Asymmetric zonal shim coils for magnetic resonance applications

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Abstract
A method is presented for the systematic design of asymmetric zonal shim coils for magnetic resonance applications. Fourier‐series methods are used to represent the magnetic field inside and outside a circular cylinder of length and radius a. The current density on the cylinder is also represented using Fourier series. Any desired field can be specified in advance on the cylinder's radius, over some nonsymmetric portion of the coil's length Periodic extension of the field is used, in a way that guarantees the continuity of the field, and therefore gives good convergence of the Fourier series. All that is required is to calculate the Fourier coefficients associated with the specified desired field, and from these, the current density on the coil and the magnetic field components then follow automatically. The method is illustrated by applying it to three sample zonal coil designs, namely, linear, quadratic, and cubic fields located asymmetrically in the coil. Current densities and corresponding coil winding patterns are shown for these three illustrative cases. Field calculations directly from the coil patterns and spherical harmonic deconvolutions of these fields indicate that the example designs match the theory well. Asymmetric shim coils can be used in conventional symmetric MRI magnets, particularly those architected for “head‐only” studies. One of their major applications is expected to be in the newly developed asymmetric magnet systems.

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