Derive the dispersion relation 2 (k) for axisymmetric perturbations of the -pinch configuration when the magnetic field is confined to the cylinders exterior, and

Derive the dispersion relation ω²(k) for axisymmetric perturbations of the Θ-pinch configuration when the magnetic field is confined to the cylinder’s exterior, and conclude from it that the Θ-pinch is stable against axisymmetric perturbations. Repeat your analysis for a general, variable separated perturbation of the form ξ ∝ e^{i(mθ+kz−ωt)}, and thereby conclude that the Θ-pinch is fully MHD stable.