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The twin‐cell convection pattern does not extend to the equator but is confined to high latitudes, which can be understood by considering the competition between the reconnection‐driven Dungey cycle and “corotation” (that is, rotation with the planet), as described by Wolf (1970) and Volland (1973). The magnetospheric ends of the field lines move under the influence of the Dungey cycle flow discussed previously, whereas the ionospheric ends experience ion‐neutral collisions with the corotating atmosphere. In the equatorial plane, the Dungey flow consists of sunward magnetic flux transport (e.g., Fig. 2.2b), which can be represented by a voltage between the dawn and dusk flanks of the magnetosphere (equal to Φ_PC), corresponding to some constant electric field E₀ (Fig. 2.5a). Corotation exerts a force to make the plasma follow circular trajectories at the Earth's rotational angular frequency (Fig. 2.5b). The combined convection and corotation potential is shown in Figure 2.5c. A teardrop‐shaped inner core of the magnetosphere corotates with the planet, avoided by the Dungey flow outside; a point of flow stagnation exists along the dusk meridian where the Dungey cycle and corotation forces cancel. Ionospheric plasma can accumulate in the inner region to form the plasmasphere, whereas the outer region is constantly replenished by plasma of solar wind origin from the magnetotail. The boundary between these two regions marks the equatorward edge of the high‐latitude convection pattern in the ionosphere. As the convection voltage increases, the stagnation point moves toward the Earth and the ionospheric convection pattern expands equatorward.

Figure 2.5 Plasma flow in the equatorial plane of the magnetosphere. (a) The Dungey cycle contribution to cold plasma flow, associated with a dawn‐to‐dusk convection electric field E₀. Flow streamlines are also contours of the convection electrostatic potential Φ, where Φ₁ < Φ₂ < Φ₃, etc. (b) The corotation contribution to cold plasma flow. (c) The resultant flow, giving rise to Dungey cycle flow in the outer magnetosphere and corotation in the inner magnetosphere, where the plasmasphere forms (shaded). A flow stagnation point exists along the dusk meridian. (d) Convection and gradient‐curvature drift of hot electrons. (e) Convection and gradient‐curvature drift of hot protons. (f) The effect of displacing the plasma sheet (shaded) sunward by convection: where gradient‐curvature drift paths (dotted circles) intersect the inner edge of the plasma sheet, divergence of the partial ring current leads to the formation of field‐aligned currents that form the region 2 FAC system.

This picture is appropriate for cold plasma, that is the bulk of the plasma sheet particles with gyroradii that are small with respect to the radial magnetic field gradient in the inner dipole. Hot plasma convects earthward from the magnetotail as described above, but experiences gradient‐curvature drift in the inner magnetosphere, with ions and electrons encircling the Earth to the west and east, respectively (Fig. 2.5d and e). This differential ion and electron flow constitutes a westward “ring current.” In addition, divergence of magnetization current in pressure gradients at the inner edge of the earthward‐convecting plasma sheet forms a “partial ring current,” with associated currents flowing along magnetic field lines between the equatorial plane and the polar ionosphere, as shown in Figure 2.5f (Cowley, 2000; Ganushkina et al., 2015). The ramifications of this are discussed in section 2.3.3.

Within the polar cap, the flow is antisunward, associated with flux sinking through the lobes toward the neutral sheet as new open flux is created at the magnetopause and flux is removed from the central plane of the tail as it is reclosed. An additional force on the polar cap field lines needs to be considered when the east‐west or B_Y component of the IMF is nonzero. If we assume that B_Y > 0 in Figure 2.2a, then the northern and southern ends of the newly reconnected field lines are tilted into and out of the page. This exerts a magnetic tension force on the footprints of the field‐lines causing westward and eastward flow in the dayside northern and southern polar caps, respectively (e.g., Heelis, 1984; Reiff & Burch, 1985; Cowley et al., 1991), with the situation reversed for B_Y < 0. The flows crossing the dayside polar cap boundary are directed westward in Figure 2.3b, appropriate for B_Y > 0 in the Northern Hemisphere. Under strong IMF B_Y conditions, the torque exerted by the magnetic tension on the northern and southern lobes can lead to a significant twist on the tail and an induced B_Y component in the lobe field lines that can then introduce east‐west asymmetries into the convection flow on the nightside.

Combined, the antisunward and sunward flows associated with the Dungey cycle and the east‐west sense of flows in the dayside polar cap produced by tension forces are clearly seen in the empirical convection patterns presented in Figure 2.1. The cross‐polar cap potential, Φ_PC, is largest for southward IMF, when the dayside reconnection rate is largest (e.g., Reiff et al., 1981; Milan et al., 2012, and references therein), that is when the magnetic shear at the subsolar magnetopause is greatest. There is evidence that Φ_PC saturates near 250 kV when driving of the magnetosphere is particularly strong (e.g., Siscoe et al., 2002, 2004; Hairston et al., 2003, 2005); although several models have been proposed to explain this saturation, it has not yet been possible to clearly discriminate between them (e.g., Shepherd, 2006; Borovsky et al., 2009).