Effect of sheared toroidal plasma flows on equilibrium and stability of tokamaks

The equilibrium of a toroidally rotating axisymmetric plasma was studied theoretically by Maschke and Perrin. They showed that the Grad-Shafranov equation can be generalised to include the effect of rotation if either the temperature or the entropy is assumed to be constant on the magnetic surfaces. They also obtained analytical solutions for certain simple cases. Some more analytical solutions were obtained by Throumoulopoulos and Pantis. However, all these solutions are for rigid rotation only. In this work we investigate the effect of velocity shear on the toroidal equilibrium and stability both numerically and analytically. We consider an isothermal plasma obeying ideal MHD confined in a perfectly conducting shell with a circular cross section. (author) 5 refs., 4 figs