Magnetohydrostatic ℓ = 1, Finite β Stellarator Equilibrium

A finite β, ℓ = 1 stellarator configuration with tightly wound helical fields and with no longitudinal current through each magnetic surface is determined using a thin-tube expansion. The independent variables are the magnetic surfaces as coordinate surfaces and the magnetic field lines and the current density lines as coordinate lines. The usual thin-tube quantities ρ, φ, and s are treated as dependent variables. The method can readily be applied to other configurations.