Recent advances in the stability theory of toroidal plasmas

Abstract

Many of the most persistent instabilities of a magnetically confined plasma have short wavelength perpendicular to the magnetic field but long wavelength parallel to it. Such instabilities are difficult to treat in a toroidal system because the simple eikonal representation of short wavelength oscillations X (r) = Y (r) with 8 1 proves to be incompatible with the other requirements of toroidal periodicity and long parallel wavelength (which would require B >VS = 0). A new method of representing perturbations in a torus will be outlined. By using this, the two-dimensional stability problem posed by an axisymmetric toroidal equilibrium can be reduced to that of solving a one-dimensional eigenvalue equation. This technique essentially completes the linear stability theory of magnetohydrodynamic modes in a toroidal plasma, and is also applicable to the investigation of micro-instabilities that are described by the Vlasov-Maxwell equations.