NMR shim coil design utilising a rapid spherical harmonic calculation method

A rapid spherical harmonic calculation method is used for the design of Nuclear Magnetic Resonance shim coils. The aim is to design each shim such that it generates a field described purely by a single spherical harmonic. By applying simulated annealing techniques, coil arrangements are produced through the optimal positioning of current-carrying circular arc conductors of rectangular cross-section. This involves minimizing the undesirable harmonies in relation to a target harmonic. The design method is flexible enough to be applied for the production of coil arrangements that generate fields consisting significantly of either zonal or tesseral harmonics. Results are presented for several coil designs which generate tesseral harmonics of degree one

Direct algorithm for the rapid calculation of magnetic field spherical harmonics

Expressions for the direct calculation of the spherical harmonics of a magnetic field, generated by a circular current-carrying are of rectangular cross section and arbitrary azimuthal length, are described. The final form contains a double integral with fixed range and no special functions. Solutions can be obtained rapidly and accurately by using Gauss-Legendre quadrature for numerical integration, and three-term recurrence relations for the calculation of associated Legendre polynomials. A comparison shows the distinct speed advantage this algorithm holds over an alternative, currently used technique, making the expressions ideal for inclusion in optimization problems, particularly with the explicit calculation of the magnetic field not required

A flexible method for rapid force computation in elliptical magnets

The design of open-access elliptical cross-section magnet systems has recently come under consideration. Obtaining values for the forces generated within these unusual magnets is important to progress the designs towards feasible instruments. This paper presents a novel and flexible method for the rapid computation of forces within elliptical magnets. The method is demonstrated by the analysis of a clinical magnetic resonance imaging magnet of elliptical cross-section and open design. The analysis reveals the non-symmetric nature of the generated Maxwell forces, which are an important consideration, particularly in the design of superconducting systems