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

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 Jülich. 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 ( E ⊥ B) 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.

Spin dynamics investigations for the electric dipole moment experiment

“…The rf Wien filter, described in [4], has been designed in order to be able to manipulate the spins of the stored particles, avoiding as much as possible effects on the beam orbit. To this end, great care was taken to minimize the unwanted field components of the Wien filter and to characterize them via the polynomial chaos expansion [5]. In the EDM mode, the main component of the magnetic induction ⃗ B WF is oriented along the y axis, and the main component of the electric field ⃗ E WF along the x axis.…”

“…The investigations presented here, carried out in the framework of the JEDI collaboration, 2 are relevant for the preparation of the deuteron EDM measurement [3]. A radio-frequency (rf) Wien filter (WF) [4][5][6] makes it possible to carry out EDM measurements in a conventional magnetic machine like COSY. The idea is to look for an EDM-driven resonant rotation of the deuteron spins from the horizontal to the vertical direction and vice versa, generated by the rf Wien filter at the spin precession frequency [7,8].…”

Computational framework for particle and spin simulations based on the stochastic Galerkin method

“…With the m = 5 dimensional problem and an expansion order of p = 4, the number of basis functions is P = 126 (see Eq. (7) of [3]), which results in a (126 × 126 × 126) C ijl tensor. The sparsity of the rank-3 tensor C ijl is illustrated by fixing, e.g., the first index to values of i = 14, 26, 37, 45, 69, 77, 86, 93, 105, and 116, which yields the 10 sparse matrices shown.…”

“…For limited-budget projects such as ours, this is therefore not an option. Recently, as a first step toward a full systematic analysis of the future EDM experiments at COSY, we conducted a study to quantify the electromagnetic performance of the above mentioned RF Wien filter under mechanical uncertainties [3]. This investigation made use of the so-called Polynomial Chaos Expansion (PCE) [4], as an efficient and yet accurate alternative to the MC method.…”

“…The same methodology as in Ref. [3] is used here, but as we have access to the equations governing the system, here an intrusive version of the PCE is employed. This paper is organized as follows.…”