A scheme for the determination of the magnetic field in the KATRIN main spectrometer

TL;DR

This paper presents a method to determine the magnetic field inside the KATRIN main spectrometer by using external sensors and solving the Laplace equation, achieving 2% accuracy in simulations.

Contribution

The paper introduces a novel approach to reconstruct the internal magnetic field from external measurements using Laplace equation relaxation techniques.

Findings

Reconstruction accuracy within 2% in simulations.

Effective use of boundary surface magnetic field samples.

Method applicable to complex magnetic configurations.

Abstract

To determine the magnetic field distribution in the KATRIN main-spectrometer with magnetic field sensors that are placed outside the main-spectrometer vessel one can utilize the absence of magnetic rotation in main-spectrometer volume. There a scalar magnetic potential V(~x) can be defined that fulfills the Laplace equation. Large numbers of magnetic field values on an outer surface of the main-spectrometer can be sampled by moving and fixed magnetic field sensors. These surface samples are used as boundary values in the relaxation of the Laplace equation for V(~x) and the magnetic field components in the volume. In a simulation involving the KATRIN reference solenoid chain, a global magnetic field and an external perturbing solenoid it is shown that with this method the original field can be reconstructed within 2 %.