A procedure which reconciles long parallel wavelength, characteristic of plasma instabilities, with periodicity in a sheared toroidal magnetic field is described. Applied to the problem of high-$n$ ballooning modes in tokamaks it makes possible a full minimization of the potential energy functional $\delta W$ and shows that previous calculations overestimated stability.

• Received 14 November 1977

DOI:https://doi.org/10.1103/PhysRevLett.40.396