Bimodal inductors for ESR spectroscopy

Bimodal inductors for ESR spectroscopy

JOURNAL OF MAGNETIC RESONANCE 9,363-377 (1973) Bimodal Inductors for ESR Spectroscopy* G.CONCIAUROAND M. PUGLISI Faculty of Engineering, Uniuev...

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JOURNAL

OF MAGNETIC

RESONANCE

9,363-377

(1973)

Bimodal Inductors for ESR Spectroscopy* G.CONCIAUROAND M. PUGLISI Faculty

of Engineering,

Uniuevsity

of Pavia,

Italy

AND C.FRANCONI, P. GALUPPI,AND E. RANDAZZO Faculty

of Industrial

Chemistry,

University

of Venice,

Italy

Presented at the Fourth International Symposium on Magnetic Resonance, Israel, August, 1971 The results of extensive tests on three types of microwave bimodal X-band spin inductors are reported and discussed. The inductors examined were a square crosssection one, a cylindrical one, and a novel type designed around two orthogonal reentrant cavities. The tests made concerned important features such as the isolation between input and output ports far from spin resonance as function of the frequency, the effectiveness at very high decoupling levels of the rotary joints included in the cavity structures to work as decoupling devices and the effects of sample substitution and removal on coupling and tuning conditions. The results confirmed that the phenomenology of these inductors is now well understood and that, in agreement with the theory already developed, the square cross-section inductor is in many ways superior to the cylindrical one. Further, the limits of the rotating joint system of leakage reduction have been found to be about 80 dB of power attenuation. The tests made on the novel reentrant bimodal cavity (cloverleaf cavity) gave positive results about the independence of the coupling and tuning adjustments and about the small effect of sample insertion on mode coupling and tuning. Further the low electric energy density at the samples regions suggests use of this cavity for ESR of lossy samples while its smaller dimensions suggests its use at lower working frequencies (L, S bands). INTRODUCTION

In the past few years we have designed and developed an induction ESR spectrometer using bimodal inductors designed to give higher and more stable isolation between modes (1-3) than earlier models (4-7). We focused attention on square cross-section bimodal inductors (l-3) which, according to theoretical considerations should exhibit an isolation which is unaffected by sample insertion and removal-a very attractive feature from a practical point of view-while previous authors had considered either inductors of cylindrical symmetry working in TE modes (4-6) or H-plane T-junctions (7). The main characteristic of a spin inductor is the isolation between input and output ports measured as attenuation of the input power far from spin resonance, and its * Research supported in part by the Consiglio Nazionale delle Ricerche. 0 1973 by Academic Press, Inc. 363

Copyright All rights

of reproduction

in any form

reserved.

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FRANCONI

ET AL.

change with working conditions. A spin inductor can be used in many types of ESR induction spectrometers, as reflex cavities can be used in many types of absorption spectrometers. Although the microwave leakage can be discriminated in most induction systems since it does not carry the modulation information which characterizes the ESR signal, it would be useful to know the frequency dependence of the leakage around the working frequency and how the cavity-sample configuration and tuning conditions affect it. For instance Portis et al. (4) designed an induction spectrometer equipped with a bimodal cavity in which a microwave leakage of proper phase is deliberately introduced in order to detect either the absorption or the dispersion component of the Bloch susceptibility. Recently we have attempted to optimize the isolation characteristics of such inductors, introducing adjusting devices such as rotary joints, screws, etc. Furthermore, we have designed cavities of a different shape which, though theoretically less favorable (8), still exhibit very good isolation characteristics. In the present work a prototype of a square cross-section bimodal inductor is presented, and the results of the extensive tests made are discussed. A bimodal inductor prototype of cylindrical symmetry has also been developed and the results of the tests made are also presented and discussed. The two prototypes have been split into two and three sections of various length, respectively connected by one or two rotary joints for minimizing the modes coupling (1-3). Extensive tests have been carried out in order to verify the usefulness and the best location of the joints. Also the best location and shape of the sample within an inductor has been studied by performing suitable experiments and the effects exhibited by different sample-cavity configurations on mode coupling and tuning are discussed. Finally, a novel type of bimodal resonator made up of two crossed reentrant cavities (cloverleaf cavity) is presented and its mode and field distribution discussed. The characteristics of this new class ofinductors are analyzed and the possibility of exploiting these resonators as ESR inductors for particular purposes is discussed.

RESULTS

FOR

THE

SQUARE

CROSS-SECTION

INDUCTOR

The development of this inductor follows the original design (I-3). The structure of the inductor is shown in Fig. 1, and it is made up of three basic (h/2) sections. The first section is unimodal, works in the TEoII mode, and carries the input iris and the tuning screws (2). The second section is a bimodal one, working in the two orthogonal TEoII and TE,,r modes; it is also (h/2) long and is connected to the input unimodal section by a rotary joint provided with two screws for a stable and line adjustment of the parallelism of the polarization planes of the first mode of the two sections (Fig. 2). The plane of the joint is supposedly a nodal plane for the microwave exciting electric El field (first mode) so that provision is made for placing the sample tube with its length paralleJ to lines of HI, the exciting magnetic field. The third section is unimodal and similar to the first one but rotated 90” about the z axis and carrying a similar rotary joint (Fig. 2). Couplings to the cavity by coaxial cable are provided at both input and output sections in order to avoid stresses to and deformations of the cavity structure. The cable used is the semirigid Amphenol cable No. 421-668 provided with connectors type OS and OSM 2443.

BIMODAL

Is’

mode

INDUCTORS

[HI]

FIG.

FOR ESR SPECTROSCOPY

2nd

1. Magnetic field distribution

mode

365

[HZ]

in the square cross-section inductor.

FIG. 2. Square cross-section bimodal at X-band: A-input unimodal section; B-output unimodal section; C-bimodal section; D-teflon sample holder; E-rotary joint flange and mode decoupling screws.

The inductor was made of brass and then silver plated. At a resonant frequency of 9,230 MHz an unloaded Q-factor of about 2000 for both modes of the cavity was obtained with a quartz sample tube inserted.

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Resonance curves and isolation measurements between cavity have been made respectively as measurements frequency and as attenuation measurements of the [L = lOlog ( W,,/ WO,,) ; dB] by a microwave Network Model 8410 A, provided with Reflection-Transmission

B R

input and output ports of the of reflected power against microwave power leakage Analyzer, Hewlett-Packard Test Unit Model 8743 and

8

I

-160

- 80

0

I

80

I

I

160 is-Uo(lVlHz~

FIG. 3. Frequency dependence of attenuation of the microwave power leakage of the square crosssection inductor of Fig. 1: A-inductor loaded with and empty quartz sample tube; both modes tuned at V, = 9,230 MHz (vO= v1 = Q) and leakage minimized at V, by adjusting separately to both optimum angles unimodal sections with respect to themselves and to the bimodal section; B-same as A but after the input unimodal section has been rotated a few degrees with respect to its optimum angle with the bimodal section; C-conditions as in A, but after sample tube removal from the inductor (v, f vi J- vZ).

Microwave Sweep Generator Model 694 B. The results are shown in Fig. 3 ; the attenuation values at the working frequency v, have actually been measured on a more expanded scale. From the determination of resonance curves, it is found that the deviation of the resonating frequency of the two modes brought about by sample tube removal is not the same for both modes. That a deviation of the frequencies of both modes would occur could be anticipated, since, because of its finite dimensions, the sample tube

BIMODAL

INDUCTORS

367

FOR ESR SPECTROSCOPY

extends to regions where both E, and E, are not zero-valued. Actually the removal of a standard sample cell (an empty quartz tube, 3 mm o.d., 2 mm i.d.) from the inductor produced a 12.5 MHz deviation of the second mode frequency and only a 2.4 deviation of the first mode frequency. The higher dependence exhibited by the second mode frequency is not totally unexpected, since in this cavity-sample configuration, the

460

-80

0

80

160 -il -lb

FIG.

F-Sam v;! = (v,

3, confinued:

D-same

as A;

E-same

as A but:

v2 = v. = 9,230

(MHzj

MHz,

vl = (LJ~ + 80)

as A but: PZ= v. = 9,230 MHz, v1= (v, - 75) MHz; G-same as A but: Ye = I+,= 9,230 + 78) MHz; H-same as A but: v1 = Y, = 9,230 MHz, Z+ = (v. - 70) MHz (see text).

MHz; MHZ,

sample is inserted with its length parallel to the two long edges of the unimodal section opening which faces the bimodal section. Thus the sample lies on a plane, which although being a nodal plane for El is not a true nodal plane for E,. There is, in fact, a penetration of both the Ez and H, field lines into the wall opening represented by the input unimodal section (Fig. 1). The different electric field distribution ofthe two modes in the sample volume would contribute further to the difference in the frequency deviation. On the other hand, a positioning of the sample to face instead the opening of the output unimodal section perpendicular to the former position would affect the first mode more than the second one (see Fig. 1). Therefore, only the use of a bimodal

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allowing TEolz and TEr,, modes, with the sample tube placed in the central nodal E,, E2 plane would avoid this effect. However only either a diagonal disposition of a sample tube or else a sample symmetric in shape with respect to both field vectors would give an equal effect for both modes. The isolation between first and second mode has been measured as power attenuation with the inductor used as a dual mode, dual cavity transmission system. At a fixed working frequency (vO),high values of the attenuation have been obtained by rotating both unimodal sections with respect to themselves and to the bimodal one. It was observed also that the isolation is frequency dependent and that for different frequencies of the two modes (vl and VJ and optimum joint adjustments, the best value of the isolation was obtained when the adjustments were made at a value of the working frequency, V, equal to the common value of the resonating frequencies (vl = J+). In Fig. 3A it can be noted that the maximum power attenuation of the cavity, obtained empirically with successive joint adjustments and at a given common frequency, is of 70 dB. The best adjustments were considered those for which the minimum frequency dependence of the attenuation was found, corresponding closely to a perpendicular positioning of the unimodal sections with respect to each other and to the two degenerate modes of the bimodal section. The same value of attenuation at the same common working frequency could, however, also be maintained after a slight displacement from the optimum angles of both unimodal sections with respect to the bimodal one when trying to keep the unimodal sections perpendicular; however, a higher frequency dependence of the isolation was found (see Fig. 3B). The latter result confirms the importance of the unimodal sections for polarizing the modes. From Fig. 3C it can be seen that the removal of the sample tube does not affect the isolation at the frequency v,,, although the frequencies v1 and v2 have now been changed. The results of attenuation measurements on the same inductor whose decoupling has been optimized at the working frequency v, as a function of mode detuning, obtained by adjusting separately the tuning screws of the first and second modes, are shown in Figs. 3D-H. It is possible to see that a detuning of the second mode affects the isolation at v, more than does the detuning of the first mode. Given the nonperfect cavity configuration, one would expect some leakage for a large detuning of the modes mainly because of the presence of the sample holes and cavity wall imperfections. Also tuning screws of different length and positions might, however, couple the modes and make the cavity asymmetric with respect to tbe two modes, even though they are placed into sections in which the crossed mode is not supposed to penetrate. The results obtained call, therefore, for better unimodal section design in order to avoid penetration of crossed modes into the unimodal sections and for the removal of the sample holes and joints from regions where wall currents have high intensity. section

RESULTS

FOR

THE

CYLINDRICAL

INDUCTOR

A cylindrical inductor has been developed and tested with the aims of further exploring the limiting possibilities of the rotary joint system of leakage reduction in a cavity with a cross section fully compatible with it and of studying the effects of a different sample-cavity configuration,

BIMODAL INDUCTORS FOR ESR SPECTROSCOPY

369

The bimodal section of this inductor works with two orthogonal TEI1, degenerate modes, with the sample tube located on their central nodal El, Ez plane and directed parallel to the HI force lines. The output unimodal section and 1/4 of the bimodal section have been machined together out of a single brass piece. The rectangular opening usually present between these sections (1-3) has actually been substituted by a thin elongated nonresonant iris in order to reduce the penetration of the crossed mode. The input unimodal section and the remaining 314 of the bimodal section have been built together out of a single piece with the same criteria, so that the single rotaryjoint actually occurs at A/4 of the bimodal section on a plane which is not crossed by wall currents. X

no

.-.

lsr

mode

[HI]

2nd

FIG.

4. Magnetic field distribution

mode

-.

[HZ]

in the cylindrical

inductor.

Further, even large rotations of the section about the symmetry z axis do not destroy the symmetry of the inductor (see Figs. 4 and 5). The increase in the longitudinal dimension of the bimodal section has been kept within the available magnet gap length by filling the cylindrical bimodal section with Teflon and by putting appropriate capacitive loads within both unimodal sections. Also for this inductor the input and output sections are provided with cavity-coaxial cable transitions for avoiding stresses to the complex resonant structure. The inductor is silver plated and at v,, = 9,480 GHz exhibits an unloaded Q-factor of about 1,500 for both modes, with an empty standard quartz sample tube inserted. Resonant frequency shifts of both modes for insertion of various solvents of different dielectric constant and loss in a flat sample cell have been measured together with those relative to the removal of a standard quartz sample tube (3 mm 0.d.; 2 mm i.d.). The results show that the detuning effect of any sample is always twice as large for the output mode as for the input mode, regardless of the size of the sample and of its penetration within the region where the electric fields are not zero valued. Comparing the absolute values of the resonant frequency shifts with those for the square cross-section inductor, it can be observed that the use of the 2(h/2) bimodal section has reduced from 12.5 MHz to 4 MHz, the resonant frequency shift of the second mode for the standard sample cell

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removal. This large frequency shift reduction may well be ascribed to the positioning of the sample in a cavity region where the E, field is not distorted by cavity openings. The shift difference still observed for the two modes in this inductor (4 MHz and 2 MI-Iz) might instead still be ascribed to the lack of symmetry of the sample tube with respect to the El, Ez fields distribution, which gives just a factor of about 2 in favor of the output mode frequency deviation. The results of some of the attenuation measurements on this inductor, made by the II-P Network Analyzer are shown in Fig. 6. The frequency dependence of the attenuation was measured with the same analyzer system used for the square cross-section

FIG. 5. Cylindrical bimodal inductor at X-band: A-input (X/2) unimodal section and 3(X/4) of bimodal section; B-output (X/2) unimodal section and (X/4) of bimodal section; C-tuning screws; D-rotary joint adjusting screws; E-teflon dielectric filler; F-sample holder; CL-coaxial connectors; H-unimodal-bimodal coupling iris.

inductor. It can be noticed first that an improvement has been obtained as regards the leakage, in that the attenuation is better than 80 dB (Fig. 6A) at the working frequency v, for which optimum decoupling has been obtained. Actually the levels of the leakage shown in the curves of Fig. 6 have been calibrated in terms of attenuation by the use of a calibrated attenuator. Stable attenuations higher than these could not be measured with our present system; however, we have qualitatively observed that higher attenuations could be measured which were not stable with time. It can also be noted that the removal of the sample tube (Fig. 6B) brings a small shift of about 2 MHz of the minimum of the attenuation vs. frequency but that the maximum attenuation remains apparently the same. In this case, at the working frequency Y, for which the isolation was optimized (Fig. 6A), the attenuation is decreased, although remaining close to 80 dB (Fig. 7B), signifying that with the TE,,, field configuration there is a small effect of the sample on mode coupling. The results of Fig. 6C showthe stability of the structure with respect to the reinsertion of a calibrated

BIMODAL

INDUCTORS

371

FOR ESR SPECTROSCOPY

sample tube. The use of uncalibrated, slightly bent, quartz tubes actually brings a certain degree of coupling. This effect is absent in the square cross-section inductor. Therefore with this inductor, samples should be symmetric and homogeneous. It is hnally noted that the operation of the rotary joint in this type of cavity is troublefree and that, therefore, both the absence of wall currents crossing the joint plane and its cylindrical symmetry combine to allow very fine and smooth adjustments of the

I -20

I

I

I

- 10

I 0

I 10

I

I 20

‘J-

%

CMHz)

FIG. 6. Frequency dependence of the microwave leakage of the cylindrical inductor of Fig. 5: attenuation optimized at v, = 9,380 MHz with sample tube inserted: A-loaded with an empty quartz sample tube 3 mm o.d., 2 mm id. (v, = v1 = vJ; B-same as A but with sample tube removed (vO f: v1 # vJ; C-same as B but with the sample tube reinserted (uO= v1 = vJ (see text).

coupling. However at these levels of isolation the stress on the tight joint screws cause a plastic deformation of them with time bringing a decoupling deterioration which impairs the usefulness of such joints for higher attenuation levels. THE CLOVERLEAF

INDUCTOR

Beside the rectangular and cylindrical inductors discussed above a bimodal inductor of the reentrant type has been developed and tested, which because of its particular geometry (see Figs. 7 and 8) may be called the cloverleaf inductor. Although there are alternative designs for a bimodal reentrant inductor, the one developed and shown in Figs. 7 and 8 is particularly suitable for ESR spectrometry. The main body of the inductor has been machined to give four symmetrical ducts and four symmetrical pole caps-staggered at 45” with respect to the ducts-facing an inner metallic cylinder isolated from the outer body by a supporting teflon sleeve 1.5 mm thick, which keeps it coaxial with the cavity z symmetry axis. The main body of the cavity has a longitudinal overall dimension of 50 mm and a transversal dimension of 75 mm and is machined out of a brass piece and silver plated. The two brass endplates are fixed into place by two sets of screws to ensure good electrical contact. 14

FRANCONI

372

ET AL.

Given the complicated configuration of this cavity, explicit expressions for the field distribution are not available. However it is possible to represent qualitatively the field pattern of its lower frequency modes because as a reentrant cavity it essentially reproduces the behavior of a lumped-element resonant circuit where the coils are equivalent to the ducts and the condenser electrodes are equivalent to the pole caps and the inner cylinder (see Figs. 7 and 8). The field distribution of the two degenerate modes of this inductor are shown in Figs. 7 and 9. In the gap regions between the four reentrant portions of the main body

B E F FIG. 7. Cutaway section of the bimodal cloverleaf inductor. A-main bimodal body; B-lower endplate; C-output port with shield and rotating loop; D--second mode tuning screw; E-decoupling screw; F-teflon sleeve; G-upper sample; H-lower sample; Z-first mode magnetic field iine; L-second mode magnetic field line.

and the inner metallic cylinder, the electric field density is higher than the magnetic field density. The reverse is true in the remaining free volume constituted by the four cylindrical ducts which are connected by two machined slots at each end of the main body of the cavity, closed by the respective endplates. Thus at each end of the cavity there is one region where the magnetic energy density is high and the magnetic field of lines of both modes cross at right angle on a plane perpendicular to the symmetry z axis, which is placed parallel to the direction of the static magnetic field II,. This resonator allows the oscillation of one fundamental double degenerate mode, the second of which obtained by a 90” rotation of the field distribution of the first one about the z symmetry axis. A sketch of the two modes is given in Fig. 7. Given the symmetry of the cloverleaf inductor, there is the possibility of placing two samples in symmetrical positions along the z axis, each facing one endplate, within regions where the magnetic field lines of the two modes cross at right angles (Fig. 7).

BIMODAL

INDUCTORS

FOR ESR SPECTROSCOPY

373

FIG. 8. The cloverleaf bimodal inductor: A-sample holder; B-upper endplate; C-main bimodal body; D-input port; E-output port; F-first mode tuning screw; G-second mode tuning screw; fI-mode decoupling screws; Z-inner metallic cylinder. OUTPUT

OUTPUT

f-9

l-7

H FIELD

FIG. 9. Field distribution

LINES

of the first fundamental

E

FIELD

LINES

degenerate mode of the cloverleaf inductor.

A paramagnetic sample is easily introduced and positioned in each sample region by means of a flat dielectric sample holder (of quartz, Teflon, etc.) allowing for a cylindrical sample volume (see Fig. 8) for loading symmetrically both modes. Each sample holder

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ET AL.

fits between one endplate and the body of the cavity. Two plates made of the same dielectric material fill the cavity openings, symmetrically placed at 90” to the holder, for symmetrizing the sample region when the sample holder is inserted within the cavity. The positioning of the samples at the endplates actually allows an easy modulation of the resonance also at rather high frequencies with single coils cemented on each endplate which can easily be made, for instance, by silver-plated fused quartz (or different dielectrics). The measured resonating frequency of the two modes of the cavity is around 1.7 GHz. The unloaded Q-factor is about 1,000. The input and output coaxial lines are coupled to the respective modes of the cavity by means of rotating shielded loops. Loop rotation is provided for each one of them and allows the matching of the lines to the respective cavity modes. The slotted shields (see Figs. 7 and 8) allow for minimizing asymmetries in the cavity volume due to loop rotation, which would otherwise affect mode isolation. Far from paramagnetic resonance the input and output ports are isolated since the magnetic field H, (excited by the input port) is very weak at the output port and furthermore its polarization plane is perpendicular to the output port slots. An important feature of such an inductor is a high and stable degree of isolation between the ports, even in the presence of a lossy sample, given the low electric field energy density within the sample regions. Small asymmetries made during the cavity machining and aligning gave rise to small differences in the resonating frequencies of the two modes and to a certain degree of coupling. However the difference in frequency could be easily and smoothly eliminated by means of two tuning screws which affect independently both modes without affecting their coupling; the unwanted coupling between modes could be minimized using four screws which protrude in the gap (Fig. 8). The resonating frequencies of the two modes were actually equally affected by these decoupling screws and it should be noted that the independence of coupling and tuning regulations made these adjustments quite simple. Only two neighboring screws would be necessary; nevertheless, the two supplementary screws allow for finer adjustments. The isolation has been measured by means of a microwave network analyzer, and it was better than 70 dB at the working frequency, this figure being the upper limit which could be measured with our instrumentation at these frequencies, with variations of 1 to 2 dB when a sample was inserted or removed. The frequency dependence of the coupling exhibited a behavior similar to that of Fig. 3A relative to the square crosssection inductor. From the tests already carried out it was found that, in practice, frequency and coupling adjustments are needed only once and need not be changed when a sample is substituted with a different one. The tested prototype was not completely satisfactory from the point of view of mechanical tolerances, and the specifications reported above could surely be improved. The degenerate modes used are the fundamental modes of this resonator. A first higher nondegenerate mode was actually present in the tested prototype, resonating at a frequency of about the same value. The field lines of this mode are distributed as shown in Fig. 10Aand couple the input port to the output one. To avoid the rise of any appreciable coupling through this mode, a frequency separation of about 300 MHz between the frequency of this mode and the frequency of the two fundamental. modes

BIMODAL

INDUCTORS

375

FOR ESR SPECTROSCOPY

used was obtained by modifying the cavity in such a way as to reduce the capacitance C1 (see Fig. IOB) as much as possible in comparison to capacitance C2.

OUTPUT

f-7

IRST MO H

FIELD

LINES

E

FIELD

LINES

FIG. 10. A-field distribution of the first higher mode of the cloverleaf inductor; B-capacitance the high electric field energy density region of the cloverleaf inductor.

of

DISCUSSION

It can be said that in the light of the theoretical analysis of bimodal inductors (a), the results of the reported tests have confirmed the possibility of using these resonators for practical purposes and have confirmed also a number ofpertinent theoretical conclusions which can be quite useful for the design of optimized configurations of inductors to be associated with ESR spectrometers.

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FRANCONI

ET AL.

As to the effect of sample insertion on mode detuning, it can be stated that the difference in the resonating frequencies of the two modes is avoided with the use of homogeneous sample and sample holders, symmetric with regard to both shape and positioning with respect to both modes. For square cross-section cavities, tubular samples can still be used if diagonally positioned in the middle nodal E planes of the TEo12 and TEIo2 modes. For cloverleaf cavities it has been shown that the cavity configuration allows this condition to be easily fulfilled. This feature is particularly attractive because it would, for instance, permit proper spectrometer operation by simply allowing the oscillator frequency to follow the common resonating frequency changes by the use of an AFC system. As far as the coupling between the input and output ports is concerned, it should be observed first that an appreciable amount of leakage is always present if decoupling devices are not included in the inductor. This is due to several causes-as emerges also from the theoretical analysis (@-the most important of them being: (1) the practical impossibility of properly machining the cavity walls with sufficient precision to permit each port to be coupled only to its mode; (2) the nonuniformity in the conductive properties of the walls, especially that deriving from contacts between different metallic sections in wall areas where the intensity of the currents is high; (3) the presence of the other modes coupled to both ports at a frequency close to that of the working modes; (4) the presence, in regions where the electric fieid lines of the two modes are not orthogonal, of dielectrics (sample, sample holder, etc.) which are of asymmetric shape, nonhomogeneous, or asymmetrically placed. The microwave leakage due to combined effects of the above mentioned causes can, of course, be suppressed by a deliberate coupling between the input and output ports. Such a coupling would give a cancelling leakage of appropriate phase and amplitude obtained by suitable adjustments of decoupling devices such as rotary joints, screws, etc. However the frequency dependence of both these opposing leakages might not be the same, so that a perfect suppression can in general be made at only one frequency. Further the dependence of the loss of isolation on the frequency in the neighborhood of the working frequency for which leakage suppression has been obtained is higher, the larger the existing intrinsic coupling due to any of the above mentioned causes. In fact the above results have shown that the smallest frequency dependence of the isolation is exhibited by the cylindrical inductor, which, among the three inductors examined, is the one that has been machined with the highest precision and exhibits the best uniformity of wall resistivity because the rotary joint is opportunely positioned. Further, the decoupling brought about by a sample substitution is minimum for the square cross-section inductor and this positive result is consistent with the presence of two modes whose electric field lines are orthogonal throughout the bimodal cavity volume. Therefore, it can be concluded that between the first two inductor configurations the square cross-section one is to be preferred provided the bimodal section is lengthened to 2(X/2), the sample positioned symmetrically to both modes in the nodal E planes, the wall resistivity uniformity improved by the removal of rotary joints from planes crossed by wall currents and the unimodal section opening heights reduced to the minimum allowable value. An inductor of such a design would also give the best results according to theory (8). Of course different suitable decoupling devices must be

BIMODAL

INDUCTORS

FOR ESR SPECTROSCOPY

377

provided in place of the rotary joints, if they cannot be placed at the proper positions to avoid wall current effects because of symmetry requirements. The cloverleaf cavity exhibits features which make it appear interesting for particular applications for which the previous types of cavities would not be suitable. Tn fact, the cloverleaf cavity is smaller than a rectangular or cylindrical resonator designed to operate at the same frequency. Therefore, this cavity appears to be a good solution for the development of ESR induction spectrometers working in lower frequency bands (L or S bands), where the size of more conventional cavities becomes prohibitively large. Due to the low electric field energy density in its sample regions, this cavity appears quite stable with respect to sample change as far as tuning and isolation are concerned, and, therefore, it appears to be quite promising for those ESR spectrometers where the ease of use is of paramount interest. A further possible use is for ESR spectroscopy of lossy samples. REFERENCES

1. C. FRANCONI, N.A.T.O. Grant no. 294: Progress Report, 1968; Final Report, 1971. 2. C. FKANCONI, Rev. Sci. Znstv. 41, 148 (1970). 3, C. FRANCONI, “Magnetic Resonance in Biological Research,” (C. Franconi, Ed.) p. 397, Gordon & Breach, London, 1971. 4. A. M. PORTIS AND D. T. TEANEY, J. Appl. Phys. 29,1602 (1958); Phys. Rev. 116, 838 (1959). 5. D. T. TEANEY, M. P. KLEIN, AND A. M. PORTIS, Rev. Sci. Znstrum. 32,721 (I 961). 6. G. RAOULT, H. CHANDENZON, M. T. CHENON, A. M. DOUCLAD, AND M. PERRIN, Proc. XZZ Colloq. AMP&RE, Bourdeaux, 167 (1963). 7. Ivf. E. BRODWIN AND T. J. BURGESS, J.E.E. Tram Znstv. Meas. IM12,7 (1963). 8. G. CONCIAURO AND E. RANDAZZO, Rev. Sci. Instrum., submitted for publication.