Statistical characterization of the interchange-instability spectrum of a separable ideal-magnetohydrodynamic model system

A significant deviation of the statistical nature of the ideal-magnetohydrodynamics (MHD) interchange spectrum from the random Poisson process of generic separable systems was analyzed. It was shown that the normal mode equations are completely separable, so both the toroidal Fourier harmonic index n and the poloidal index m are good quantum numbers. The statistics of the ideal-MHD spectrum departed somewhat from the Poisson distribution, even for arbitrarily large m_max, unlike the generic separable two-dimensional system. It was found that this departure from Poissonian statistics may be understood qualitatively from the nature of the distribution of rational numbers in the rotational transform profile.