An analytical methodology for magnetic field control in unilateral NMR

Traditionally, unilateral NMR systems such as the NMR-MOUSE have used the fringe field between two bar magnets joined with a yoke in a 'U' geometry. This allows NMR signals to be acquired from a sensitive volume displaced from the magnets, permitting large samples to be investigated. The drawback of this approach is that the static field (B0) generated in this configuration is inhomogeneous, and has a large, nonlinear, gradient. As a consequence, the sensitive volume of the instrument is both small and ill defined. Empirical redesign of the permanent magnet array producing the B0 field has yielded instruments with magnetic field topologies acceptable for varying applications. The drawback of current approaches is the lack of formalism in the control of B0. Rather than tailoring the magnet geometry to NMR investigations, measurements must be tailored to the available magnet geometry. In this work, we present a design procedure whereby the size, shape, field strength, homogeneity, and gradients in the sensitive spot of a unilateral NMR sensor can be controlled. Our design uses high permeability pole pieces, shaped according to the contours of an analytical expression, to control B0, allowing unilateral NMR instruments to be designed to generate a controlled static field topology. We discuss the approach in the context of previously published design techniques, and explain the advantages inherent in our strategy as compared to other optimization methods. We detail the design, simulation, and construction of a unilateral magnet array using our approach. It is shown that the fabricated array exhibits a B0 topology consistent with the design. The utility of the design is demonstrated in a sample nondestructive testing application. Our design methodology is general, and defines a class of unilateral permanent magnet arrays in which the strength and shape of B0 within the sensitive volume can be controlled.