Calculation of pitch angle and energy diffusion coefficients with the PADIE code

We present a new computer code (PADIE) that calculates fully relativistic quasi-linear pitch angle and energy diffusion coefficients for resonant wave-particle interactions in a magnetized plasma. Unlike previous codes, the full electromagnetic dispersion relation is used so that interactions involving any linear electromagnetic wave mode in a predominantly cold plasma can be addressed for any ratio of the plasma-frequency to the cyclotron frequency ωpe /∣Ωe∣. The code can be applied to problems in astrophysical, magnetospheric, and laboratory plasmas. The code is applied here to the Earth's radiation belts to calculate electron diffusion by whistler mode chorus, electromagnetic ion cyclotron (EMIC), and Z mode waves. The high-density approximation is remarkably good for electron diffusion by whistler mode chorus for energies E ≥ 100 keV, even for ωpe/∣Ωe∣ ≈ 2 but underestimates diffusion by orders of magnitude at low energies (∼10 keV). When a realistic angular spread of propagating waves is introduced for EMIC waves, electron diffusion at ∼0.5 MeV is only slightly reduced compared with the assumption of field-aligned propagation, but at ∼5 MeV, electron diffusion at pitch angles near 90° is reduced by a factor of 5 and increased by several orders of magnitude at pitch angles 30°–80°. Scattering by EMIC waves should contribute to flattening of the distribution function. The first results for electron diffusion by Z mode waves are presented. They show that unlike the whistler and EMIC waves, energy diffusion exceeds pitch angle diffusion over a broad range of pitch angles less than 45°. The results suggest that Z mode waves could provide a significant contribution to electron acceleration in the radiation belts during storm times.

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