Least squares magnetic-field optimization for portable nuclear magnetic resonance magnet design

Jeffrey L. Paulsen, John Franck, Vasiliki Demas, Louis S. Bouchard

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Single-sided and mobile nuclear magnetic resonance (NMR) sensors have the advantages of portability, low cost, and low power consumption compared to conventional high-field NMR and magnetic resonance imaging (MRI) systems. We present fast, flexible, and easy-to-implement target field algorithms for mobile NMR and MRI magnet design. The optimization finds a global optimum in a cost function that minimizes the error in the target magnetic field in the sense of least squares. When the technique is tested on a ring array of permanent-magnet elements, the solution matches the classical dipole Halbach solution. For a single-sided handheld NMR sensor, the algorithm yields a 640 G field homogeneous to 16 100 ppm across a 1.9 cm3 volume located 1.5 cm above the top of the magnets and homogeneous to 32 200 ppm over a 7.6 cm3 volume. This regime is adequate for MRI applications. We demonstrate that the homogeneous region can be continuously moved away from the sensor by rotating magnet rod elements, opening the way for NMR sensors with adjustable "sensitive volumes."

Original languageEnglish (US)
Pages (from-to)4582-4590
Number of pages9
JournalIEEE Transactions on Magnetics
Issue number12
StatePublished - Dec 2008
Externally publishedYes


  • Least-squares optimization
  • Magnetic devices
  • Magnetic resonance
  • Magnetostatics
  • Nuclear magnetic resonance

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering


Dive into the research topics of 'Least squares magnetic-field optimization for portable nuclear magnetic resonance magnet design'. Together they form a unique fingerprint.

Cite this