Literature

The functionality of bfieldtools is based on a stream-function discretization of surface current onto a triangle mesh.

For a more theoretical and in-depth overview of the physics and computations used in bfieldtools, please see

  • A. J. Mäkinen, R. Zetter, J. Iivanainen, K. C. J. Zevenhoven, L. Parkkonen, and R. J. Ilmoniemi. Magnetic-field modeling with surface currents. Part I. Physical and computational principles of bfieldtools. Journal of Applied Physics, 128(6):063906, 2020. doi:10.1063/5.0016090.

For a more software-centred of bfieldtools and an overview of coil design, please see

  • R. Zetter, A. J. Mäkinen, J. Iivanainen, K. C. J. Zevenhoven, R. J. Ilmoniemi, and L. Parkkonen. Magnetic field modeling with surface currents. Part II. Implementation and usage of bfieldtools. Journal of Applied Physics, 128(6):063905, 2020. doi:10.1063/5.0016087.

For a detailed description of the thermal noise computation method used in bfieldtools, please see

  • J. Iivanainen, A. J. Mäkinen, R. Zetter, K. C. J. Zevenhoven, R. J. Ilmoniemi, and L. Parkkonen. A general method for computing thermal magnetic noise arising from thin conducting objects. ArXiv, 2020. URL: https://arxiv.org/abs/2007.08963.

Selected papers

A selection of useful papers can also be found below:

General introduction to stream functions

  • G.N. Peeren. Stream function approach for determining optimal surface currents. PhD thesis, Philips Research, 2003. doi:10.6100/IR570424.

  • G. N. Peeren. Stream function approach for determining optimal surface currents. Journal of Computational Physics, 191(1):305–321, 2003. doi:10.1016/S0021-9991(03)00320-6.

  • K. C. J. Zevenhoven, S. Busch, M. Hatridge, F. Öisjöen, R. J. Ilmoniemi, and J. Clarke. Conductive shield for ultra-low-field magnetic resonance imaging: Theory and measurements of eddy currents. Journal of Applied Physics, 115(10):1–12, 2014. doi:10.1063/1.4867220.

Coil-design papers using the similar methods as bfieldtools

  • M. S. Poole. Improved equipment and techniques for dynamic shimming in high field MRI. PhD thesis, University of Nottingham, 2007.

  • S. Pissanetzky. Minimum energy MRI gradient coils of general geometry. Measurement Science and Technology, 3(7):667, 1992. doi:10.1088/0957-0233/3/7/007.

  • G. Bringout and T. M. Buzug. Coil design for magnetic particle imaging: application for a preclinical scanner. IEEE Transactions on Magnetics, 51(2):1–8, 2014. doi:10.1109/TMAG.2014.2344917.

On the calculation of Laplace-Beltrami eigenfunctions (Surface Harmonics)

  • M. Reuter, S. Biasotti, D. Giorgi, G. Patanè, and M. Spagnuolo. Discrete Laplace–Beltrami operators for shape analysis and segmentation. Computers & Graphics, 33(3):381–390, 2009. doi:10.1016/j.cag.2009.03.005.

  • B. Levy. Laplace-Beltrami eigenfunctions towards an algorithm that “understands” geometry. In IEEE International Conference on Shape Modeling and Applications 2006 (SMI’06), 13–13. 2006. doi:10.1109/SMI.2006.21.

Thermal noise

  • S. Uhlemann, H. Müller, J. Zach, and Max. Haider. Thermal magnetic field noise: electron optics and decoherence. Ultramicroscopy, 151:199 – 210, 2015. doi:https://doi.org/10.1016/j.ultramic.2014.11.022. Special Issue: 80th Birthday of Harald Rose; PICO 2015 – Third Conference on Frontiers of Aberration Corrected Electron Microscopy.

  • B. J. Roth. Thermal fluctuations of the magnetic field over a thin conducting plate. Journal of Applied Physics, 83(2):635–638, 1998. doi:10.1063/1.366753.