Noise Modeling From Conductive Shields Using Kirchhoff Equations

Progress in the development of high-sensitivity magnetic-field measurements has stimulated interest in understanding the magnetic noise of conductive materials, especially of magnetic shields based on high-permeability materials and/or high-conductivity materials. For example, SQUIDs and atomic magnetometers have been used in many experiments with mu-metal shields, and additionally SQUID systems frequently have radio frequency shielding based on thin conductive materials. Typical existing approaches to modeling noise only work with simple shield and sensor geometries while common experimental setups today consist of multiple sensor systems with complex shield geometries. With complex sensor arrays used in, for example, MEG and Ultra Low Field MRI studies, knowledge of the noise correlation between sensors is as important as knowledge of the noise itself. This is crucial for incorporating efficient noise cancelation schemes for the system. We developed an approach that allows us to calculate the Johnson noise for arbitrary shaped shields and multiple sensor systems. The approach is efficient enough to be able to run on a single PC system and return results on a minute scale. With a multiple sensor system our approach calculates not only the noise for each sensor but also the noise correlation matrix between sensors. Here we will show how the algorithm can be implemented.