Comparison of unstable modes and growth rates in ideal magnetohydrodynamics and guiding center plasmas

Unstable modes and growth rates are compared for helically symmetric equilibria based on the models of ideal magnetohydrodynamics and guiding center plasmas. After appropriate expansions and approximations, it is shown that any unstable mode in ideal magnetohydrodynamics is present in exactly the same form and with the same growth rate in a guiding center plasma. Except for a small class of modes whose existence is doubted but cannot be proved with the analysis given, the converse statement also holds.