Magnetospheric banded chorus is enhanced whistler waves with frequencies ωr<Ωe, where Ωe is the electron cyclotron frequency, and a characteristic spectral gap at ωr≃Ωe/2. This paper uses spacecraft observations and two-dimensional particle-in-cell simulations in a magnetized, homogeneous, collisionless plasma to test the hypothesis that banded chorus is due to local linear growth of two branches of the whistler anisotropy instability excited by two distinct, anisotropic electron components of significantly different temperatures. The electron densities and temperatures are derived from Helium, Oxygen, Proton, and Electron instrument measurements on the Van Allen Probes A satellite during a banded chorus event on 1 November 2012. The observations are consistent with a three-component electron model consisting of a cold (a few tens of eV) population, a warm (a few hundred eV) anisotropic population, and a hot (a few keV) anisotropic population. The simulations use plasma and field parameters as measured from the satellite during this event except for two numbers: the anisotropies of the warm and the hot electron components are enhanced over the measured values in order to obtain relatively rapid instability growth. The simulations show that the warm component drives the quasi-electrostatic upper band chorus and that the hot component drives the electromagnetic lower band chorus; the gap at ∼Ωe/2 is a natural consequence of the growth of two whistler modes with different properties.

[1] Two-dimensional electromagnetic particle-in-cell simulations are performed to study the temporal development of an ion Bernstein instability driven by a proton velocity distribution with positive slope in the perpendicular velocity distribution f p (v ? ), where ? denotes directions perpendicular to the background magnetic field B 0 . A subtracted Maxwellian distribution is first used to construct the positive slope in f p (v ? ), and linear kinetic dispersion analysis is performed. The results of a simulation using such an initial proton distribution agree well with the linear kinetic analysis. The simulation results demonstrate that the ion Bernstein instability grows at propagation angles nearly perpendicular to B 0 and at frequencies close to the harmonics of the proton cyclotron frequency. The distribution in the simulation is further generalized to contain a proton shell with a finite thermal spread and a relatively cold ion background. The simulation results show that the presence of the cold background protons and the increase of the shell velocity shift the excited waves close to the cold plasma dispersion relation for magnetosonic waves, i.e., w r = kv A , where w r is the wave frequency, k is the wave number, and v A is the Alfvén velocity. The general features of the simulated field fluctuations resemble observations of fast magnetosonic waves near the geomagnetic equator in the terrestrial magnetosphere. A test particle computation of energetic electrons interacting with the simulated electromagnetic fluctuations suggests that this growing mode may play an important role in the acceleration of radiation belt relativistic electrons.

[1] Linear kinetic dispersion theory for electromagnetic fluctuations in a homogeneous, magnetized, collisionless plasma is used to study the properties of an ion Bernstein mode instability driven by a proton velocity distribution f p (v) such that ∂f p (n ? )/∂n ? > 0, where ? denotes directions perpendicular to the background magnetic field B o . Here f p (v) = f 1 (n) − f 2 (n), where f 1 and f 2 are Maxwellian velocity distributions with slightly different densities and temperatures; plasma parameters are taken from magnetospheric observations. Then the growth rate of this instability has relative maxima at w r ' nW p , where n = 1, 2, 3, … and W p is the proton cyclotron frequency; wave vector k at 0 < k k ( k ? , where k and ? denote the directions parallel and perpendicular to B o ; and wavelengths of the order of or smaller than the proton gyroradius. The maximum instability growth rate is a monotonically decreasing function of the electron-to-proton temperature ratio but has its largest value at an intermediate value of the proton b (∼0.5 for the parameters considered here).

[1] We present a comparison between the classical quasilinear diffusion coefficients and those calculated using a general test particle code. The trajectories of a large number of electrons are followed as they traverse a numericallyconstructed, broadband, small-amplitude wave field, using a general relativistic test particle code. The change in each electron's pitch angle and energy is shown to be stochastic and the resulting diffusion of the entire population is found to be in excellent agreement with quasilinear theory. We also demonstrate that the diffusion coefficients presented by Summers, derived specifically for parallel propagating waves, are a factor of two larger than the test particle results if the power spectral density is one-sided (w > 0). Our results demonstrate the general validity of using quasilinear theory to describe the effects of broadband small amplitude waves on radiation belt electrons. Citation: Tao, X., J. Bortnik, J. M.Albert, K. Liu, and R. M. Thorne (2011), Comparison of quasilinear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations, Geophys. Res. Lett., 38, L06105,

[1] Relativistic electron scattering by electromagnetic ion cyclotron (EMIC) fluctuations is studied using test particle computations coupled to the results of a hybrid simulation code. The enhanced EMIC fluctuations are derived from a 1-D, self-consistent hybrid simulation model and are due to the growth of the Alfvén cyclotron instability driven by the ion temperature anisotropy, T i? > T ik (where the subscripts ? and k refer to directions perpendicular and parallel to the background magnetic field, respectively), in a magnetized, homogeneous, collisionless plasma with a single ion species. The test particle computations follow the motion of relativistic test electrons in the input EMIC fluctuations. The time evolution of the mean square pitch angle change of the test electrons is calculated and used to determine the pitch angle diffusion coefficient. Finally, the results are compared with quasi-linear diffusion theory. The diffusion coefficients given by the test particle computations agree with the ones from quasi-linear theory very well except for large-amplitude waves (dB/B 0 ≥ 0.03 in the case presented, where dB is the wave magnetic field amplitude and B 0 is the background magnetic field) when the weak turbulence approximation in quasi-linear theory breaks down. Quasi-linear theory overestimates the pitch angle diffusion coefficient for large-amplitude waves and may, consequently, overestimate the pitch angle diffusion of relativistic electrons in the radiation belts at high L values.