Non-axisymmetric local magnetostatic equilibrium

In this work we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas (Miller et al. 1998 Phys. Plasmas 5, 973). Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozer coordinates is clarified.