There are a number of large-scale magnetospheric magnetic field models that give the field configuration as a function of either solar wind conditions or magnetospheric activity parameters (Tsyganenko, 1989, 1995; Tsyganenko et al., 2003). While these models give the large-scale evolution of the field quite well, the smaller-scale and shorter-term variations associated with substorms cannot be accurately represented by these models (Ganushkina et al., 2004). Figure 19 shows results from Ganushkina et al. (2005), who modeled the large-scale magnetic field evolution during a storm on May 2 – 4, 1998 by fitting an empirical model with free parameters to observed magnetic field values. The figure shows three snapshots of the current configuration at the equatorial plane as well as in the noon-midnight meridian plane prior to the storm, during the storm main phase, and during the recovery phase. Before the storm, the ring current is weak and the tail current intensity varies in response to substorm activity. After the storm onset, the ring current in the inner magnetosphere as well as the magnetotail current are strongly enhanced. During the storm recovery, both current systems weaken, but the ring current decay time is much longer than that of the tail current. On top of these large-scale field variations, there are rapid, large-amplitude, and localized variations of the magnetic field as well in the inner magnetosphere as in the magnetotail.
The rapidly varying magnetic field induces an electric field (∇× E = −∂B∕∂t) in the magnetosphere. These induced electric fields are much larger than the large-scale, weak convection electric field imposed by the solar wind flow past the magnetosphere. The small-scale fields can be very intense, include high-frequency fluctuations, and be highly localized in space, which makes their characterization difficult. The large-scale convection field can be given in a simple formulation parametrized by magnetospheric activity or by solar wind parameters (see Section 4). Because of the associated difficulties, there are to date only very few attempts to describe the time-varying, smaller-scale electric fields. However, Li et al. (1998) and Sarris et al. (2002) have described the substorm-associated magnetic field dipolarization and Earthward plasma flows in terms of Earthward-propagating, localized electric field pulses. By computing the magnetic field changes from the electric field and adding those to a simple dipole field and tracing particle drifts under the resulting electromagnetic fields, they were able to reproduce the substorm-associated energetic electron signatures at geostationary orbit. The role of electric fields in the ring current formation and acceleration is treated in more detail below.
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