  Several fast methods for computing stellarator coil shapes are compared,
including the classical NESCOIL procedure [Merkel, Nucl. Fusion 27, 867
(1987)], its generalization using truncated singular value decomposition, and a
Tikhonov regularization approach we call REGCOIL in which the squared current
density is included in the objective function. Considering W7-X and NCSX
geometries, and for any desired level of regularization, we find the REGCOIL
approach simultaneously achieves lower surface-averaged and maximum values of
both current density (on the coil winding surface) and normal magnetic field
(on the desired plasma surface). This approach therefore can simultaneously
improve the free-boundary reconstruction of the target plasma shape while
substantially increasing the minimum distances between coils, preventing
collisions between coils while improving access for ports and maintenance. The
REGCOIL method also allows finer control over the level of regularization, it
preserves convexity to ensure the local optimum found is the global optimum,
and it eliminates two pathologies of NESCOIL: the resulting coil shapes become
independent of the arbitrary choice of angles used to parameterize the coil
surface, and the resulting coil shapes converge rather than diverge as Fourier
resolution is increased. We therefore contend that REGCOIL should be used
instead of NESCOIL for applications in which a fast and robust method for coil
calculation is needed, such as when targeting coil complexity in fixed-boundary
plasma optimization, or for scoping new stellarator geometries.
