Coil optimization methods for a planar coil stellarator

The planar coil stellarator design is a novel approach to producing the confining magnetic field of a stellarator plasma. The work presented here details the optimization of the two types of planar coils that are used in the planar coil design: the plasma encircling coils, and the shaping coils. The plasma encircling coils provide the mean magnetic field and linking current, similar to the toroidal field (TF) coils in a tokamak. The plasma encircling coils can be rotationally symmetric TF-like coils and produce a B ∝ 1 / R field, but optimizing their placement, tilt, and shaping can substantially reduce the magnetic field error. In addition, an array of dipole-like shaping coils, that lie on a surface between the plasma boundary and the encircling coils, correct for the residual magnetic field error following encircling coil optimization. As a proof-of-concept, it is shown that by optimizing both types of coils, subject to realistic engineering constraints, reasonable magnetic field errors of ∼1% have been achieved. Comparison to a traditional modular coil set reveals that similarly low magnetic field errors can be attained with the planar coil stellarator.