Robert Dewar Department of Theoretical Physics, The Australian National University Quantum chaos theory and the spectrum of ideal-MHD instabilities in toroidal plasmas Wednesday 25th, August 14:05-14:55pm, Carslaw Lecture Theatre 273. Normal mode analysis is a standard method for analysing the stability of plasma containment devices. In a fully 3-D plasma containment system (a stellarator) the toroidal mode number n ceases to be a good quantum number-all ns within a given mode family being coupled-and the WKB semiclassical quantisation method breaks down due to chaotic ray orbits (when MHD is regularised to keep the wave vector finite, otherwise the rays escape to infinity). In quantum chaos theory, 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 neighbouring eigenvalues is as derived from random matrix theory and goes to zero at zero separation. This contrasts with the Poissonian distribution found in generic separable systems, showing that a signature of quantum chaos is level repulsion. In order to determine whether eigenvalues of the regularised 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 (1-D) equilibrium and a Mercier-unstable stellarator equilibrium, regularised by a simple cutoff in the poloidal mode number m. Unlike the generic separable two-dimensional system, the statistics of the ideal-MHD spectrum departs somewhat from the Poisson distribution, even for arbitrarily large m_max. A qualitative understanding of this can be had from the number-theoretic properties of the magnetic field rotation number profile. In the 3-D case we find strong evidence of level repulsion within mode families, but mixing mode families produces Poissonian statistics.