Test Particle Simulation of the Pitch Angle Response of Ions to ULF Waves: Van Allen Probes Observations and Formation of Butterfly Distributions

Abstract:

Full Lorentz force test particle and simplified ULF wave models are used to reproduce the pitch angle and energy dependence of ion differential fluxes observed by the Van Allen Probes spacecraft on October 6^th, 2012. The observed ion fluxes exhibit 100s period modulations that match the period of poloidal mode Alfven waves observed in-situ and by ground magnetometers of the CARISMA array in northern Canada. The in-situ measurements show that electric field strengths near the equatorial magnetosphere are on the order of 4mVm^-1 . The largest amplitude modulations are associated with increased numbers of ions in a narrow range of energy and pitch angle. Simulation of the event reveals these ions have experienced drift resonance with ULF waves of azimuthal wavenumber m~35 and frequency f~10mHz. The drift-bounce resonance condition ω-mω_d=Nω_b for ions of energy 150keV and 35^o pitch angle is satisfied for N=0. Here, ω_d and ω_b are the drift and bounce angular speeds, respectively, and ω=2πf. The ion distribution functions evolve to a butterfly shape due to the pitch angle dependence of ions that have zero net angular drift in the wave frame. The simulations provide quantitative verification of drift-bounce resonance theory and demonstrate that satellite observations of particle acceleration in Earth’s inner magnetosphere can be quantified using relatively simple ULF wave and transport models.