Polynomial Chaos Expansion method as a tool to evaluate and quantify field homogeneities of a novel waveguide RF Wien Filter

TL;DR

This paper introduces a Polynomial Chaos Expansion-based surrogate modeling approach to efficiently evaluate and quantify field homogeneities and sensitivities in a novel waveguide RF Wien filter, aiding precise electric dipole moment measurements.

Contribution

It presents a novel application of Polynomial Chaos Expansion for efficient sensitivity analysis of field quality in a waveguide RF Wien filter considering manufacturing tolerances.

Findings

Polynomial Chaos Expansion effectively models field variations due to tolerances.

The method reduces computational cost compared to Monte Carlo simulations.

Sensitivity analysis identifies key factors affecting field homogeneity.

Abstract

For the measurement of the electric dipole moment of protons and deuterons, a novel waveguide RF Wien filter has been designed and will soon be integrated at the COoler SYnchrotron at J\"ulich. The device operates at the harmonic frequencies of the spin motion. It is based on a waveguide structure that is capable of fulfilling the Wien filter condition ($\vec{E} \perp \vec{B}$) \textit{by design}. The full-wave calculations demonstrated that the waveguide RF Wien filter is able to generate high-quality RF electric and magnetic fields. In reality, mechanical tolerances and misalignments decrease the simulated field quality, and it is therefore important to consider them in the simulations. In particular, for the electric dipole moment measurement, it is important to quantify the field errors systematically. Since Monte-Carlo simulations are computationally very expensive, we discuss here an efficient surrogate modeling scheme based on the Polynomial Chaos Expansion method to compute the field quality in the presence of tolerances and misalignments and subsequently to perform the sensitivity analysis at zero additional computational cost.