Stability of a Taylor-relaxed cylindrical plasma separated from the wall by a vacuum layer

The minimum energy principle of Taylor is extended to the case where a vacuum layer is situated between the weakly resistive plasma and the perfectly conducting wall. The second variation is investigated for periodic perturbations (m and/or k≠0) as well as for symmetric perturbations (m=k=0). A necessary and sufficient criterion for stability is derived by means of the Rayleigh ratio method and turns out to be identical with the result of the resistive mode analysis. Stability diagrams λ vs k are presented. A new instability region at m=1 is found at negative values of k, already present when λ is small. The symmetric mode becomes more unstable as the vacuum layer grows thicker. 11 refs.; 7 figs.; 92 schemes