The key assumption made when using the frozen-in theory is that magnetic fields must vary slowly in space and time in comparison to particle gyroradii and gyroperiods. This is true throughout much of the magnetospheric system, although at the magnetopause this is not quite the case. As discussed previously, there is a large magnetic shear at this boundary, meaning magnetic gradients in this region are of comparable length scales to particle gyroradii and as a result, the frozen-in conditions break down. This allows the diffusive term of the induction equation, (equation2.36) to become dominant and as a result, magnetic field lines from the IMF and magnetosphere diffuse across the boundary and construct an x-type magnetic field geometry, as seen in Figure 2.12. This process
Figure 2.12: Magnetic reconnection at the magnetopause current sheet. Diagonal
shading lines represent the current sheet with the current density point out of the page. The black solid lines show the magnetic field lines with the large grey arrows showing
their direction of motion. FromCowley et al.(2003).
was first introduced by Dungey (1961) who called it magnetic reconnection. The reconnection site is cleared of newly opened magnetic field lines by magnetic tension acting to straighten the highly curved fields, pulling them along the magnetopause cur- rent sheet and allowing more IMF and magnetospheric field lines to replace them ready to continue the process. The contracting magnetic field lines transfer magnetic energy to the particles frozen into the field, exciting and accelerating them, leading to a heating of the plasma.
A key consequence of the breakdown of the frozen-in theorem is the mixing of solar wind and magnetospheric plasma as the newly reconnected field lines contain plasma from both regions. These new field lines are open, meaning that one end remains connected to the Earth’s magnetic field up in the high latitude polar region and the other end is still connected with the solar wind and they satisfy the frozen-in flux conditions away from the reconnection region.
Magnetic reconnection has a large contribution to magnetospheric dynamics and drives convection throughout the magnetosphere. Consider the configuration of solar wind and magnetospheric magnetic fields depicted in Figure 2.13 where the IMF is directed
southward. Magnetospheric convection begins at the dayside of the system; when both ends of the field line are connected to the magnetosphere, it is closed. As this field line reaches the magnetopause, it undergoes reconnection and merges with an IMF field line and at this point, one end of the newly formed field line is still connected to the magnetosphere and the other is now connected to the IMF. It is now open and is illustrated by point 2 in Figure 2.13. The newly opened field line is swept anti- sunward via the momentum of the solar wind, and over time it becomes elongated. From here, kinetic energy of the solar wind is converted into magnetic energy, stretching the magnetotail into a tear drop shape up to about 1000 RE in length (Dungey, 1961, 1965). As more magnetic field lines convect around the Earth and populate the tail, magnetic pressure forces them to lower latitudes and anti-parallel lines from the northern and southern hemispheres come into close proximity. They form the tail current sheet and reconnection X-line field structure somewhere beyond 100 RE downtail. Tailward of this point, the disconnected section of magnetic field line, whose ends are now both connected to the IMF continue flowing downstream away from the Earth and rejoin the solar wind. Earthward of the reconnection point, the magnetic field is now closed again and magnetic tension draws the field lines sunward and around the Earth to eventually repeat the process again. This convective motion, seen in the insert of Figure2.13, can be mapped to the ionosphere and is seen as a twin-cell convection pattern. The open magnetic field lines convect anti-sunward at high latitudes and the closed field lines convect sunward at lower latitudes.
Magnetic reconnection is not a steady-state process, in fact it is highly variable and depends on solar wind and IMF conditions. The rate of dayside reconnection is in- dependent of the nightside reconnection rate, and while on average the two processes are balanced, at any given moment, either process could be dominant in driving mag- netospheric convection (Cowley and Lockwood, 1992). While southward directed IMF produces the highest rate of reconnection, during periods of northward directed IMF, reconnection still occurs even though the magnetospheric and IMF magnetic field lines are directed parallel to each other, but instead of happening at the subsolar point, it is at higher latitudes that IMF field lines and southward pointing open magnetic field lines reconnect (Dungey,1963). It is important to note that the IMF can have a component in the dawn-dusk and earthward-sunward directions and thus has implications on mag- netospheric flows. When this occurs, it introduces asymmetries in the magnetospheric structure due to magnetic tension exerting a torque on the newly formed open field lines (Cowley,1981a,b).
Figure 2.13: Illustration depicting the flow of plasma within the Earth’s magneto- sphere due to magnetic reconnection. The numbered magnetic field lines show the evolution of reconnection beginning at 1 as it is transported tailward. 6 indicates the region of reconnection in the tail. The insert highlights the ionospheric footprint of the
open field lines in the northern hemisphere. FromHughes (1995a).