Toroidal field effects on dipole equilibrium and stability at finite plasma pressure

The influence of a toroidal magnetic field on the equilibrium and stability of a plasma confined by the magnetic field of a point dipole is considered, since it may be necessary to introduce a toroidal magnetic field to smooth electron heating or other asymmetries in the toroidal direction that can lead to toroidal electric fields and a loss of confinement due to radial E×B drift. To begin, a toriodal magnetic field is shown to restore confinement by reducing electron heating departures from axisymmetry. Then the Grad–Shafranov equation for a point dipole in the presence of a toroidal field is solved to explicitly demonstrate that an equilibrium exists. Finally, it is shown that a toroidal magnetic field destabilizes the otherwise stable point dipole ballooning modes at high plasma pressure. Consequently, if a toroidal magnetic field is necessary to remove toroidal heating asymmetries in a dipole equilibrium, the heating may have to be performed transiently or at lower plasma pressures.