Ideal MHD stability of m ≥ 2 modes in diffuse high-β, ℓ = 1 equilibria

Abstract

A time-dependent explicit finite-difference code is developed for computing growth rates of gross magnetohydrodynamic modes in helically symmetric high-6, 8= 1 equilibria. The effect of numerical dispersion on current-and pressure-driven modes and the convergence of the growth rate with the grid size for modes in screw-pinch, O-pinch, and helical equilibria are discussed. In the case of diffuse MHD equilibria with a long helical period length, the eigenvalues computed by this code are in agreement with those of a 6W-analysis and of experiments and are a factor of about two smaller than predicted by the surface current theory. The growth rates o f m i 2 modes are given as functions of the helical periodicity number, the helical amplitude of the magnetic axis, beta, and the longitudinal wave number k. * This work was performed under the terms of the agreement on association between Max-Planck-Institut fflr Plasmaphysik and Euratom.

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

“…Recent experimental work shows that this criterion is much too pessimistic [15]. This can be explained in part by the fact that the magnetohydrodynamic growth rate for m > 2 modes is considerably less for a diffuse rather than sharpboundary profile [16,17].…”

“…Feedback-system parameters. The equation of motion of the gross motion mode with feedback can be written -T (17) where £ is the sideways displacement of the plasma, 7 is growth rate of the m = 1 instability, T is the feedback-system delay and a. and T X are feedback gain parameters. The product yr is crucial and must be less than about 1 if Eq.…”