Anderson Localization of Ballooning Modes, Quantum Chaos and the Stability of Compact Quasiaxially Symmetric Stellarators
Authors: M.H. Redi, J.L. Johnson, S. Klasky, J. Canik, R.L. Dewar, and W.A. Cooper
Date of PPPL Report: November 2001
Presented at: the American Physical Society Division of Plasma Physics meeting in Long Beach, CA., October 29 - November 2, 2001. Published in Physics of Plasmas 9 No. 5 (May 2002) 1990-1996.
The radially local magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHD stability is analysed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space (s, s, qk); s is the edge normalized toroidal flux, a is the field line variable, and qk is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong "quantum chaos." The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-n MHD computations are required to predict the beta limit.