Magnetohydrodynamic Waves and Instabilities in Rotating Tokamak Plasmas

One of the most promising ways to achieve controlled nuclear fusion for the commercial production of energy is the tokamak design. In such a device, a hot plasma is confined in a toroidal geometry using magnetic fields. The present generation of tokamaks shows significant plasma rotation, primarily in the toroidal direction. This plasma flow has an important impact on stability and confinement, aspects of which can be described quite well by the theory of magnetohydrodynamics (MHD). This work contains a comprehensive theoretical analysis, supported by numerical simulations, of the MHD equilibrium, waves, and instabilities of rotating tokamak plasmas. A new general description of the thermodynamic state of the equilibrium is presented. Next, a stability criterion is derived that generalizes various previous results by including toroidal rotation. This criterion shows that a radially decreasing rotation profile can be stabilizing. The previously unknown origin of this stabilization is shown to be the Coriolis effect, with a mediating role for the pressure. Various factors that affect stability also influence stable waves and eigenmodes of the plasma. New modes that are created by rotation are found, and the effect of rotation on a type of experimentally well-known modes is described. Finally, the step to nonlinear magnetohydrodynamics is made by extending an existing reduced MHD code to the full viscoresistive MHD equations. This allows a study of the nonlinear evolution of the equilibria, waves, and instabilities described in this thesis.