Uniform Field Resonators for EPR Spectroscopy: A Review

Abstract

Cavity resonators are often used for electron paramagnetic resonance (EPR). Rectangular TE₁₀₂ and cylindrical TE₀₁₁ are common modes at X-band even though the field varies cosinusoidally along the Z-axis. The authors found a way to create a uniform field (UF) in these modes. A length of waveguide at cut-off was introduced for the sample region, and tailored end sections were developed that supported the microwave resonant mode. This work is reviewed here. The radio frequency (RF) magnetic field in loop-gap resonators (LGR) at X-band is uniform along the Z-axis of the sample, which is a benefit of LGR technology. The LGR is a preferred structure for EPR of small samples. At Q-band and W-band, the LGR often exhibits nonuniformity along the Z-axis. Methods to trim out this nonuniformity, which are closely related to the methods used for UF cavity resonators, are reviewed. In addition, two transmission lines that are new to EPR, dielectric tube waveguide and circular ridge waveguide, were recently used in UF cavity designs that are reviewed. A further benefit of UF resonators is that cuvettes for aqueous samples can be optimum in cross section along the full sample axis, which improves quantification in EPR spectroscopy of biological samples.

Keywords: Dielectric tube resonator; EPR; Q-band; Ridge waveguide; Uniform field; W-band.

Figure 1.

Methods for creating UFs in cavities. Region of interest at cut-off is matched to end-section (a) oversized with connecting septum, (b) re-entrant ring with capacitive posts (black circles), (c) dielectric section of length λ/4. Magnetic field vectors are illustrated with dotted lines (Figure derived from (5). Reprinted from Journal of Magnetic Resonance, 282, JW Sidabras, T Sarna, RR Mett, JS Hyde, Uniform Field Loop-Gap Resonator and Rectangular TEU02 for Aqueous Sample EPR at 94GHz, 129-135, Copyright 2017, with permission from Elsevier.)

Figure 2.

(a)Half-structure drawing illustrating the W-band rectangular TE_U02 geometry with oversized end-sections, sample access port, light access, and sample end-section shield, (b) magnetic field magnitude profile showing the 6 mm region-of-interest, and (c) magnetic field magnitude profile with dual iris (thickness 0.1mm) and sample placement (dashed). Dotted line represents the cavity wall illustrating the light access slots beyond cut-off. Red is large magnetic field and dark blue zero magnetic field

Figure 3.

LGR cross sections. Shaded areas are sample loops. a,a’ are one-loop-one-gap; b,b’ are three-loop-two-gap; c,c’ are five-loop-four-gap. a,b,c have small sample loops and large return flux loops. a’,b’,c’ have inner and outer loop sizes reversed

Figure 4.

Cross-sectional profiles of axial RF magnetic field energy H²_z in a plane bisecting the three-loop-two-gap resonator through the gaps obtained for the n = 0 mode by computer simulation. Red to blue indicates a maximum to zero intensity. (a) 1 mm long LGR. (b) 10 mm long LGR, untrimmed for RF magnetic field uniformity. (c) 10 mm long LGR, trimmed for RF magnetic field uniformity using metal strips bridging the gaps (Figure obtained from (6). Reprinted by permission from Springer Customer Service Centre GmbH: Springer Nature, Applied Magnetic Resonance, Uniform radio frequency fields in loop-gap resonators for EPR spectroscopy, RR Mett, JW Sidabras, JS Hyde, 2007.)

Figure 5.

Contour plots of the cavity radius (a) and lambda value (b) for sapphire as functions of the average tube radius and thickness at 9.5 GHz (Figure obtained from (7). Reprinted by permission from Springer Customer Service Centre GmbH: Springer Nature, Applied Magnetic Resonance, EPR Uniform Field Signal Enhancement by Dielectric Tubes in Cavities, JS Hyde, RR Mett, 2017.)

Figure 6.

Cross-sectional views of the magnitude of (a) electric field and (b) magnetic field inside a metallic cavity designed with two end sections that support an axially uniform RF field in the central section. The polycrystalline dielectric tube extends uniformly along the axial extent of the structure (Figure obtained from (7). Reprinted by permission from Springer Customer Service Centre GmbH: Springer Nature, Applied Magnetic Resonance, EPR Uniform Field Signal Enhancement by Dielectric Tubes in Cavities, JS Hyde, RR Mett, 2017.)

Figure 7.

Visualization of a dual-, quad-, and octo-ridge waveguide. The design parameters R, w, h are defined (Figure obtained from (22), reproduced courtesy of The Electromagnetics Academy.)

Figure 8.

(a) Cross-sectional view of the circular ridge waveguide. (b) Side view of the reentrant cavity showing region-of-interest. (c,d) Ansys HFSS simulations corresponding to a and b (Figure obtained from (8). Quantitative data on Fig. 8d are given in Table 1 (8). Reprinted by permission from Springer Customer Service Centre GmbH: Springer Nature, Applied Magnetic Resonance, Uniform Field Re-entrant Cylindrical TE_01U Cavity for Pulse Electron Paramagnetic Resonance Spectroscopy at Q-band, JW Sidabras, EJ Reijerse, W Lubitz, 2017.)

Figure 9.

Ansys HFSS simulation showing the normalized H₁ field of the cylindrical re-entrant TE_01U (short dashed line) compared with the cylindrical TE₀₁₁ cavity (long dashed line). The vertical dotted lines mark the region-of-interest. The solid line was calculated using the method of Fig. 1a for the matching pseudocavity