  Coil complexity is a critical consideration in stellarator design. The
traditional two-step optimization approach, in which the plasma boundary is
optimized for physics properties and the coils are subsequently optimized to be
consistent with this boundary, can result in plasma shapes which cannot be
produced with sufficiently simple coils. To address this challenge, we propose
a method to incorporate considerations of coil complexity in the optimization
of the plasma boundary. Coil complexity metrics are computed from the current
potential solution obtained with the REGCOIL code (Landreman 2017 Nucl. Fusion
57 046003). We compute the local sensitivity of these metrics with respect to
perturbations of the plasma boundary using the shape gradient (Landreman & Paul
2018 Nucl. Fusion 58 076023). We extend REGCOIL to compute derivatives of these
metrics with respect to parameters describing the plasma boundary. In keeping
with previous research on winding surface optimization (Paul et al. 2018 Nucl.
Fusion 58 076015), the shape derivatives are computed with a discrete adjoint
method. In contrast with the previous work, derivatives are computed with
respect to the plasma rather than the winding surface parameters. To further
reduce the required resolution, we present a more efficient representation of
the plasma surface using a single Fourier series to describe the radial
distance from a coordinate axis and a spectrally condensed poloidal angle. This
representation is advantageous over the standard cylindrical representation
used in the VMEC code (Hirshman & Whitson 1983 The Physics of Fluids 26
3553-3568), as it provides a uniquely defined poloidal angle, eliminating a
null space in the optimization of the plasma surface. The resulting shape
gradient highlights features of the plasma boundary consistent with simple
coils and can be used to couple coil and fixed-boundary optimization.
