Constrained multiobjective shape optimization of superconducting rf cavities considering robustness against geometric perturbations

High current storage rings, such as the Z-pole operating mode of the FCC-ee, require accelerating cavities that are optimized with respect to both the fundamental mode and the higher order modes. Furthermore, the cavity shape needs to be robust against geometric perturbations which could, for example, arise from manufacturing inaccuracies or harsh operating conditions at cryogenic temperatures. This leads to a constrained multi-objective shape optimization problem which is computationally expensive even for axisymmetric cavity shapes. In order to decrease the computation cost, a global sensitivity analysis is performed and its results are used to reduce the search space and redefine the objective functions. A massively parallel implementation of an evolutionary algorithm, combined with a fast axisymmetric Maxwell eigensolver and a frequency-tuning method is used to find an approximation of the Pareto front. The computed Pareto front approximation and a cavity shape with desired properties are shown. Further, the approach is generalized and applied to another type of cavity.

[1]  Johann Heller,et al.  Quantification of Geometric Uncertainties in Single Cell Cavities for BESSY VSR using Polynomial Chaos , 2014 .

[2]  P. Arbenz,et al.  Multi-objective shape optimization of radio frequency cavities using an evolutionary algorithm , 2018, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment.

[3]  Sergey Belomestnykh,et al.  HIGH-β CAVITY DESIGN - A TUTORIAL * , 2005 .

[4]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[5]  Axel Neumann,et al.  DESIGN OF SRF CAVITIES WITH CELL PROFILES BASED ON BEZIER SPLINES , 2012 .

[6]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[7]  Yves Roblin,et al.  Innovative Applications of Genetic Algorithms to Problems in Accelerator Physics , 2013 .

[8]  P. Arbenz,et al.  CONSTRAINED MULTI-OBJECTIVE SHAPE OPTIMIZATION OF SUPERCONDUCTING RF CAVITIES TO COUNTERACT DANGEROUS HIGHER ORDER MODES , 2019 .

[9]  Michael Benedikt,et al.  Towards future circular colliders , 2016, Proceedings of Sixth Annual Conference on Large Hadron Collider Physics — PoS(LHCP2018).

[10]  V. Akcelik,et al.  Modeling imperfection effects on dipole modes in TESLA cavity , 2007, 2007 IEEE Particle Accelerator Conference (PAC).

[11]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[12]  I. Sobol.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[13]  Habib N. Najm,et al.  Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes , 2005, SIAM J. Sci. Comput..

[14]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[15]  S. G. Zadeh,et al.  FCC-ee HYBRID RF SCHEME , 2018 .

[16]  Andreas Adelmann,et al.  On Nonintrusive Uncertainty Quantification and Surrogate Model Construction in Particle Accelerator Modeling , 2019, SIAM/ASA J. Uncertain. Quantification.

[17]  R. Ringrose,et al.  Accelerating cavity development for the Cornell B-factory, CESR-B , 1991, Conference Record of the 1991 IEEE Particle Accelerator Conference.

[18]  Roger M. Jones,et al.  Optimisation of the new low surface field accelerating structure for the ILC , 2014 .

[19]  Yixun Shi,et al.  Algorithm 748: enclosing zeros of continuous functions , 1995, TOMS.

[20]  R. Calaga,et al.  A Higher Harmonic Cavity at 800 MHz for HL-LHC , 2015 .

[21]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[22]  L. Palumbo,et al.  Wake fields and impedance , 1994 .

[23]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[24]  Constantine Bekas,et al.  A fast and scalable low dimensional solver for charged particle dynamics in large particle accelerators , 2013, Computer Science - Research and Development.

[25]  F. Marhauser,et al.  802 MHz ERL Cavity Design and Development , 2018 .

[26]  Peter Arbenz,et al.  On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices , 2008 .

[27]  Peter Arbenz,et al.  On a Parallel Multilevel Preconditioned Maxwell Eigensolver , 2004 .

[28]  Wolfgang Ackermann,et al.  Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking , 2018, Computer Methods in Applied Mechanics and Engineering.

[29]  Ralph C. Smith,et al.  Uncertainty Quantification: Theory, Implementation, and Applications , 2013 .

[30]  Oscar Chinellato.  The complex-symmetric Jacobi-Davidson algorithm and its application to the computation of some resonance frequencies of anisotropic lossy axisymmetric cavities , 2005 .

[31]  Charles Sinclair,et al.  Multivariate optimization of a high brightness dc gun photoinjector , 2005 .

[32]  U. van Rienen,et al.  Investigation of Geometric Variations for Multicell Cavities Using Perturbative Methods , 2016, IEEE Transactions on Magnetics.

[33]  Cosmin Safta,et al.  Uncertainty Quantification Toolkit (UQTk) , 2015 .

[34]  U. Rienen,et al.  Systematical study on superconducting radio frequency elliptic cavity shapes applicable to future high energy accelerators and energy recovery linacs , 2016 .

[35]  V. Shemelin.  Optimal choice of cell geometry for a multicell superconducting cavity , 2009 .

[36]  Sebastian Schöps,et al.  Isogeometric Analysis simulation of TESLA cavities under uncertainty , 2015, 2015 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[37]  Ursula van Rienen,et al.  Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems , 2018, J. Comput. Phys..

[38]  Peter Arbenz,et al.  Parallel general purpose multiobjective optimization framework with application to electron beam dynamics , 2019, Physical Review Accelerators and Beams.

[39]  F Gerigk,et al.  The Higher-Order Mode Dampers of the 400 MHz Superconducting LHC Cavities , 1998 .

[40]  Hamed Shah-Hosseini,et al.  The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm , 2009, Int. J. Bio Inspired Comput..

[41]  Ursula van Rienen,et al.  Comparison of techniques for uncertainty quantification of superconducting radio frequency cavities , 2014, 2014 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[42]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .