A Theoretical Design Approach for Passive Shimming of a Magic-Angle-Spinning NMR Magnet.

This paper presents a passive shimming design approach for a magic-angle-spinning (MAS) NMR magnet. In order to achieve a 1.5-T magic-angle field in NMR samples, we created two independent orthogonal magnetic vector fields by two separate coils: the dipole and solenoid. These two coils create a combined 1.5-T magnetic field vector directed at the magic angle (54.74° from the spinning axis). Additionally, the stringent magnetic field homogeneity requirement of the MAS magnet is the same as that of a solenoidal NMR magnet. The challenge for the magic-angle passive shimming design is to correct both the dipole and solenoid magnetic field spherical harmonics with one set of iron pieces, the so-called ferromagnetic shimming. Furthermore, the magnetization of the iron pieces is produced by both the dipole and solenoid coils. In our design approach, a matrix of 2 mm by 5 mm iron pieces with different thicknesses was attached to a thin-walled tube, 90-mm diameter and 40-mm high. Two sets of spherical harmonic coefficients were calculated for both the dipole and solenoid coil windings. By using the multiple-objective linear programming optimization technique and coordinate transformations, we have designed a passive shimming set that can theoretically reduce 22 lower-order spherical harmonics and improve the homogeneity of our MAS NMR magnet.

High-Resolution Magnetic Field Mapping System With an NMR Probe.

This paper presents a high-resolution magnetic field mapping system in development that is capable of collecting spatial magnetic field data for NMR magnets. An NMR probe was designed and built with a resonant frequency of 5.73 MHz. The measured Q-factor of the NMR probe is ~191 with a half-power bandwidth in the range of 5.72-5.75 MHz. An RF continuous-wave technique with magnetic field modulation was utilized to detect the power dispersion of water molecules. The zero-crossing frequency of the NMR dispersion signal corresponds to the magnetic field at the center of the water sample. An embedded system was developed to sweep the frequency and record the reflected RF power simultaneously. A numerically controlled digital oscillator is able to provide a precise frequency step as small as 0.02 Hz, which is equivalent to 4.7 e-7 mT for hydrogen atoms. An RF preamplifier was built to supply up to 4 W of RF power to a bidirectional coupler. The coupler supplies RF power to the NMR probe and channels reflect the RF power back to the detection circuit, which detects the reflected RF power from the NMR probe during the frequency sweep. The homogeneity of an NMR magnet can be determined by magnetic field data.

An Analytical Approach towards Passive Ferromagnetic Shimming Design for a High-Resolution NMR Magnet.

This paper presents a warm bore ferromagnetic shimming design for a high resolution NMR magnet based on spherical harmonic coefficient reduction techniques. The passive ferromagnetic shimming along with the active shimming is a critically important step to improve magnetic field homogeneity for an NMR Magnet. Here, the technique is applied to an NMR magnet already designed and built at the MIT's Francis Bitter Magnet Lab. Based on the actual magnetic field measurement data, a total of twenty-two low order spherical harmonic coefficients is derived. Another set of spherical harmonic coefficients was calculated for iron pieces attached to a 54 mm diameter and 72 mm high tube. To improve the homogeneity of the magnet, a multiple objective linear programming method was applied to minimize unwanted spherical harmonic coefficients. A ferromagnetic shimming set with seventy-four iron pieces was presented. Analytical comparisons are made for the expected magnetic field after Ferromagnetic shimming. The theoretically reconstructed magnetic field plot after ferromagnetic shimming has shown that the magnetic field homogeneity was significantly improved.