Abstract
For a precise determination of the rf properties of superconducting materials, a calorimetric measurement is carried out with the aid of a so-called quadrupole resonator (QPR). This procedure is affected by certain systematic measurement errors with various sources of uncertainties. In this paper, to reduce the impact of geometrical uncertainties on the measurement bias, the modified steepest descent method is used for the multiobjective shape optimization of a QPR in terms of an expectation measure. Thereby, variations of geometrical parameters are modeled by the polynomial chaos expansion technique. Then, the resulting Maxwell's eigenvalue problem with random input data is solved using the polynomial chaos-based stochastic collocation method. Furthermore, to assess the contribution of the particular geometrical parameters, the variance-based sensitivity analysis is proposed. This allows for modifying the steepest descent algorithm, which results in reducing the computational load needed to find optimal solutions. Finally, optimization results in the form of an efficient approximation of the Pareto front for a three-dimensional model of the QPR are shown.
Highlights
In modern particle accelerators, superconducting rf (SRF) cavities are widely used to provide high-accelerating gradients to a beam of particles while ensuring moderate power losses
The quadrupole resonator (QPR) design has two advantages: (i) it allows a direct measurement of the surface resistance with a subnΩ resolution and (ii) the applied temperature, frequency, and magnetic field values are of the typical range for accelerator operation
We applied the Polynomial Chaos (PC) and the variance-based sensitivity (VBS) analysis to find a robust design of the QPR
Summary
In modern particle accelerators, superconducting rf (SRF) cavities are widely used to provide high-accelerating gradients to a beam of particles while ensuring moderate power losses. That these approaches, which eventually are based on deterministic assumptions, need to be carefully applied, since the cavity shape significantly influences the eigenmodes and eigenvectors as well as other figures of merit For this reason, a local measure in the form of partial derivatives may not provide reliable results for both the forward and the optimization problem [10]. Important objectives are to increase the homogeneity of the magnetic field distribution on the sample and to reduce the field within the coaxial gap, which results in decreasing the unwanted heating of the normal-conducting flange which helps to mitigate the measurement bias, observed for the third mode For these reasons, the shape optimization problem is formulated in terms of the expected values of suitably chosen figures of merit. VII involves concluding remarks and promising directions of ongoing research
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