Simulating Butterfly Pitch Angle Distributions in the Inner Zone: Sensitivity to Wave Models

Abstract:

“Peculiar” or “butterfly” pitch angle distributions have recently been found to be common in the inner radiation belts. These PADs, with local minima at 90 deg. equatorial pitch angle, are believed to reflect enhancement of particles at lower pitch angle, due to local heating by resonant waves, rather than rapid loss of equatorially mirroring particles. Beyond their intrinsic interest, they provide a sensitive test of overall modeling of inner zone electrons.

Assuming the framework of quasi-linear diffusion, the effectiveness of energization relative to pitch angle scattering is favored by the Landau resonance (n=0) rather than cyclotron resonance. Magnetosonic waves are typically resonant with n=0, over the proper range of pitch angle, to produce or enhance butterfly PADs as observed [Ma et al., 2016]. However, plasmaspheric hiss also typically involves only Landau resonance for the relevant range of pitch angle. Albert et al. [2016] found that the VLF (hiss+LGW) model of Glauert et al. [2014], based on a statistical model of CRRES wave measurements, can generate realistic butterfly PADs, at all 3 levels of the input parameter AE, with or without modeled magnetosonic waves. The associated energy distribution of particle flux in steady state is also remarkably similar to that observed, including very low flux near 1 MeV.

Li et al. [2015] provided an alternative treatment of the frequency spectrum of hiss, based on Van Allen Probes wave data. Combined with the latitude-dependent wave normal angle of Ni et al. [2013] and the Kp-dependent wave amplitude model of Spasojevic et al. [2015], this constitutes a complete hiss model from which diffusion coefficients and then particle flux can be calculated. Compared to the earlier results, we find that diffusion coefficients from this wave model, in the absence of MS waves, are not as conducive to the production of prominent butterfly PADs. Comparing the resulting pitch angle, energy, and cross diffusion coefficients between the two models shows general agreement but also significant differences, particularly in the energy diffusion rates due to Landau resonance. We investigate which detailed differences in the wave models account for this, and what this implies more generally about the sensitivity of modeling inner radiation belt electrons.