Software for Design NMR Probes Using the Shielded Split Ring and the Shielded Symmetrical Band Resonators

This article presents a software (NMR PROBES) for design NMR probes using closed-forms formulas of the primary and secondary parameters of the shielded split ring [1] and the shielded symmetrical band resonators [2]. These formulas are based on rigorous analysis by finite element method (FEM) [3], [4], method of moment (MoM) [5] and curves fitting techniques. The presented software permits the design of NMR probes for a wide-range of discontinuity angles and it is suitable for all NMR probes with shielded split ring and shielded symmetrical band resonators which have respectively an outer-inner conductors radius ratio between 2 and 10 and between 2 and 7. As applications of this software, we present results obtained from the design of NMR probes operating at 500 MHz and 1 GHz. INTRODUCTION Nuclear magnetic resonance (NMR) probes are vital to mate-rials research and medical applications. The frequency region above 200Mhz and bellow 2Ghz represents a difficult problem for high sensitivity magnetic resonance. Standard cavity resonator can not be used because its radio-frequency field is inhomogeneous. Capacitively tuned solenoidal coils, which for frequencies up to ∼100Mhz are good choices, become impractical at higher frequencies because they become self-resonant [6], [7]. W. N. Hardy and L. A. Whitehead [8] have developed a shielded split ring resonator with excellent field homogeneity. Beginning with this structure, it is suggested that another type of resonator be constituted from a shielded symmetrical band resonator. With the capability of being easy to fabricate, a shielded split ring and a shielded symmetrical band resonators which have a high quality factor (Q) in the 200-to-2000-MHz range [7], [8] are flexible enough to adapt to a different range of sizes at a particular frequency. Many NMR experiments involving very high homogeneity and high power required the redefinition of the probe. To study a sample, the probe must transmit RF energy and convert it to magnetic energy. The probe is a resonant circuit with a selfic element (solenoid, shielded symmetrical band line, shielded split ring line,...) and other components used for the adapter (figure 1). The selfic element has a fundamental role in the spectrometer. This resonator must have high Q and good magnetic field homogeneity. NMR PROBE USING THE SHIELDED SPLIT RING AND THE SHIELDED SYMMETRICAL BAND RESONATORS [9] The cross section of the shielded split ring and the shielded symmetrical band resonators are respectively presented in figures 2 and 3. These resonators are assumed to be lossless with inner conductors of radius ro, negligible thickness w, a discontinuity angle θ and an outer shield of radius rb. Dielectric materials with permittivities εr1 and εr2 are placed respectively in the inner of the central conductors and between the central conductors and the shield. Coaxial line According and adaptation Selfic