Shim coils for NMR and MRI solenoid magnets

The design of high-purity magnetic field shim coils for NMR and MRI laboratory solenoid magnets is discussed. The individual shim consists of several current carrying elements which have the form of a circle or circular arc. The influence of the needed connecting conductors can usually be neglected. The magnetic field components of the mentioned elements can be expressed in terms of spherical harmonics. The design is based on unique recursion relations for the coefficients of the most important expansion component. Using the Monte Carlo method, the procedure of optimizing the element positions is illustrated for an X-shim design. The results obtained by measuring the field of the implemented shim are compared with those of the theoretical evaluation.