A general method for computing thermal magnetic noise arising from thin conducting objects

TL;DR

This paper introduces a versatile computational method to accurately determine the spectral properties of thermal magnetic noise from arbitrarily-shaped thin conductors, aiding sensitive measurements in physics and engineering.

Contribution

It presents a novel approach modeling divergence-free currents with a stream function on conducting surfaces, enabling precise numerical calculations of magnetic noise spectra.

Findings

Numerical results agree with analytical formulas.

The method is implemented in open-source software, bfieldtools.

It accurately captures spatial correlations and frequency dependence of magnetic noise.

Abstract

Thermal motion of charge carriers in a conducting object causes magnetic field noise that interferes with sensitive measurements nearby the conductor. In this paper, we describe a method to compute the spectral properties of the thermal magnetic noise from arbitrarily-shaped thin conducting objects. We model divergence-free currents on a conducting surface using a stream function and calculate the magnetically independent noise-current modes in the quasi-static regime. We obtain the power spectral density of the thermal magnetic noise as well as its spatial correlations and frequency dependence. We describe a numerical implementation of the method; we model the conducting surface using a triangle mesh and discretize the stream function. The numerical magnetic noise computation agrees with analytical formulas. We provide the implementation as a part of the free and open-source software package bfieldtools.