Magnetic resonance is a relatively modern research topic and technology for its application is rapidly evolving. This thesis is concerned with magnet design and analysis for magnetic resonance imaging and related purposes.
Of primary importance in a magnetic resonance imaging experiment is the quality of the magnetic field. Acceptable tolerances for variation in the main magnetic field are measured in millionths. It is useful to characterize the magnetic field by a spherical harmonic expansion, which represents a sensitive measure of impurities.
A method for the direct and rapid computation of magnetic field spherical harmonics for a thick cylindrical arc conductor is presented. The method allows spherical harmonic values to be computed directly from conductor geometry by taking advantage of the orthogonality properties of the magnetic field expansion. This is ideal for efficient magnet analysis and design. By incorporation into numerical optimization routines, shim coil and gradient coil design may be considered.
Multi-dimensional optimization by simulated annealing is used to design shim coils that generate magnetic fields with desirable spherical harmonic attributes. Several pure coils that generate X and ZX spherical harmonics are designed and the optimization procedure described in detail.
A Z gradient coil for an openable, high strength gradient set is described. The nature of the set requires analysis of spherical harmonic impurities that would not usually be present for such a coil. Nevertheless, a relatively pure design is achieved through optimization by simulated annealing and the spherical harmonic computation method. Images obtained with the gradient set are shown.
Clinical magnetic resonance imaging apparatus are restricted to main magnetic field strengths of 4 T. These high strength fields, desirable for enhanced image quality, cause significant forces in magnet structures. Magnetic force is therefore an important parameter in magnet design.
Methods for the flexible and rapid computation of magnetic force in cylindrical and elliptical magnet systems are presented. These rely on knowledge of the magnetic field, thus methods for computing the magnetic field generated by thick cylindrical and elliptical arc conductors are discussed. A series of force pattern diagrams reveal the nature of forces in multi-conductor magnets. The value of the respective methods is demonstrated through the design of force reduced cylindrical magnets and the analysis of a prototype elliptical magnet.