Ship-Wave Eigenmodes of Drift Type in Rotating Tokamak Plasmas

Ship waves of drift type in rotating plasma of axisymmetric, large aspect-ratio tokamaks with concentric, circular magnetic surfaces are investigated. Plasma rotation is driven by an electrostatic radial electric field and the waves under consideration may be excited by plasma flow past some static obstacle. The analysis performed is based on rigorously derived eigenmode equations coupled in poloidal mode numbers through toroidal effects. The existence of two qualitatively different types of ship wave eigenmodes is demonstrated. Namely (i) global modes that have a structure of quasimodes localised in both radial and poloidal directions and correspond to the bounded states in a potential well which are marginally stable and (ii) propagating modes that experience shear convective damping. The dispersion relations for both types of eigenmodes are obtained both in the weak and the strong coupling approximation. We find the analytical solutions of the dispersion relations and the regions of their existence which are defined, mainly, by the value and direction of the poloidal rotation velocity. An accumulation point for global ship eigenmodes is determined. For propagating ship waves the real and the imaginary parts of the poloidal wavenumber are found. It is shown that the imaginary part always corresponds to convective damping of these waves