Particle‐in‐cell simulation of Maxwellian ring velocity distribution

Abstract

[1] Electrostatic electron cyclotron harmonic (ECH) and electromagnetic whistler wave emissions are sometimes observed simultaneously in the near-Earth nightside equatorial magnetotail region. The excitation mechanism for these two wave emissions, however, is quite different with ECH waves excited by a positive slope in the velocity distribution function perpendicular to the ambient magnetic field (such as due to a loss cone or ring velocity distribution), while whistler waves are excited by a temperature anisotropy whereby the perpendicular temperature is larger than the parallel temperature. Here we examine, using a two-dimensional electromagnetic particle-in-cell computer simulation, the excitation of both waves as a consequence of a warm electron ring distribution in the presence of cold background electrons. Initially, ECH waves are excited by the ring distribution in the linear stage, which results in heating of the cold electrons and smearing of the ring distribution. During a nonlinear consequence of the ECH excitation and ensuing electron wave-particle interactions, whistler waves are also excited by the different instability. Thus both waves are excited during the same simulation run, which may account for the magnetospheric observations of both ECH and whistler waves at the same location where electron loss cone distributions form in the equatorial magnetotail at about 6-9 RE from the Earth.

Simulation and Quasi‐linear Theory of Magnetospheric Bernstein Mode Instability

“…Since the present theory and simulation assume perpendicular propagation, we excluded the whistler instability at the outset. Note that Umeda et al (2007) show in their two-dimensional simulation of ring distribution of electrons that the whistler instability takes place after the saturation of dynamical processes associated with instabilities involving perpendicular modes. Consequently, we believe that it is important to incorporate the parallel whistler dynamics eventually.…”

Van Allen Probes observations of direct wave‐particle interactions

“…Such distributions provide a positive gradient parallel and perpendicular relative to the magnetic field. Umeda et al [2007Umeda et al [ , 2012 showed that electromagnetic chorus and electron cyclotron harmonic (ECH) waves could be generated by such distributions. Model chorus waves, for example, were unstable in two relatively narrow bands above and below f ce /2, similar to the observed frequency spectra in Figures 2 and 4.…”

“…One can speculate that some aspect of the wave-particle interaction was turning the electromagnetic part of the instability on and off. For example, Umeda et al [2007] showed that it was possible to shift the wave growth from the whistler mode instability to the electrostatic ECH instability by adjusting the parameters of a ring distribution. The chorus wave fields could also accelerate or scatter the electrons to generate, parasitically, the peaks in the electron pitch angle distributions.…”

Whistler Instability Driven by Electron Thermal Ring Distribution With Magnetospheric Application

“…We investigate this problem by employing both quasi‐linear (QL) theory and one‐dimensional particle‐in‐cell (PIC) simulation. In the literature, simulations of whistler anisotropy instability have already been done (Gary & Madland, ; Gary & Wang, ; Ossakow et al, ; Umeda et al, )—see also Lee et al (), a related simulation study involving a ring beam distribution of electrons. However, comparison with the QL method has not been carried out for the loss cone model.…”