Free Boundary Long Helical Wavelength Equilibria

A straight high beta helical equilibrium approximating a theta pinch is perturbed into a large aspect ratio torus by the addition of other helically symmetric fields in such a way that stability of the torus to most significant modes is unaffected. The ideal magnetohydrodynamic free boundary model is employed. The straight helical equilibrium is obtained by an expansion in the two parameters which are small but of the same order of magnitude, the ratio of helical magnetic field to theta pinch field and the product of helical wavenumber times plasma column radius. Neither beta nor the distortion of the plasma column from a true cylinder are taken small and the helical fields are principally L = 1. The equilibrium without net z current has desirable stability properties to m = 1 long wavelength modes, although higher m modes are unstable. The stability conditions are more readily satisfied than earlier ones where it was assumed that the plasma column deformation was small and helical wavenumber times plasma radius was not small.