Gradient-based eigenvalue optimization for electromagnetic cavities with built-in mode matching

Shape optimization with respect to eigenvalues of a cavity plays an important role in the design of new resonators or in the optimization of existing ones. This paper proposes a gradient-based optimization scheme, which is enhanced with closed-form shape derivatives of the system matrices. Based on these, accurate derivatives of eigenvalues, eigenmodes, and the cost function can be computed with respect to the geometry, which significantly reduces the computational effort of the optimizer. The work is demonstrated by applying it to the 9-cell TESLA cavity, for which the design parameters of the computational model are considered as optimization variables to match the design criteria for devices in realistic use cases. Since eigenvalues may cross during the shape optimization of a cavity, a new algorithm based on an eigenvalue matching procedure is proposed, to ensure the optimization of the desired mode in order to also enable successful matching along large shape variations.