  We extend the single-stage stellarator coil design approach for
quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into
account coil manufacturing errors. By modeling coil errors independently from
the coil discretization, we have the flexibility to consider realistic forms of
coil errors. The corresponding stochastic optimization problems are formulated
using a risk-neutral approach and risk-averse approaches. We present an
efficient, gradient-based descent algorithm which relies on analytical
derivatives to solve these problems. In a comprehensive numerical study, we
compare the coil designs resulting from deterministic and risk-neutral
stochastic optimization and find that the risk-neutral formulation results in
more robust configurations and reduces the number of local minima of the
optimization problem. We also compare deterministic and risk-neutral approaches
in terms of quasi-symmetry on and away from the magnetic axis, and in terms of
the confinement of particles released close to the axis. Finally, we show that
for the optimization problems we consider, a risk-averse objective using the
Conditional Value-at-Risk leads to results which are similar to the
risk-neutral objective.
