Mode Classification for Cavities using Eigenvalue Tracking

Master thesis, Bachelor thesis

1. Context

Eigenmodes of accelerator cavities are cataloged based on their electromagnetic fields in order to analyze the performance of the device. The nomenclature is originally defined for cylindrical pillbox cavities where the eigenfrequencies and corresponding field distributions are known analytically. Due to the complex shape of real-world cavities,in practice the eigenmodes need to be determined using numerical simulations. The attempt to automatically classify eigenmodes by post-processing the numerical field solution is still cumbersome [1]. Therefore, the focus of this work is to investigate automaticmode recognition by deforming the cavity geometry to a pillbox and tracking the eigenmodes during the deformation.

2. Tasks

  • Literature study on eigenvalue tracking and isogeometric analysis
  • Modelling of TESLA cavities using the isogeometric code GeoPDEs
  • Construction of geometric mappings and application of eigenvalue tracking
  • Comparison with the heuristic approach [1]
  • Possible extensions: comparison of different methods for eigenvalue tracking; FEM and mesh deformation; continuation of invariant subspace algorithm

3. Prerequisites

Basic knowledge of or interest in Maxwell’s equations and numerical methods. Experience with programming languages such as MATLAB/Octave.

4. References

[1] K. Brackebusch et al. Automated Mode Recognition Algorithm for Accelerating Cavities, IPAC, 2014.