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

Abstract

Feedback stabilization of the Scyllac 120° toroidal sector is reported. The confinement time was increased by 10-20 us using feedback to a maximum time of 35-45 /us, which is over 10 growth times of the long-wavelength m = I instability. These results were obtained after circuits providing flexible waveforms were used to drive auxiliary equilibrium windings. The resultant improved equilibrium agrees well with recent theory. It was observed that normally stable short-wavelength m = I modes could be driven unstable by feedback. This instability, caused by local feedback control, increases the feedback system energy consumption. An instability involving direct coupling of the feedback 1 = 2 field to the plasma 1 = 1 motion was also observed. The plasma parameters were: temperature, T,. a T, a !©0eV; density, n. a 2 X 10" cm" 1 ; radius, a a 1 cm; and P 2 0.7. Beta decreased significantly in 40 ^s, which can be accounted for by classical resistivity and particle loss from the sector ends.

A numerical study of high-beta stellarator equilibria

“…The open triangles represent data taken from three-dimensional calculations of £ = 0 equilibria with R/a = 400 and the same £ = 0 field. Both the two-and three-dimensional results for 5 0 scale as (1 -jS)" 1 as does the surface current theory for small £ = 0 fields [9], and not as the long-wavelength, diffuse-equilibrium solution [1].…”

“…Finite-difference approximations to these equations are solved numerically by a method whose principal features are described in detail in Refs [5,6] and are listed here: (1) The reduction of computational diffusion by the use of a co-moving computation mesh; (2) an implicit formulation of the difference equations to cope with incommensurable time scales within the same calculation; (3) the use of variable zoning to resolve incommensurable length scales on an arbitrarily shaped domain; (4) the ability to apply arbitrary forces to the surface of the plasma by coupling solutions of the flow equations to solutions of the vacuum field equations across a plasma vacuum interface.…”

“…A partial list of the relevant experiments includes the early tests of the stellarator force in a straight geometry on Scylla-IV-3 [22], the 5-metre and 8-metre Scyllac toroidal sectors [12], the confinement experiments on the Scyllac full-torus [23], and Isar Tl-A [24] and Tl-B [25], the feedback stabilization experiments on a toroidal sector [26,27] and the final sector experiments on Scyllac with adjustable equilibrium fields [1,28].…”

“…The numerical study of high-beta stellarator equilibria described here was motivated by evidence that equilibria had not been achieved in the Scyllac experiments [1], by the apparently intractable difficulties encountered in seeking analytic solutions of the equilibrium equations [2], and even by the conjecture that three-dimensional equilibria do not exist [3].…”

Theta-pinch research at Los Alamos

“…In the context of Scyllac experiments, feedback stabilization is accomplished by optically detecting the transverse motion of the plasma column and then applying appropriate auxiliary fields in order to restore the plasma to the centre of the vacuum vessel. This method was successfully demonstrated in a series of sector experiments between 1975 and 1977 [36,37]. One important refinement in the final experimental configuration was the use of 2 = 2 fields in combination with 2 = 1, instead of the 2 = 0 used in early experiments.…”