Shape Optimization of an Electron Gun
S-DALINAC (Superconducting-DArmstadt-LINear-ACcelerator) is a superconducting electron accelerator at TU Darmstadt, running since 1991. It was initially constructed as a twice-recirculating accelerator with a maximum energy of 130 MeV in continuous wave (cw) operation. In 2016 it has been converted into a thrice-recirculating accelerator, see here. For the next upgrade an interdisciplinary team is working on the numerical shape optimization of a new compact DC high-voltage photo-electron gun. The main objective is to reduce the peak value of the electric field in the vacuum chamber in order to avoid the damaging of the device. The axisymmetric structure of the device is exploited, and the geometry of its cross-section is described by Non-Uniform Rational B-Spline (NURBS). This choice ensures the capability of representing common CAD geometries and simplifies the step from design to simulations by isogeometric analysis and eventually to manufacturing.
Mathematically speaking, the problem is a PDE-constraint optimization problem where the PDE is given by the electrostatic approximation to Maxwell’s equations, i.e., a Poisson-type equation, see Figure. The goal function aims at reducing the peak electric field and the volume while preserving a sufficient beam quality which involves a particle tracking problem. Preliminary simulation results promise a reduction of the peak field by 10% while reducing the volume by 2% without affecting the beam quality.