Ideal ballooning stability in tokamak plasmas with rigid-body toroidal rotation

The problem of ideal ballooning stability in the presence of a rigid-body toroidal rotation is revisited. The equations describing the stability of a tokamak plasma to high-n ideal ballooning modes are derived without further approximations other than those of ideal magnetohydrodynamics. The equilibrium temperature profile is taken to be such that temperature is constant on a flux surface. A simplification of the model is obtained by considering a large aspect ratio ordering, from which it is found that ballooning stability is governed by a second-order differential equation (as in the case with no flow). In a large aspect ratio equilibrium in which the pressure profile has a narrow region of enhanced pressure gradient it is shown that the effect of the rotation is simply to modify the pressure gradient parameter, alpha , and that the structure of the equations describing the stability is not altered.