An empirical phase space analysis of ring current dynamics: Solar wind control of injection and decay

This empirical analysis of the terrestrial ring current, as measured by Dst, uses conditional probability density in Dst phase space to determine the evolution of the ring current. This analysis method does not assume a dynamic equation, but merely requires that the evolution of Dst depends on Dst and the solar wind. Our simple model, with seven nontrivial parameters, describes the dynamics of 30 years of hourly Dst with solar wind data provided by the OMNI database. The solar wind coupling is assumed to be determined by VBs. We arrive at a dynamic equation nearly identical to the Burton equation (Burton et al., 1975) with a slight correction. The method is restricted to Dst > -150 nT owing to the rarity of larger excursions. We show that the ring current decay lifetime varies with VBs but not with Dst, and we relate this variation to the position of convection boundaries in the magnetosphere. Convection boundaries closer to the Earth result in shorter charge exchange decay times owing to the higher neutral density near the Earth. The decay time in hours varies as tau = 2.40 exp [9.74/(4.69+VBs)] with VBs in millivolts per meter. We also show that the energy injection function as derived by Burton et al. is essentially correct. The injection Q is zero for VBs < E-c. = 0.49 mV/m, and it is Q = -4.4( VBs - E-c) for VBs > E-c. We derive the correction for magnetopause contamination: Dst* = Dst-7.26P(1/2) + 11 nT, where P is solar wind dynamic pressure in nanopascals. Finally, we apply the model to a moderate storm and to an intense storm. We demonstrate that, in spite of the fact that spacecraft observe compositional changes in the ring current at intense Dst, the dynamics of the two storms are not obviously different in the context of our model. We demonstrate that the generally observed dependence of the decay parameter on Dst is actually an alias of the coincidence of intense Dst and intense VBs.