Development and investigation of perturbative methods for the computation of electromagnetic fields.

The geometry of an accelerator cavity determines its eigenmodes and thereby its performance characteristics. Therefore, accelerating performance and wakefield characteristics may be improved by an intentional modification of the geometry. However, undesired geometry perturbations due to manufacturing tolerances and operational demands can likewise impair it. Therefore, parameter studies of geometric variations are an essential part of the performance optimization and error estimation in the design of cavities.

Using conventional eigenmode solvers these parameter studies tend to be computationally extensive and inefficient since the cavity shape has to be modified numerous times and any geometric variation no matter how slight, involves a full eigenmode recomputation.

Perturbative methods constitute an efficient alternative for the computation of a multitude of geometric variations. They require a conventional eigenmode computation of solely one (so called unperturbed) geometry. The eigenmodes of modified (so called perturbed) geometries can be deriving from the unperturbed geometry by expanding the perturbed eigenmodes as a series of the unperturbed ones. Thus, the computational effort for parameter studies may be significantly reduced by using perturbative computation methods.

1. Use of existing and development of new perturbative approaches
2. Code development for the automated and efficient application of the perturbative methods based on analytically or numerically (conventional field simulation software) determined unperturbed fields
3. Validation of the obtained results (accuracy, computational effort)
4. Application in the design of real cavity structures (optimization, error analysis)

• iHEAL: Smart sensor system for diagnosing Cruciate Ligament ruptures 
  http://iheal.uni-rostock.de/

• K. BRACKEBUSCH, T. GALEK, U. VAN RIENEN, Automated Mode Recognition Algorithm for Accelerating Cavities, Proceedings of 5th IPAC, Dresden, Germany, June 15-20, 2014.

• T. GALEK, K. BRACKEBUSCH, U. VAN RIENEN, Study of Higher Order Modes in Multi-Cell Cavities for BESSY-VSR Upgrade, Proceedings of 5th IPAC, Dresden, Germany, June 15-20, 2014.

• K. BRACKEBUSCH, U. VAN RIENEN, Eigenmode Computation for Elliptical Cavities Subject to Geometric Variation Using Perturbative Methods, Proceedings of 4th IPAC, Shanghai, China, May 12-17, pp. 900-902, 2013.

• T. GALEK, K. BRACKEBUSCH, T. FLISGEN, U. VAN RIENEN, B. RIEMANN, T. WEIS, A. NEUMANN, J. KNOBLOCH: BERLINPRO Seven-cell SRF Cavity Optimization and HOMs External Quality Factors Estimation, Proceedings of 4th IPAC, Shanghai, China, May 12-17, pp. 2331-2333, 2013.

• A. NEUMANN, W. ANDERS, J. KNOBLOCH, K. BRACKEBUSCH, T. FLISGEN, T. GALEK, K. PAPKE, U. VAN RIENEN, B. RIEMANN, T. WEIS: Results and Performance Simulations of the Main Linac Design for BERLinPro, Proceedings of LINAC 2012, Tel-Aviv, Israel, September 9-14, pp. 333-335, 2012.

• K. BRACKEBUSCH, U. VAN RIENEN: Implementational Aspects of Eigenmode Computation Based on Perturbation Theory, Proceedings of 11th ICAP, Warnemünde, Germany, August 19-24, pp. 48-50, 2012.

• A. NEUMANN, W. ANDERS, J. KNOBLOCH, K. BRACKEBUSCH, T. FLISGEN, T. GALEK, K. PAPKE, U. VAN RIENEN, B. RIEMANN, T. WEIS: Status of the HOM Calculations for the BERLinPro Main Linac Cavity, Proceedings of 11th ICAP, Warnemünde, Germany, August 19-24, pp. 278-280, 2012.

• K. BRACKEBUSCH, U. VAN RIENEN, Eigenmode Computation for Cavities with Perturbed Geometry based on a Series Expansion of Unperturbed Eigenmodes, Proceedings of 3rd IPAC,  New Orleans, USA, May 20-25, pp. 277-279, 2012.

• K. BRACKEBUSCH, H.-W. GLOCK, U. VAN RIENEN: Calculation of High Frequency Fields in Resonant Cavities based on Perturbation Theory, Proceedings of 2nd IPAC, San Sebastian, Spain, September 4-9, pp. 2235-2237, 2011.