Beyond the Dipole

The ideal MHD case is simpler and easier to visualize, as we can treat the ?eld lines as being "frozen" to the plasma [26]. By "frozen," we mean that the magnetic ?eld must move with the plasma; as a consequence, the system can be decomposed into tubes of equal magnetic ?ux. If a ?ux tube moves radially outward, it moves into a region of lower magnetic ?eld [27], which increases the volume of the ?ux tube and adiabatically cools it. For a ?ux tube to move outward, it must exchange places with another ?ux tube moving inward, whose volume will be reduced in the region of stronger magnetic ?eld and lead to adiabatic heating. This swapping of ?ux tubes is known as an electrostatic interchange (or ?ute) instability [28]. Note that by de?nition there is no change to the magnetic topology and there are no parallel currents. This mode is the plasma equivalent of the Rayleigh-Taylor instability in neutral ?uids, in which a heavy ?uid is supported a against gravity by a lighter ?uid. In neutral ?uids the instability grows when the pressure gradient is anti-parallel to the gravitational force; in plasmas it grows when the pressure gradient is antiparallel to the radius of curvature of the magnetic ?eld; such plasmas are often referred to as having "bad" curvature.