Saddle coils for uniform static magnetic field generation in NMR experiments

The magnetic flux density field (called, henceforth, “magnetic field,” for the sake of simplicity) generated by a saddle coil system is numerically calculated in the whole space and experimentally tested in two different spatial planes. The uniformity of the magnetic field is studied using Taylor series expansions of the three components separately. The optimum geometry is revised and obtained from the second-order Taylor expansions. The most favorable relationship between saddle coil geometric parameters is determined in case the optimum geometry cannot be achieved (because of experimental restrictions). Approximated manipulable analytical expressions are obtained via fourth-order Taylor expansions of the three components of the magnetic field and compared with exact expressions. They were found to differ in less than 10−3% within a sample region, when typical sample and coil dimensions are considered. Deviations of the magnetic field produced by an optimum-compensating saddle coil system were contrasted with typical NMR field-cycling magnetic field inhomogeneities. Possible influences of such deviations in NMR experiments are discussed.