Torus Factor—The Relationship between Radiofrequency Field and Radial Position in Toroid Cavity Probes - Woelk, Klaus (Journal of magnetic resonance (1997), 2000)
Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is sufficient to describe the relationship between this radiofrequency field and the radial distance from the center axis of the torus. Because accurate determination of the torus factor is essential to optimize toroid cavity NMR experiments or conduct toroid cavity imaging, a fast numerical algorithm for accurate, precise, and convenient determination of torus factors from pulse width-dependent signal intensities is introduced. In addition, the new algorithm provides for 99% confidence intervals around the refined torus factors. A computer program in which the optimization progress is visualized during the torus factor refinement is presented. Upon completion of the program, the best-fit simulated data and the residuals between best fit and experimental data are provided.