Modeling the loss of inner belt protons by magnetic field line curvature scattering
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The sudden loss of energetic protons in the inner radiation belt has been observed during geomagnetic storms. It is hypothesized that this sudden loss occurs because of changes in the geomagnetic field configuration which lead to a breakdown of the first adiabatic invariant, mu, in a process called magnetic field line curvature scattering or mu scattering. Comparison of observations to various analytic model predictions for mu scattering induced loss has, however, yielded discrepancies. To better understand how well the analytic models predict the proton loss, test particle simulations are carried out for various magnetic field configurations. Although our simulation results agree well with the analytic models for single-scattering events, the results after cumulative mu scattering can show significant disagreement with the theoretical predictions based on analytic models. In particular, we find the assumption that protons with predicted initial delta mu/mu 0.01 or epsilon > 0.1 are ultimately lost overestimates the proton loss. Based on the test particle simulation results, we develop a new empirical model, called the "epsilon-onset" model, to predict the minimum value of e at which all protons of a given pitch angle and energy can be assumed to be lost due to mu scattering. By applying our epsilon-onset model as the variable cutoff condition between trapping and detrapping, we obtain very good agreement between theoretical predictions and the simulation results for a range of Kp, suggesting that the epsilon-onset model can potentially serve as an easy-to-use and more reliable predictor of inner belt proton loss due to mu scattering than the previously used fixed-valued cutoff conditions.