Solution of the resistive two-fluid wave equations for Alfvènic modes in spherical tokamak plasmas

Abstract

Low aspect ratio tokamak (LART) configurations represent a promising approach to thermonuclear fusion. They require auxiliary non-ohmic power for heating, current drive and turbulent transport suppression. This paper pioneers the pre-requisite for the quantitative evaluation of these effects, namely the formulation and solution of the full wave equation for pre-heated (i.e. prior to the addition of any auxiliary heating or current drive) LARTs, the case in which mode-converted Alfven waves ( $\omega ) are used as an additional non-ohmic power source. Arbitrary aspect ratio and magnetic shear tokamaks with non-circular cross-section are properly considered; this general approach includes, as a particular case, that of low aspect ratio (spherical) tokamaks. The problem is formulated in terms of the vector and scalar potentials ( ${\bf A}, \Phi$ ), thus avoiding the numerical pollution occurring in the case of the ( ${\bf E},{\bf B}$ ) formulation. Adequate boundary conditions at the vacuum–metallic wall interface and regularity conditions at the magnetic axis are enforced. For the pre-heated stage, a quite general two-fluid, resistive dielectric tensor operator able to describe the anisotropic plasma response in spherical tokamaks is derived and used; except for its linear character, no geometrical limitations are imposed on it. Consistent equilibrium profiles also including effects of neoclassical conductivity and bootstrap current are used (Wilson 1994). The wave equations are solved with the aid of a suitable $2\frac{1}{2}{\rm D}$ finite-element algorithm, taking advantage of the up-down symmetry of the problem. Illustrative solutions obtained for Culham's START device are presented and discussed; this includes a sensitivity study to the antenna parameters (geometry, frequency and wavenumbers). Finally, as one of the possible applications of these results, illustrative ensuing ponderomotive forces and the non-inductive current drive in a START-like device are calculated.