In a fully 3-D system such as a stellarator, the toroidal mode number n ceases to be a good quantum number, all ns within a given mode family [1] being coupled. It is found that the discrete spectrum of unstable ideal MHD instabilities ceases to exist unless MHD is modified (regularized) by introducing a short-perpendicular-wavelength cutoff (numerical truncation or FLR). Attempts to use WKB (semiclassical) ray tracing to estimate the regularized MHD spectrum fail due to the occurrence of chaotic ray trajectories [2].
In quantum chaos theory [3], strong chaos in the semiclassical limit leads to eigenvalue statistics the same as those of a suitable ensemble of random matrices. For instance, the probability distribution function for the separation between neighboring eigenvalues is as derived from random matrix theory and goes to zero at zero separation. This contrasts with the Poissonian distribution found in separable systems, showing that a signature of quantum chaos is level repulsion.
In order to determine whether eigenvalues of the regularized MHD problem obey the same statistics as those of the Schrödinger equation in both the separable 1-D case and the chaotic 3-D cases, we have assembled data sets of ideal MHD eigenvalues for a Suydam-unstable cylindrical equilibrium and a Mercier-unstable W7X-like equilibrium.
In the 1-D case, we have generalized the transformation to Schrödinger form [4] so both low- and high-m eigenvalues are calculated in a uniform fashion. In the 3-D case we use the CAS3D code [1] and find strong evidence of level repulsion.

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