Effect of perturbation theory on the spectrum of ideal magnetohydrodynamic and guiding centre plasmas

For a high β screw pinch it is shown explicitly how the perturbation theory distorts the spectrum of ideal magnetohydrodynamics and guiding centre plasmas. In particular it is seen why the Cauchy integrals (present in the nonperturbative linearized guiding centre plasma model, and which are necessary for the isotropic pressure guiding centre plasma eigenvalue problem to differ from that for magnetohydrodynamics) are absent in the perturbation theory. This result holds also for axially and helically symmetric systems. The distortions in the m = 1 growth rates are also presented.