Theory and development of biplanar active shim coils for a permanent NMR analyzer

Abstract

The general expression for magnetic induction in the z axis direction is derived from magnetic scalar potential, and magnetic induction for biplanar shimming coils (BSCs) is also derived from magnetic vector potentials and Green functions, which simultaneously include Sin and Cos harmonic fields. The relationship between these expressions is discussed, and we show they are partially consistent. Magnetic induction generated Sin and Cos stream functions, which are presented and discussed, and we conclude that the type of stream function determines the type of harmonic field, and that BSCs can not only generate specific harmonic fields directly using Cos stream function, but also generate the rest of the harmonic fields through some specific operations. The detailed design process is presented in the form of a diagram. Subsequently, nine BSCs were calculated using the proposed method and applied to a low field NMR relaxation analyzer. The magnetic field homogeneity after shimming increases significantly, which verifies its practical value.

Magnetic-field modeling with surface currents. Part I. Physical and computational principles of bfieldtools

“…This expansion can represent a spatially smoothly varying magnetic field with a few parameters, which can be helpful, e.g., when designing coils that generate these types of fields. 18,40,58 A disadvantage of the multipole expansion is, however, that the series can diverge in regions where the actual field is wellbehaving. For more general purposes, we introduce a representation of magnetic fields based on a stream function, which can be viewed as an equivalent source of the field.…”

Magnetic-field modeling with surface currents: Physical and computational principles of bfieldtools

“…This expansion can represent a spatially smoothly varying magnetic field with a few parameters, which can be helpful, e.g., when designing coils that generate these types of fields. 15,39,57 A disadvantage of the multipole expansion is, however, that the series can diverge in regions where the actual field is well-behaving. For more general purposes, we introduce a representation of magnetic fields based on a stream function, which can be viewed as an equivalent source of the field.…”