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Multi-Objective Shape Optimization of TESLA-like Cavities: Addressing Stochastic Maxwell's Eigenproblem Constraints

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... Although we present a particular application of the QPR model, the proposed approach is general and can be applied to stochastic multi-physics modeling devices such as multi-cell cavities or couplers from accelerator physics [1,15,23]. ...
... Moreover, the work presented in [30,31] addresses certain aspects of the shape derivative for Maxwell's eigenproblem, from a deterministic perspective in a mathematically rigorous manner. The optimization problem constrained by the stochastic formulation of Maxwell's eigenproblem has been successfully studied in our previous work [6,23]. ...
... This paper presents a novel approach to uncertainty quantification analysis and shape perturbation ‡ Even though the proposed approach for manufacturing processes representation is quite general [20,21], we prefer the robust formulation, consisting of the expectation's weighted functions and the standard deviation as in [18,22,23,24]. § In the CST Studio Suite ® -software used for our simulations -a shape sensitivity analysis is implemented only for built-in functions like frequency [26]. . ...
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... In context of cavities, there already exists several references to multiobjective optimization, e.g., [35,52] as well as parameter optimization, e.g., [48]. Further, for solving multi-objective optimization problems, we refer to [36] for the use of an evolutionary algorithm, and to [46], addressing a stochastic Maxwell's eigenvalue problem. ...
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The electromagnetic properties of SRF cavities are mostly determined by their shape. Due to fabrication tolerances, tuning and limited resolution of measurement systems, the exact shape remains uncertain. In order to make assess-ments for the real life behaviour it is important to quan-tify how these geometrical uncertainties propagate through the mathematical system and influence certain electromag-netic properties, like the resonant frequencies of the struc-ture's eigenmodes. This can be done by using non-intrusive straightforward methods like Monte-Carlo (MC) simulations. However, such simulations require a large number of deter-ministic problem solutions to obtain a sufficient accuracy. In order to avoid this scaling behaviour, the so-called gen-eralized polynomial chaos (gPC) expansion is used. This technique allows for the relatively fast computation of uncer-tainty propagation for few uncertain parameters in the case of computationally expensive deterministic models. In this paper we use the gPC expansion to quantify the propagation of uncertain geometry on the example of single cell cavities used for BESSY VSR as well as to compare the obtained results with the MC simulation.
Article
The main superconducting radio frequency (SRF) linacs of the international linear collider (ILC) operate at a frequency of 1.3GHz with a π phase advance per cell in the standing wave mode. An option being considered to reduce the overall footprint and project cost is to enhance the cavity gradient. The present baseline design for the main linacs of ILC demands the cavities to be able to reach a gradient of 35MV/m—although during commissioning and operation the gradient will be 31.5MV/m. This research concerns itself with the new cavity design with a view to reaching higher gradients. This design is focussed on minimising the surface electromagnetic fields and maximising the bandwidth of the accelerating mode. This new shape, which is referred to as the New Low Surface Field (NLSF) design. A design of a complete nine-cell cavity, including power couplers and higher order mode damping couplers is presented.
Article
One considers the context of the concurrent optimization of several criteria Ji(Y)Ji(Y) (i=1,…,ni=1,…,n), supposed to be smooth functions of the design vector Y∈RNY∈RN (n⩽Nn⩽N). An original constructive solution is given to the problem of identifying a descent direction common to all criteria when the current design-point Y0Y0 is not Pareto-optimal. This leads us to generalize the classical steepest-descent method to the multiobjective context by utilizing this direction for the descent. The algorithm is then proved to converge to a Pareto-stationary design-point.RésuméOn se place dans le contexte de lʼoptimisation concourante de plusieurs critères Ji(Y)Ji(Y) (i=1,…,ni=1,…,n), fonctions régulières du vecteur de conception Y∈RNY∈RN (n⩽Nn⩽N). On donne une solution constructive originale au problème de lʼidentification dʼune direction de descente commune à tous les critères en un point Y0Y0 non optimal au sens de Pareto. On est conduit à généraliser la méthode classique du gradient au contexte multiobjectif en utilisant cette direction pour la descente. On prouve que lʼalgorithme converge alors vers un point de conception Pareto-stationnaire.