# Error analysis of a heating oven for a spin-exchange relaxation-free magnetometer

## TL;DR

This paper describes the design and error analysis of a heating oven for a magnetometer, focusing on thermal control and minimizing magnetic interference.

## Contribution

A novel non-magnetic heating oven design for SERF magnetometers with detailed error analysis and practical guidelines for reducing magnetic noise.

## Key findings

- A thermal shell reduced temperature gradients from 14.94°C to 6.43°C, improving thermal uniformity.
- Wiring errors were identified as the main source of discrepancies in magnetic field simulations.
- Monte Carlo simulations revealed the impact of fabrication tolerances and wiring configurations on magnetic performance.

## Abstract

We present the design and error analysis of a non-magnetic electric heating oven for spin-exchange relaxation-free (SERF) magnetometers, where precise thermal control and minimal magnetic disturbance are critical. A compact oven using a double-layer polyimide-constantan heating film was developed and evaluated through finite element simulations and experiments. Temperature simulations showed good agreement with measurements using a convective heat transfer coefficient of \documentclass[12pt]{minimal}
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\begin{document}$$7.6~\mathrm {W/m^2\cdot K}$$\end{document}. However, a temperature difference of \documentclass[12pt]{minimal}
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\begin{document}$$14.94~^\circ$$\end{document}C was observed due to heat loss near the vapor cell stem. Adding a thermal shell in the simulation reduced this gradient to \documentclass[12pt]{minimal}
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\begin{document}$$6.43~^\circ$$\end{document}C, indicating improved thermal uniformity. Magnetic field simulations initially showed large discrepancies with experimental results. Including a twisted wire pair improved agreement, but differences remained. To further investigate the remaining discrepancies, Monte Carlo simulations were performed by introducing realistic variations in fabrication tolerances, mounting positions, and wiring configurations. The results revealed that wiring errors had the greatest influence on the measured magnetic field. These findings provide key insights into structural factors affecting magnetic performance and offer practical guidelines for reducing magnetic noise in SERF magnetometer systems.