∂fp/∂v⊥>0, which can be a source for these waves. Linear theory analyses and PIC simulations use plasma and field parameters measured in situ except that the modeled proton distribution is modified to have larger ∂fp/∂v⊥ under the assumption that the observed distribution corresponds to a marginally stable state when the distribution has already been scattered by the excited waves. The results show that the positive slope is the source of the proton cyclotron harmonic waves at propagation quasi‐perpendicular to the background magnetic field, and as a result of interactions with the excited waves the evolving proton distribution progresses approximately toward the observed distribution.
Dipolarization fronts (DFs) as earthward propagating flux ropes (FRs) in the Earth's magnetotail are presented and investigated with a three‐dimensional (3‐D) global hybrid simulation for the first time. In the simulation, several small‐scale earthward propagating FRs are found to be formed by multiple X line reconnection in the near tail. During their earthward propagation, the magnetic field Bz of the FRs becomes highly asymmetric due to the imbalance of the reconnection rates between the multiple X lines. At the later stage, when the FRs approach the near‐Earth dipole‐like region, the antireconnection between the southward/negative Bz of the FRs and the northward geomagnetic field leads to the erosion of the southward magnetic flux of the FRs, which further aggravates the Bz asymmetry. Eventually, the FRs merge into the near‐Earth region through the antireconnection. These earthward propagating FRs can fully reproduce the observational features of the DFs, e.g., a sharp enhancement of Bz preceded by a smaller amplitude Bz dip, an earthward flow enhancement, the presence of the electric field components in the normal and dawn‐dusk directions, and ion energization. Our results show that the earthward propagating FRs can be used to explain the DFs observed in the magnetotail. The thickness of the DFs is on the order of several ion inertial lengths, and the electric field normal to the front is found to be dominated by the Hall physics. During the earthward propagation from the near‐tail to the near‐Earth region, the speed of the FR/DFs increases from ~150 km/s to ~1000 km/s. The FR/DFs can be tilted in the GSM (x, y) plane with respect to the y (dawn‐dusk) axis and only extend several Earth radii in this direction. Moreover, the structure and evolution of the FRs/DFs are nonuniform in the dawn‐dusk direction, which indicates that the DFs are essentially 3‐D.
We report the first three-dimensional (3D) ion particle simulation of mode conversion from a fast mode compressional wave to kinetic Alfvén waves (KAWs) that occurs when a compressional mode propagates across a plasma boundary into a region of increasing Alfvén velocity. The magnetic field is oriented in the z direction perpendicular to the gradients in the background density and magnetic field (x direction). Following a stage dominated by linear physics in which KAWs with large wave numbers k(x)ρ(i)∼1 (with ρ(i) being the ion Larmor radius) are generated near the Alfvén resonance surface, the growth of KAW modes with k(y)ρ(i)∼1 is observed in the nonlinear stage when the amplitude of KAWs generated by linear mode conversion becomes large enough to drive a nonlinear parametric decay process. The simulation provides a comprehensive picture of mode conversion and shows the fundamental importance of the 3D nonlinear physics in transferring energy to large perpendicular k(y) modes, which can provide large transport across plasma boundaries in space and laboratory plasmas.
Recently, the generation of rising‐tone chorus has been implemented with one‐dimensional (1‐D) particle‐in‐cell (PIC) simulations in an inhomogeneous background magnetic field, where both the propagation of waves and motion of electrons are simply forced to be parallel to the background magnetic field. In this paper, we have developed a two‐dimensional (2‐D) general curvilinear PIC simulation code and successfully reproduced rising‐tone chorus waves excited from an anisotropic electron distribution in a 2‐D mirror field. Our simulation results show that whistler waves are mainly generated around the magnetic equator and continuously gain growth during their propagation toward higher‐latitude regions. The rising‐tone chorus waves are observed off the magnetic equator, which propagate quasi‐parallel to the background magnetic field with the wave normal angle smaller than 25°. Due to the propagating effect, the wave normal angle of chorus waves is increasing during their propagation toward higher‐latitude regions along an enough curved field line. The chirping rate of chorus waves is found to be larger along a field line with a smaller curvature.
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