  This paper deals with the design optimization of a synchronous reluctance
machine to be used in an X-ray tube, where the goal is to maximize the torque,
by means of gradient-based free-form shape optimization. The presented approach
is based on the mathematical concept of shape derivatives and allows to obtain
new motor designs without the need to introduce a geometric parametrization. We
validate our results by comparing them to a parametric geometry optimization in
JMAG by means of a stochastic optimization algorithm. While the obtained
designs are of similar shape, the computational time used by the gradient-based
algorithm is in the order of minutes, compared to several hours taken by the
stochastic optimization algorithm. Finally, we show an extension of the
free-form shape optimization algorithm to the case of multiple objective
functions and illustrate a way to obtain an approximate Pareto front.
