Finite-β stabilization of a diffuse helical ℓ = 1 MHD equilibrium

The stability of helically symmetric finite-β, ℓ = 1 magnetohydrostatic equilibria with arbitrary pressure profile and vanishing longitudinal current is investigated by means of Mercier's criterion, a sufficient criterion by Lortz, Rebhan and Spies, and Shafranov's condition for a high–β magnetic well. The new finite–β effects are that (1) a magnetic well is created throughout the plasma region for 0.2 ≲ β ≲ 0.95 and 0.3 ≤ aτ ≤ 0.6 (a is the plasma radius, τ the torsion of the magnetic axis); (2) the mean magnetic well extends out into the vacuum region for 0.75 ≲ β and bτ ≲ 0.6 (b is the wall radius); (3) with the exception of a very narrow region (< 0.1 aτ) around the magnetic axis, the Mercier criterion is satisfied for 0.75 ≲ β ≲ 0.95 and 0.12 ≲ aτ ≲ 0.3.