Simulations of phase space distributions of storm time proton ring current

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Abstract
We use results of guiding‐center simulations of ion transport to map phase space densities of the stormtime proton ring current. We model a storm as a sequence of substorm‐associated enhancements in the convection electric field. Our pre‐storm phase space distribution is an analytical solution to a steady‐state transport model in which quiet‐time radial diffusion balances charge exchange. This pre‐storm phase space spectra at L∼2‐4 reproduce many of the features found in observed quiet‐time spectra. Using results from simulations of ion transport during model storms having main phases of 3, 6, and 12 hr, we map phase space distributions from the pre‐storm distribution in accordance with Liouville's theorem. We find stormtime enhancements in the phase space densities at energies E∼30‐160 keV for L∼2.5‐4. These enhancements agree well with the observed stormtime ring current. For storms with shorter main phases (∼3 hr), the enhancements are caused mainly by the trapping of ions injected from open night side trajectories, and diffusive transport of higher‐energy (≳ 160 keV) ions contributes little to the stormtime ring current. However, the stormtime ring current is augmented also by the diffusive transport of higher‐energy ions (E≳ 160 keV) during storms having longer main phases (≳ 6 hr). In order to account for the increase in Dst associated with the formation of the stormtime ring current, we estimate the enhancement in particle‐energy content that results from stormtime ion transport in the equatorial magnetosphere. We find that transport alone cannot account for the entire increase in |Dst| typical of a major storm. However, we can account for the entire increase in |Dst| by realistically increasing the stormtime outer boundary value of the phase space density relative to the quiet‐time value. We compute the magnetic field produced by the ring current itself and find that radial profiles of the magnetic field depression resemble those obtained from observational data.

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