1. Resonator for Optimization of Liquid-Phase EPR Concentration-
Sensitivity for Spin Labels at Q-Band: Practical Considerations
Richard R. Mett,1,2 James R. Anderson,1 Jason W. Sidabras,1 Timothy S. Thelaner,1 and James S. Hyde1
1Department of Biophysics, Medical College of Wisconsin, Milwaukee, WI, USA
2Department of Physics and Chemistry, Milwaukee School of Engineering, Milwaukee, WI, USA
Summary Progress on the fabrication of a previously reported resonator1 that optimizes liquid-phase concentration sensitivity at Q- band (35 GHz) is presented. The resonator has a coaxial TM020 mode, which is uniform in all but the radial direction. For maximum EPR signal, the DC magnetic field must be parallel to the resonator axis. The 50 l sample volume in the form of a thin (0.09 mm) cylindrical shell of an 8 mm radius is predicted to give a saturable EPR signal 21 times the standard 0.5 l sample in the cylindrical TE011. With an aqueous sample, the device is predicted to have a loaded Q-value of about 1500 and a resonator efficiency parameter of 0.72 G/W1/2. Sample access on one end of the cavity is provided by a circular cut on an rf current null. Design criteria and results of simulations are presented. Changes to the original design have been made as sample handling and resonator construction methodologies have developed. Fabrication of the resonator in two parts and the Rexolite sample holder, also in two parts, is underway.
Design The cylindrical TM020 mode is the smallest cavity mode with a cylindrical electric field node between the cavity walls. The electric fields of this mode are parallel to the cylinder axis, and the magnetic fields are perpendicular. The rf fields are uniform in the two dimensions of the node, making the mode a natural choice for EPR. The mode is coupled from the inside with a cylindrically symmetric long slot capacitive iris. A central conducting wall houses a cylindrical TM010 mode inside the center conductor. This center cavity facilitates coupling between the rectangular waveguide and the iris, Fig. 1. The iris symmetry and placement suppress most of the undesired modes in both the coaxial and cylindrical cavities. Dimensions are shown in Table 1. The axial cavity length was chosen such that nearby TE111 and TE112 modes in the coupling cavity are not close to the 35 GHz operating frequency. The transition from rectangular WR-28 to cylindrical TM010 mode (Fig. 1) is made by narrowing the rectangular waveguide to a width such that the waveguide wavelength is equal to the diameter of the TM010 cylinder (cutoff) at 35 GHz. At that point, the broad waveguide face is open to the cylinder. The mode was found to be relatively insensitive to sample non-uniformities.
Performance of the TM020 resonator according to finite element simulations is shown in Table 1. Coupled, loaded, saturable EPR signal is 22 times larger and the sample volume 93 times larger than the standard Q-band cylindrical TE011 resonator. The signal is significantly higher even though the resonator efficiency parameter at the sample is 13 times smaller and the Q-value about half as large. Tuning of the cavity is accomplished by moving a 1 mm wide 2 mm diameter metallic disc, Fig. 1, between the middle and side of the waveguide taper. This permits the cavity to be critically matched to a wide range of Q-values that can be caused by changes in temperature, sample and machining tolerances. Autodesk Inventor was used to create models of the resonator parts, Figs. 2-4.
Fabrication of the two-part resonator assembly in Aluminum T6 was done first by CNC lathe (IDC Precision, Mukwonago, WI), Figs. 5, 6. Then, the rectangular waveguide and taper were made by plunge EDM, Fig. 7. The procedure was more difficult than anticipated. A chip formed when breaking through to the cavity and
TE10 - TM01
transition
taper
TM010
coupling
cavity
WR-28 flange
TM020 cavity
long slot iris
aqueous sample
Rexolite sample holder
tuning disc
Fig. 4 – Assembly view of the upper and lower cavity parts and the two Rexolite sample holding sleeves.
Fig. 1 – Driven mode finite element simulation of the TM020 uniform-field cavity and coupling system. Electric field magnitude at GHz is shown.
Fig. 5 – Cavity bottom.
Table 1 - Cylindrical Resonator Properties
TM020
TE011
coupling cavity OD
6.56 mm
n/a
cavity ID
7.57 mm
cavity OD
23.46 mm
11.29 mm
cavity length
12 mm
sample radius
7.74 mm
sample thickness
0.085 mm
0.24 mm
sample volume
47.5 l
0.51 l
sample holder wall thickness
0.2 mm
0.1 mm
long slot iris thickness
0.06 mm
0.05 mm
loaded coupled Q-value
1523
2950 Λ
0.72 G/W1/2
9.37 G/W1/2
EPR saturable signal
21.2 W1/2/G
0.963 W1/2/G
Fig. 2 - The cavity and coupling system are designed from two Al alloy parts (gray) and the sample holder (pink) from two Rexolite sleeves. The cavity disassembles concentrically at an rf current null on one end of the cavity.
Fig. 6 – Cavity top.
Fig. 3 – Expanded view of the sample holder and the associated locating groove in the cavity wall. Yellow corresponds to the sample filling hole, see also Fig. 2.
had to be removed before completing the cut. During the final approach, a fluid flushing hole was made in the cutter to permit clean corners to be cut. A 54 µm deep rectangular groove milled into each end of the cavity is designed to hold the Rexolite sample holder sleeves at a precise radius, Figs. 3, 5. A uniformly expanding mandrel was used to hold each sleeve as it was ground on a lathe. A wax seal is designed at the cavity ends.
Reference 1Mett, Anderson, Sidabras, and Hyde, EPR Symposium Poster, 52nd RMCAC, Snowmass, CO, 3 August 2010.
Acknowledgements This work was supported by grants P41 EB and R01 EB from the National Institutes of Health.
Fig. 7 – Waveguide slot being cut by plunge EDM.