Shape Determination for Deformed Cavities

A realistic superconducting RF cavity has its shape deformed comparing to its designed shape due to the loose tolerance in the fabrication process and the frequency tuning for its accelerating mode. A PDE-constrained optimization problem is proposed to determine the deformation of the cavity. A reduce space method is used to solve the PDE-constrained optimization problem where design sensitivities were computed using a continuous adjoint approach. A proof-of-concept example is given in which the deformation parameters of a single cavity-cell with two different types of deformation were computed