Stability of toroidal plasmas: the influence of magnetic shear, periodicity and rotation

This paper describes work on an important class of plasma instabilities in toroidal confinement systems. These are instabilities with large mode number in the toroidal direction but long wavelength parallel to the magnetic field. After a brief historical introduction the now standard method-the ballooning representation-for calculating such modes is described. This method is remarkably successful for most stationary plasmas, but breaks down for configurations with low magnetic shear or with significant sheared rotational flow. These are two areas of great current interest because of their association with 'transport barriers' in tokamaks. Some extensions of ballooning theory for dealing with these situations are described and some preliminary results, in particular showing the stabilizing effect of sheared rotation, are presented.