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

Tian Xia,Yefeng Yao,Zhiying Miao,Shanshan Chen,Hongzhi Wang,Luis Carretero

doi:10.1371/journal.pone.0181552

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.

Highlights

Low field NMR (LF-NMR) relaxation analysis technics has been widely employed in oil exploration, food safety, life sciences, high molecular material, and mineral engineering since it was developed in the 1980s[1,2,3,4,5]
LF-NMR usually adopts rare earth permanent magnets to generate the main magnetic field, which generally has significantly lower homogeneity than that generated by superconducting magnets
This paper proposes a biplanar shim coils (BSCs) approach for LF-NMR to improve homogeneity to 0.5 ppm over a relative large region of interest (ROI) (F × H = 25.4 mm × 40 mm)

Summary

Introduction

Low field NMR (LF-NMR) relaxation analysis technics has been widely employed in oil exploration, food safety, life sciences, high molecular material, and mineral engineering since it was developed in the 1980s[1,2,3,4,5]. Eq (36) shows that the shim coil for a given degree l and order k can generate an infinite number of harmonic fields depending on the value of i. 4. The current coefficient matrix U was solved by Eq (40), and the stream function S(ρ, φ) of generating X type harmonic field was obtained by substituting U into Eq (21). 4. The current coefficient matrix U was be solved by Eq (40), and the stream function S(ρ, φ) generating X harmonic fields was obtained by substituting U into Eq (21). There were nine independent groups of constant current sources to power the nine BSC pairs, respectively

Experiments to test shimming effects

Discussion and conclusion