Multipurpose loop-gap resonator

JOURNAI.

OF MAGNETIC

RESONANCE

82,223-230

(1989)

Multipurpose Loop-Gap Resonator JAMES S. HYDE National Biomedical ESR Center, Medical College of Wisconsin, Milwaukee, Wisconsin 53226 AND

W. FRONCISZ AND T. OLES Department of Biophysics, Institute ofMolecular

Biology, Jagidonian

University, Krdcow, Poland

Received July 18, 1988 A three-loop-two-gap resonator is described that has properties that are similar to the widely used X-band rectangular TEu,* multipurpose cavity. Both structures accommodate the same cavity accessories interchangeably: variable temperature Dewar insert, liquid nitrogen Dewar, electrochemical cell, tissue cell, and flat cell. However, optimum performance with the loop-gap resonator (LGR) is achieved with 1 mm flat cells rather than 0.4 mm cells used in the cavity. The lower Q of the LGR decreases the demodulation of phase noise when tuned to the dispersion. The geometry is flexible and it is suggested that it can serve as a convenient general purpose resonator for ESR spectroscopy. 0 1989 Academic Press. Inc.

Wood et al. have described a three-loop-two-gap resonator ( LGR) for S band ( I ) . Figure 1 illustrates the geometry. A simple approximate lumped-circuit equation for the resonant frequency is readily derived. If

where L, , L2 are the lumped inductances of the central and outer loops, respectively, and C is the capacitance of each gap, then

PI and we can write [31 If R $ r, u a r-’ and, vice versa, if r % R, v a R-‘. Thus when the loop dimensions R, r are very different, the resonant frequency is determined by the smaller loop(s) and the larger loop(s) serves for the return flux. In the structures studied by Wood et al., R, r were of similar order of magnitude and both affected the resonant frequency. 223

0022-2364189 $3.00 Copyright Q 1989 by Academic Pew, Inc. All rights of reproduction in any form n’esewed.

224

HYDE,

Wa”eg”i

c4ing iris \

FRONCISZ,

- --

AND OLES

WallCurrents

\

kmple

access

/

-+1,.

%-held E-held

FIG. 1. Three-loop-two-gap resonator coupled to a waveguide. Notation for Table 1 is defined in the figure, and Table 1 gives the critical dimensions.

We describe here an X-band resonator of this geometry in which the central loop is the same diameter (11 mm) as the sample-access stack of a Varian multipurpose E-23 1 X-band cavity. The initial design concept was that such a structure could accommodate the standard unmodified cavity accessories: liquid nitrogen Dewar insert, variable temperature Dewar insert, flat cell, tissue cell, and electrochemical cell. It could therefore serve as a replacement for the Varian cavity, which is no longer in production. With R B r,

v=c 4 l/2 2ar (?rw 1

141

independent of 2 and R . Equation [ 41 is a very approximate one indeed, neglecting fringing of the electric field into the loops, the magnetic field in the gaps, and the fields above and below the resonator. It predicts a frequency about 2 / 3 of that actually observed, but is convenient in thinking about the physics of the resonator. Wood et al. (I) give more accurate expressions that include the neglected effects. See also Froncisz and Hyde ( 2). As discussed in Ref. ( 1) and illustrated in Fig. 1, a nodal plane exists across the central loop where the electric field is zero. It is apparent that the resonator has properties that are similar to the rectangular TE i02 cavity. Indeed, it has been mounted in a housing, Fig. 2, that resembles closely the familiar E-231 multipurpose cavity geometry. Even the coupling structure resembles that of the Varian coupler, with a conducting slug moving down over a slot cut parallel to the axis of one of the small outer loops. One can think of this coupling geometry as a two-stage transformer: from waveguide to outer loop and outer loop to central loop. This type of coupling to loop-

MULTIPURPOSE LOOP-GAP RESONATOR coupling \

225

Sampleaccess /

Waveguide

FIG.2. Outline drawing of the loop-gap resonator.

gap resonators was used previously by us at 35 GHz in a two-loop-one-gap structure(3). Field-modulation coils were modeled after those in the Varian cavity and mounted in a similar manner. The homogeneity and phase of the modulation field have been fully characterized but the data are not given here because of the close similarity with the TEio2 cavity modulation field. The sample-access stacks above and below the resonator were copied after the Varian dimensions, and the Varian collet system is interchangeable. In the remainder of this paper, performance data are given and the central question is addressed: Since the resonator is so similar to the TE102 cavity, what indeed are the differences in performance? PERFORMANCE AND ANALYSIS The resonator was fabricated from Macor and silver-plated 20 PM. Technical data are given in Table 1. The height and width of the resonator assembly including the shield, Fig. 1, are the same as the major and minor dimensions of X-band waveguide, 2.29 and 1.02 cm, respectively. The active length is 2.48 cm compared to the X-band rectangular TEio2 active length of 4.32 cm. Thus the resonator is substantially smaller in one of the three dimensions. This could possibly be of convenience in liquid helium emersion Dewars. The LGR resonator would be expected to have uniform magnetic fields in the lumped-circuit limit for Z p 2 R . In the present case Z/ 2 R = 1.1, and end effects can be expected to lower the homogeneity. Homogeneity data at positions a, c (Fig. 3) were taken using the perturbing metal sphere technique (4), and data at position b using a speck of DPPH calibrated from the perturbing metal sphere data. (Note that it is assumed in the perturbing metal sphere method that the electric field is zero, which is true only in the nodal plane.) The data of Fig. 3 have been extrapolated to 1 W incident power. The microwave efficiency parameter A, Table 1, is for the offcenter position a. Calculated microwave field values for the cavity resonator are also

226

HYDE,

FRONCISZ, AND OLES TABLE 1

Technical Parameters Inner radius, R Outer radii, r Gap width, w Gap separation, t Resonator height, Z Resonant frequency, v0 Unloaded Q Microwave efficiency, B, /P#2, A Field-modulation efficiency

cm 0.21 cm 0.25 cm 0.2 1 cm 1.27 cm 9.4 GHz

0.57

2500 0.85 GW-‘12

13.5 G/A

shown in Fig. 3 normalized to curve a of the LGR. The calculated curve with longer dashed lines is on-axis of the TE ,02, and the curve with shorter dashed lines for a line parallel to the axis and displaced 5 mm from the nodal surface in the x direction (corresponding to mode index 2). The variation of field along z is reduced in the LGR, which should be of convenience in saturation studies using line samples. The higher field at position a compared with position c in the LGR can be contrasted with the independence of field intensity in the cavity resonator on dimension y (corresponding to mode index 0). Feher (5) shows that the ESR signal height is equal to 01 = xvQP;‘*,

151

where x is the RF susceptibility, TJthe filling factor, Q the loaded quality factor, and POthe incident power. This expression is valid for nonsaturating samples where the signal increases linearly without limit as the incident power increases.

0.0 ’ 0

a POINT

I 4

SAMPLE

I

a

I

I

12

16

POSITION

(mm)

FIG. 3. Plot of microwave magnetic field along the z axis at indicated positions a, b, c, solid lines. The dashed lines are calculated values for a rectangular TE ro2 cavity. The ordinate values for the LGR are absolute for 1 W incident power but are only relative for the cavity. See the text for more details.

MULTIPURPOSE

LOOP-GAP

RESONATOR

227

We have

s

sin*$B:dV,

1=

s

sc

3 B:dl/,

El

where the integrals are over the sample s and cavity c, and 4 is the angle between the polarizing magnetic field B. and B, . Here 4 = 90”. For a matched resonator Q=w

energy stored incident power *

[71

We can form the ratio of signal heights for the cavity (subscript 1) and the loop-gap resonator (subscript 2) as

The simplification

occurs because

s c

BydV, a energy stored.

191

Define the microwave efficiency factor as A = B,/P;‘2.

[lOI

If we neglect the difference between the cosine variation of B1 along z in the cavity resonator and the experimental variation, curve c of Fig. 3,

AT !i= 2’ 212 A2

1111

Rataiczak and Jones (6) give data on the TE 1o2cavity from which a value A (cavity) = 1.17 can be calculated. From curve c, Fig. 3, A (LGR, on axis) = 0.75. For the same line sample extending through the two structures at the same low (i.e., nonsaturating) microwave power, 5 = 2.43. v2

[Ql

Figure 4 shows experimental data for capillaries of different diameters. The ratio of signal heights for the smallest capillary (radius 0.2 mm) is 2.37, in excellent agreementwithEq. [12]. This factor would appear to favor the TEio2 cavity, and such is the case for a nonsaturable sample in a capillary of fixed diameter. However, for a saturable sample, the incident microwave power should be readjusted such that B, at the sample is held

228

HYDE, FRONCISZ,

0.1

0.2 CAPILLARY

AND OLES

0.4 RADIUS

0.6 (mm)

1 .o

FIG. 4. Experimental relative signal heights for capillaries containing spin label at fixed nonsaturating incident microwave power. Circles, cavity; squares, LGR.

constant at some predetermined at constant B, ,

level of saturation. Then combining Eqs. [ 81, [lo] Vi -c-E

Al

v2

A2

1.56.

Equation [ 131 gives the predicted ratio for a saturable sample of limited availability. But the lower Q of the loop-gap resonator permits one to use a capillary larger than that for the cavity resonator. The experimental data of Fig. 4 show exactly the same maximum signal height (140 in arbitrary units) when a 1.4 mm diam capillary is used in the LGR and a 1 mm diam capillary is used in the cavity resonator. Figure 4 is at constant incident power. If the power were readjusted to give constant microwave field, scaling of the experimental data predicts that 2 = 0.64. v2

Thus the LGR would be superior in capillary geometry for saturable samples, but two times more sample would be required. The flat-cell geometry is subject to analysis of greater precision because of the favorable symmetry than is the case for the capillary geometry. We restrict the following discussion to saturable samples: essentially all spin labels and free radicals. Using the same reasoning that led to Eq. [ 131, VI A2qiQ1 -=~2

t151

b2Q2’

Wilmshurst (7) shows for saturable samples that the flat-cell sample thickness should be adjusted such that the Q is dropped to l/3 of its empty value. Since the height and width of the two structures being compared are similar, we can write 01 -=-

a,x,

v2

h2Jf2

,

t161

MULTIPURPOSE LOOP-GAP RESONATOR

229

where Xi, X2 are the cell thicknesses required to provide the desired degree of loading. From the free-space Maxwell equation

VXEd?!!L

[I71

dt ’

and since B1 has been adjusted to be a constant, V X E is the same in each structure. Then, +x,/2

(sample losses), = (sample losses)2

s -x1/2

x:dX =-=-x:

+x2/2 s -x2/2

x;dx

X:

Qo2

Qo,*

[I81

Finally

1191 If we take the on-axis A value of the loop-gap resonator (0.75)) the cavity resonator is favored by 8%. If we take the off-axis value, Table 1, the LGR is favored by 5%. It is concluded that the LGR and cavity sensitivities for saturable aqueous samples are about the same but that the LGR requires 1.4 times more sample, Eq. [ 181. In Ref. (8) we assessed the role of loop-gap resonators in observing the dispersion. The lower Q decreases the demodulation of phase noise. Experimental data on noise are given in Fig. 5. In principle, curves 1,2 should be displaced vertically by the ratio of Q’s, which is about 3. The observed displacement is a factor of 2.2. The optimum flat-cell thickness is given by Stoodley (9) as about 0.4 mm for the TEio2 cavity resonator for a nonsaturating sample. The optimum cell thickness for a saturable sample using Wilmshurst’s result that the Q should be dropped from 2/ 3 of the free space value to l/3 is 0.6 mm. Equation [ 191 predicts then the optimum value for the LGR should be increased by a further factor of ( Qol / Qo2) iI3 = 1.44, to

MICROWAVE

POWER

AlTENUATION

(dB)

FIG. 5. Noise as a function of incident power when tuned to the dispersion. Triangles, LGRs with 1 mm thick flat cell; squares, LGR empty; circles, cavity empty.

230

HYDE,

FRONCISZ,

AND OLES

a value of 0.9 mm. We have had good success using 1 mm aqueous flat cells with the LGR, and data are given on demodulation of phase noise in this geometry in Fig. 5. There is a net advantage in detecting dispersion using the LGR, but the advantage is partly negated by the lower A values of the LGR, which requires higher incident power to achieve a fixed value of B, at the sample. CONCLUSIONS

It is apparent that the two structures under comparison in this paper perform very similarly. There is one potential advantage of the LGR that has not yet been implemented: It should be possible to make a sample access port for one of the outside loops. The microwave efficiency parameter, A, for the outside loops is estimated to be 1.63. This will give increased sensitivity for nonsaturating samples or samples of limited availability. In some circumstances, particularly tissue samples or very viscous samples, the greater thickness of the 1 mm flat cell is an advantage. We are of the impression that the range of coupling of the LGR is greater. Thus there was insufficient coupling range to study capillaries of diameter greater than 1 mm in the cavity resonator, Fig. 4. A disadvantage of the LGR is that light irradiation is less convenient. Overall it is concluded that the three-loop-two-gap geometry as described here is flexible and that the structure can serve as a useful general purpose resonator for ESR spectroscopy. ACKNOWLEDGMENTS This work was supported by Grants GM27665 and RR0 1008 from the National Institutes of Health. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

R. L. WOOD, W. FRONCISZ, AND J. S. HYDE, J. Magn. Reson. 58,243 (1984). W. FRONCISZ AND J. S. HYDE, .I. Mum. Reson. 47,5 15 (1982). W. FRONCYISZ, T. OLES, AND J. S. HYDE, Rev. Sci. Znstrum. 57,1095 (1986). J. H. FREED, D. S. LENIART, AND J. S. HYDE, J. Chem. Phys. 47,2762 (1967). G. FEHER, BeliSyst. Tech. J. 36,449 (1956). R. D. RATAICZAKAND M. T. JONES, .I. Chem. Phys. 56,3898 (1972). T. H. WILMSHURST, “Electron Spin Resonance Spectrometers,” Adam Hilger, London, J. S. HYDE, W. FRONCISZ, AND A. KUSUMI, Rev. Sci. Znstrum. 53,1934 (1982). L. G. ST~~DLEY, J. Electron. Control 14,43 I (1963).

1967.