Measurement and tricubic interpolation of the magnetic field for the OLYMPUS experiment

TL;DR

This paper details the measurement, modeling, and efficient interpolation of the magnetic field in the OLYMPUS experiment's spectrometer, enabling precise particle trajectory analysis with optimized computational methods.

Contribution

It introduces a spline-based interpolation scheme optimized for SIMD that reduces memory usage and improves speed for magnetic field calculations in spectrometer analysis.

Findings

Achieved accurate magnetic field interpolation throughout the spectrometer volume.

Reduced memory requirements for field coefficient storage by a factor of eight.

Developed a fast, cache-efficient interpolation method suitable for high-speed analysis.

Abstract

The OLYMPUS experiment used a 0.3 T toroidal magnetic spectrometer to measure the momenta of outgoing charged particles. In order to accurately determine particle trajectories, knowledge of the magnetic field was needed throughout the spectrometer volume. For that purpose, the magnetic field was measured at over 36,000 positions using a three-dimensional Hall probe actuated by a system of translation tables. We used these field data to fit a numerical magnetic field model, which could be employed to calculate the magnetic field at any point in the spectrometer volume. Calculations with this model were computationally intensive; for analysis applications where speed was crucial, we pre-computed the magnetic field and its derivatives on an evenly spaced grid so that the field could be interpolated between grid points. We developed a spline-based interpolation scheme suitable for SIMD implementations, with a memory layout chosen to minimize space and optimize the cache behavior to quickly calculate field values. This scheme requires only one-eighth of the memory needed to store necessary coefficients compared with a previous scheme [1]. This method was accurate for the vast majority of the spectrometer volume, though special fits and representations were needed to improve the accuracy close to the magnet coils and along the toroid axis.