ABSTRACT
External kink modes, believed to be the drive of the ß-limiting resistive wall mode, are strongly stabilized by the presence of a separatrix. We thus propose a novel mechanism explaining the appearance of long-wavelength global instabilities in free boundary high-ß diverted tokamaks, retrieving the experimental observables within a physical framework dramatically simpler than most of the models employed for the description of such phenomena. It is shown that the magnetohydrodynamic stability is worsened by the synergy of ß and plasma resistivity, with wall effects significantly screened in an ideal, i.e., with vanishing resistivity, plasma with separatrix. Stability can be improved by toroidal flows, depending on the proximity to the resistive marginal boundary. The analysis is performed in tokamak toroidal geometry, and includes averaged curvature and essential separatrix effects.
ABSTRACT
The theory of tokamak stability to nonlinear "ballooning" displacements of elliptical magnetic flux tubes is presented. Above a critical pressure profile the energy stored in the plasma may be lowered by finite (but not infinitesimal) displacements of such tubes (metastability). Above a higher pressure profile, the linear stability boundary, such tubes are linearly and nonlinearly unstable. The predicted saturated flux tube displacement can be of the order of the pressure gradient scale length. Plasma transport from these displaced flux tubes may explain the rapid loss of confinement in some experiments.
ABSTRACT
Formulas based on the theory of Weyl are widely used to obtain the average number of modes at or below a given frequency in acoustic and vibrational waveguides. These formulas are valid at asymptotically high frequencies; at finite frequencies they are subject to some error, due to fluctuations in the mode count, which depend on the shape of the waveguide. The periodic orbit theory of semiclassical physics is used to give estimates of the variance of these fluctuations and these results are compared with numerical estimates based on eigenvalues obtained by root-finding. The comparison is good but shows errors that can be related to the nature of the periodic orbit theory. Engineering formulas are provided that give an accurate approximation without significant computational cost. The results are valid for membranes, ducts, and thin plates with clamped and/or simply supported boundary conditions.
