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Magnet field profiling: analysis and correcting coil design.

F Roméo, D I Hoult

    Magnetic Resonance in Medicine
    |March 1, 1984
    PubMed
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    This study presents a mathematical framework for designing precise magnetic fields, crucial for nuclear magnetic resonance (NMR) studies. It details methods for analyzing and constructing these fields using spherical harmonics and basic components.

    Area of Science:

    • Applied Physics
    • Electromagnetism
    • Magnet Design

    Background:

    • Highly homogeneous magnetic fields are essential for advanced scientific research, particularly in nuclear magnetic resonance (NMR) spectroscopy.
    • Existing methods for magnetic field production and analysis can be complex, requiring sophisticated mathematical frameworks for optimization.

    Purpose of the Study:

    • To present a comprehensive mathematical framework for the analysis and production of localized magnetic field profiles.
    • To provide a design philosophy for creating highly homogeneous fields, with a focus on applications in NMR studies.
    • To detail methods for constructing specific magnetic field harmonics using fundamental 'building blocks'.

    Main Methods:

    • Analysis of magnetic fields using spherical harmonics.

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  • Field plotting techniques to directly measure the presence of specific harmonics.
  • Combining basic 'building blocks' such as coils, arcs, sinusoids of current, and rings/arcs of steel to generate desired magnetic field profiles.
  • Consideration of fabrication errors and their impact on lower-order harmonics in high-order designs.

    • Main Results:

    • A systematic approach to analyzing magnetic field profiles using spherical harmonic decomposition.
    • Demonstration of how to construct specific zonal and tesseral harmonics by combining fundamental magnetic components.
    • Identification of potential issues arising from fabrication errors and their influence on field homogeneity.

    Conclusions:

    • The presented mathematical framework and design philosophy offer a versatile approach to magnet design for various applications, especially NMR.
    • Practical methods for generating and correcting magnetic fields, including the use of shims, are provided.
    • The study emphasizes the importance of understanding harmonic content for achieving precise magnetic field control.