Basic Convection

Axford [1964] suggested the viscous interaction with the solar wind and an effectively closed magnetosphere was responsible for convection in the mag- netosphere. As the solar wind flows past the flanks of the magnetosphere it induces a two cell circulation inside the magnetosphere. Figure 1.14 shows this two cell circulation mapped down to the northern hemisphere ionosphere, as proposed by Axford [1964]. Axford [1964] compared this convection to the convection within a falling rain drop. It is now well known that while the process does occur and does provide some of the required energy it cannot provide it all [Cowley, 1982].

Dungey [1961] suggested that magnetic reconnection at the magne- topause played a key role in the convection within the magnetosphere. Pro-

posed was that during periods of southward IMF (when Bz is negative) the

IMF is anti-parallel to the Earth’s magnetic field at the magnetopause. In this configuration, a thin current sheet layer exists at the magnetopause, whose length scale is much smaller such that the diffusion term in equation 1.30 become significant. Because of this the frozen in condition (that exists both

Figure 1.14: A simplified view of the ionospheric flows lines resulting from viscous interaction of the solar wind and the magnetosphere during northward IMF. A similar but stronger convection pattern occurs during periods of southward IMF. Labelled on the figure is the magnetic latitude and the magnetic local time, where 1200 o’clock defines the position of the Sun. Reproduced from Axford [1964]

in the magnetosphere and the solar wind) breaks down. In this thin bound- ary layer magnetic reconnection occurs. Magnetic reconnection involves the change of magnetic connectivity of plasma fluid elements due to a localised diffusion region in a magnetic null (where there is a field reversal) x-point [Parker, 1957; Petschek, 1964]. Figure 1.15 shows an example of an x-point field configuration in the Sweet-Parker model of reconnection. Figure 1.16 shows a cartoon model of the steps that occur during the reconnection process and convection of the magnetic field. Field lines 1′ (from solar wind) and 1 form an x-point (a magnetic configuration in which reconnection can occur) at the magnetopause. Reconnection occurs between these two field lines - the previous closed geomagnetic field line is now connected to the IMF whilst still being attached to the Earth. The frozen in condition still applies out in the

Figure 1.15: The x-point reconnection configuration in the Parker-Sweet model. The diffusion region is shaded grey. Reproduced from Aschwanden [2006]

IMF and so the new field lines, 2’ and 2, are dragged anti-sunward with the solar wind. The movement of these field lines induces an effective electric field (equation 1.33) and, in a steady state, the field lines are equipotential. The electric potential is mapped onto the ionosphere and is directed from dawn to dusk. This electric field drives (or results from, depending on your viewpoint) anti-sunward flows from noon to midnight.

Eventually the field lines are stretched out into the tail and added to the existing flux there. This transport of flux, while easy to visualise, is not completely correct. Since the magnetic flux in the tail does not increase in- definitely there must be a process that convects the magnetic flux back to the dayside.

In the magnetotail, in a similar manner to the magnetopause under cer- tain conditions, there can be a magnetic neutral x-point in which reconnection occurs. Figure 1.16 shows that field line 6 and 6’ reconnect in the tail. Field line 7’ is disconnected from Earth and reconnected purely to the solar wind, whereas field line 7 is now reconnected solely to the Earth. These newly con-

Figure 1.16: A diagram that shows how field lines reconnect and are convected in the magnetosphere by the soar wind. In the bottom of the figure the field lines are mapped down to their foot points in the on Earth. Reproduced from Kivelson and Russel [1995]

nected field lines flow around either the dawn or dusk side of the Earth where they return to the dayside. At the bottom of figure 1.16 the foot-points of the field lines involved in the convection cycle are mapped onto the ionosphere. From the foot-points it is clear that this cycle produces a similar convection pattern to that in figure 1.14.

This picture of convection is greatly simplified. While key components, such as the return of flux from night side to day side must occur, it need not be that the rate of reconnection at the magnetopause is steady and matches that in the magnetotail. Magnetic energy may be stored in the tail for some time before reconnection in the tail occurs [Baker et al., 1997]. The release of this

energy in the tail tends to happen rapidly (∼ 30 minutes) and the resulting

magnetopheric perturbations are known as magnetospheric substorms, which are discussed in section 1.5.1 [Baker et al., 1997].

Reconnection at the dayside can also occur under northward IMF con- ditions. Reconnection in this scenario occurs in the cusp regions [Crooker, 1979]. The convection cell topology is usually more complicated than a two- cell system in this scenario. During northward dominated IMF (i.e. the |By|

component is small compared toBz ) there is typically a 4-cell configuration,

an example of which is shown in figure 1.17. The lower latitude potential cells on the nightside are associated with the typical two-cell configuration, with the negative cell on the duskside and the positive cell on the dawnside (i.e. anti-sunward flow of plasma). However, the two high latitude cells indi- cate a sunward flow of plasma or a dusk to dawn directed electric field. The magnitude of the cross-polar cap potential is different during southward and

northward IMF conditions. With potential differences of ϕc∼10−30kV and

Figure 1.17: Diagram showing how FAC might be generated from a perturbation of the inner edge of the plasma sheet. Reproduced from Forster et al. [2008]

ences of 30 < ϕc < 120kV and flow speeds 1000ms−1. Where ϕc < 120kV

is the empirically derived cross-polar potential saturation point [Nagatsuma, 2002].