Fluid, Kinetic and Electromagnetic Effects on Rippling Instabilities in Tokamaks

Tokamak plasmas are unstable against small perturbations that convect resistivity across the confining magnetic field, (')B. The rippling instability is due to the presence of a current along (')B, and a resistivity gradient across (')B. In this thesis the impact on the rippling instability of electron and ion diamagnetic drifts, electron parallel heat conductivity, and electron viscosity is considered. Electromag - netic effects are accounted for, albeit approximately, by means of a vector potential, (')A (PARLL) (')B. The linear, normal mode stability calculations are carried out for a plasma slab in a sheared magnetic field. The Vlasov and Braginskii equations, for ions and electrons respectively, are solved for the current density perturbation, (')J(,1), in terms of the perturbed potentials (phi), (')A(,(PARLL)). Then, the quasineutrality condition ((')(DEL)(.)(')J(,1) = 0), and Ampere's law are used to set up an eigenvalue problem. In the zero-(beta) limit, the problem is solved by perturbations, and a numer- ical JWKB-method. In the finite-(beta) limit, the numerical integration fails to converge if the conditions (phi)((INFIN)), (')A(,(PARLL))((INFIN)) = 0 are used. These diffi- culties are overcome by imposing generalized Sommerfeld radiation conditions derived from first-order asymptotic solutions. It is found that when the electron temperature, T(,e), is low the rippling mode is unstable and becomes more so as T(,e) decreases. For T(,e) large, the mode is stable and tends toward marginal stability. This latter trend is overridden by viscosity. Stabilization is due to heat conduction, and stability is enhanced by ion FLR effects. The real frequencey (omega)(,r) is determined by the electron diamagnetic drift frequencies (omega)(,*('e)), (omega) , but is sensitive to w(,*('i)), (omega) , and (eta)(,i) (=(d ln T(,i))/ (d ln n(,i))). For (eta)(,i) = (eta)(,e) = 1, (omega)(,r) tends asymptotically to (omega) \as T(,e) increases above 350 eV, but dips below (omega) \on account of viscosity. At high temperature, (phi) and (')A(,(PARLL)) are centered on the mode-rational surface. For T(,e) (TURN) 0, (')A(,(PARLL)) is centered on said surface, but (phi) is not. The general conclusion is that the rippling mode is essentially electro- static, and poses no threat to confinement save at the edge of tokamaks where T(,e) is fairly low.