Quantum Chaos Analysis of the Ideal Interchange Spectrum in a Stellarator

Abstract

The eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence. Quantum chaos theory provides tools for characterizing the spectrum statistically, from the regular spectrum of the separable case (integrable semiclassical dynamics) to that where the semiclassical ray dynamics is so chaotic that no simple classification of the individual eigen-values is possible (quantum chaos). Using the CAS3D code, a data set of several hundred growth-rate eigenvalues has been calculated for a Mercier-unstable three-dimensional stellarator equilibrium with a rather flat, non-monotonic rotational transform profile. Statistical analysis of eigenvalue spacings for individual mode families shows evidence of quantum chaos, strongest for the N = 0 family, but to test this we compare it with the distribution of eigenvalue spacings in a similar separable case - ideal interchange modes in a Suydam-unstable plasma cylinder - using a similar rotational transform profile to the stellarator case. The statistics in the cylindrical model appear Poissonian, as expected for generic integrable systems and in clear contrast to the three-dimensional stellarator results.