Biomedical EPR Part-B Methodology Instrumentation and Dynamics - Sandra R. Eaton

books. In 1965 a UHF LGR was used in a dynamic nuclear polarization experiment on metallic sodium (Reichert and Townsend). The modern use of lumped-circuit resonators in magnetic resonance dates from the publication by Schneider and Dullenkopf (1977) of the slotted tube resonator for NMR, by Hardy and Whitehead (1981) of the split-ring resonator for NMR, and the publication in 1981-82 of the loop-gap resonator for EPR (Hyde and Froncisz, 1981; Froncisz and Hyde, 1982). Since then, there have been many implementations of various forms of loop-gap resonators (LGR) in EPR, and in NMR. A central theme in these applications is the considerable design flexibility presented by the LGR, permitting a resonator to be designed for a sample, rather than selecting a sample size and shape that can be used in a pre-existing cavity resonator.

An explanation of the concept of cavity resonators, in the context of the design of a klystron, shows a picture of a “loop and a circular plate condenser” (Harrison, 1947) that is similar to a LGR used for EPR. A textbook introduces the concept of a cavity resonator by starting with a discrete circuit of an inductor (L) and capacitor (C), and then putting many inductors in parallel connected to the capacitor, and finally merging these into an enclosed cavity (Squires, 1963). Recently, Hyde has found value in making the reverse transformation, starting with cavity resonators, and pushing walls together in various ways to form capacitive elements, and then converting this into a design for a loop-gap resonator (personal communication, 2002). These concepts are important in understanding how to optimize resonators for EPR measurements.

There is an extensive, parallel, development of resonators for NMR, including such topologies as the crossed coil, birdcage, Alderman-Grant, and various helix and saddle coil designs. For an entrée to this literature, see the Encyclopedia of NMR (e.g., Hill, 1996; Hayes, 1996). Some of the NMR resonators are conceptually loop-gap resonators. The coaxial NMR cavity described by Kan et al. (1973), the slotted tube resonator (Schneider and Dullenkopf, 1977), the decoupling coil described by Alderman and Grant (1979) that has become known as the Alderman-Grant resonator, and the split-ring resonator (Hardy and Whitehead, 1981) all are conceptual forerunners of the class of resonators that are collectively called loop-gap resonators in EPR. Grist and Hyde (1985) used a LGR for NMR at 1.5 T. Lurie et al. (2002) used an Alderman-Grant resonator for EPR at 564 MHz and a solenoid for NMR at 856 KHz in a proton-electron double resonance imaging (PEDRI) measurement.

3.WHY SHOULD ONE USE LOOP-GAP RESONATORS?

Loop-gap resonators are advantageous for CW EPR measurements at frequencies below X-band, where cavity resonators are inconveniently large, and for measurements of limited size samples at X-band, where a LGR can have a higher filling factor than a cavity resonator. The lower Q of a LGR relative to a cavity results in less demodulation of source noise, and consequently better signal-to-noise (S/N) in dispersion spectra (Hyde et al. 1982b).

The advantages of LGRs for pulsed EPR include: Large filling factor

Good S/N for small samples

Reasonable physical size at low frequencies Large per square root watt

Use of lower power results in less detector overload (and lower cost) Fairly uniform over the sample

Easy to achieve low Q for short ringdown time

Cooling the resonator along with the sample may decrease thermal background noise

Larger bandwidth (lower Q) allows two or more simultaneous frequencies

Ability to rotate an entire EPR spectrum with a pulse, and hence do FT EPR

Facilitates EPR at low frequencies where cavity resonators would be impractical.

The corresponding disadvantages include:

The critically-coupled Q is lower than for a cavity resonator, but the impact of this on reducing sensitivity is partially offset by higher filling factor for a LGR than for a cavity resonator.

Small capacitive gaps may lead to arcing at high pulse power Careful sample positioning is required to take advantage of uniformity, especially if the length of the LGR is small.

LGR heating occurs if the thermal mass is small Background signals from the materials of construction.

Microphonics can be a problem, but LGRs may not be inherently worse than cavities; this merits further study

Large frequency shift as the coupling is changed, resulting in difficulty in tuning and maintaining field/frequency relationship as temperature is varied and when samples are changed

Reviews of loop gap resonator design and application have been published by Hyde and Froncisz (1986, 1989). A fairly comprehensive survey of LGRs is available from the National Biomedical ESR Center. This chapter provides an introduction to the basic concepts of loop gap resonators and analogous resonators, with the equations needed to understand them. A few selected examples of applications are included to inspire future use of LGRs, but no attempt has been made at comprehensiveness in citation of the literature, either of LGRs or their application.

4.BASICS

In EPR one is interested in measuring the effect of electron spin on the sample’s magnetic susceptibility. The role of the resonator is to concentrate the RF magnetic field, in the sample and make the signal produced by a change in magnetic susceptibility at resonance as large as possible. By “lumped-element” resonator, is meant a structure in which the region of high electric field and high magnetic field are readily identifiable and spatially separated. The sample is placed in the inductive element, where the B field is large and the E field is small.

In the following, SI units are used in the equations. However, we follow

The EPR signal for CW is given by Eq. (1) Similar expressions can be found in most introductions to EPR; we use the notation of Rinard et al. (1999a).

The of a LGR is in general lower than that for a cavity resonator at the same frequency. Despite this fact, the filling factor in a LGR can be many times that for a high Q cavity and the product is often comparable to that for a cavity. A LGR may also be desirable over a cavity for lossy samples, because of its lower Q and the fact that the E and B fields usually

are separated better in a LGR than in a cavity resonator. In addition, cavity resonators are not practical for frequencies below about 1 GHz.

The filling factor, is a measure of how effective the sample is in affecting the resonator and is proportional to the ratio of integrated over sample to integrated over the entire resonator (Poole, 1967). It has a maximum value of one. In practice, the filling factor is usually much less than 1. A sample in a standard 4 mm o.d. tube (ca. 3 mm i.d.) in a X- band resonator has a filling factor of roughly 0.01, while that for a LGR can be more than an order of magnitude larger. A LGR inherently has a larger filling factor than does a cavity resonator at the same frequency, and the filling factor can be increased by making the return flux cross section large relative to the sample loop cross section. The filling factor of a LGR is limited by the wall thickness of the sample tube. For example, if the loop is 4.2 mm diameter to hold a 4 mm o.d. tube and the sample is 3 mm od, and long relative to the resonator so that the length can be ignored, the filling factor is reduced relative to that for a completely full loop by a factor of

The parameters and depend on resonator geometry. In general, for a LGR, depends on the ratio of the area of the resonator loop to the area of the path for the reentant magnetic flux outside of the resonator. This reentrant loop should have an area about an order of magnitude larger than the resonator loop. The filling factor will be higher if the sample is long enough to include the fringing flux outside the loop. However, this results in a non-uniform over the sample. Increasing the length of the loop, provided it is filled with sample, will increase the filling factor. For the best filling factor in limited sample applications, the loop should be designed, as much as practical, to match the sample size.

The inductance of the loop is proportional to the square of its diameter and, for a given frequency, the smaller the loop the larger the capacitance of the gap must be (see Eqs. 2, 4). The capacitance of the gap can be increased by increasing its area and by decreasing the gap spacing (see Eq. (3)). For room temperature operation it may be necessary to fill the gap with a low loss dielectric such as Teflon, not only to increase the capacitance, but also to prevent arcing for high power pulse applications. In general, such dielectrics should be avoided for cryogenic operation because of the high temperature coefficients of their dielectric constant and of their dimensions.

The resistive loss in a resonator can be due to the materials of construction (e.g., aluminum has higher resistance than copper, and hence an aluminum resonator has lower Q than an otherwise identical copper resonator), or due to the sample itself. The word “lossy” characterizing a sample, or the solvent in which a sample is dissolved, means that power is “lost” in the sample by conversion of electromagnetic radiation to heat by

interaction with the molecular dipoles or ionic conduction in the substance. Thus, water reduces the Q of the resonator, and saline solution reduces it even more.

It is not possible to completely separate the E and B fields in the LGR and the fields are less separable at a given frequency the larger the loop, or at higher frequencies for a loop of a given size. For these cases the gap spacing will in general be larger and there will be more fringing of the E field into the loop. The larger the loop, the closer the resonator becomes to a cavity where the fields are well mixed. The E field fringing from the edges of the capacitive element is often the limiting feature that determines the size and placement of a lossy sample in a LGR.

5.TOPOLOGIES OF LOOP GAP RESONATORS

The descriptor LGR virtually speaks for itself in terms of resonator geometry. However, the LGR can take on a number of different forms depending on the frequency, resonator shield, field modulation provision, and support structure. One particularly simple embodiment of the LGR can be constructed by wrapping thin copper around a sample tube (Lin et al., 1985; LoBrutto et al., 1986). The copper can be self-supporting. It is also possible to make resonators from thin-film, copper coated Teflon etched to create desired patterns using circuit board techniques (Ghim et al., 1996). The resonator can be supported by the sample tube itself. This approach complicates changing sample tubes, but shows just how simple it can be to implement a LGR.

To help localize the electric field in the LGR, it is convenient to shield the gap with another conductor, creating what have become known as bridged LGRs. The first report was by Ono and co-workers (Ono et al., 1986a,b; Ogata et al., 1986; Hirata and Ono, 1996). Bridged LGRs were extensively developed by Schweiger and coworkers (Pfenninger et al., 1988; Forrer et al., 1990). Rotating the shield relative to the gaps makes a frequency-tunable LGR (Symons, 1995).

The basic field distribution of a LGR is rather like a dipole pattern, extending into space unless confined by a conducting shield. There usually is a hole in the shield for convenient sample placement. The size and conductivity of the shield affect the resonant frequency, and per square root watt. If the resonator is not properly shielded, there will be “hand waving effects” due to motion near the resonator. As described above, the shield should be at least 3 to 4 times the diameter of the LGR to maintain a good filling factor. The shield may be a simple conducting cylinder concentric with the resonator (Froncisz and Hyde, 1982) or may consist of a

26 GEORGE A. RINARD AND GARETH R. EATON

reentrant loop, which may be considered a part of the resonator itself (Sotgiu, 1985; Sotgiu and Gualtieri, 1985; Quine et al., 1996).

When a separate shield is used, some means of supporting the LGR is required. The original Froncisz and Hyde paper (1982) depicted the LGR as free in space. Obviously, some means for supporting the LGR is required. The trick is to support the LGR with non-lossy dielectric material such as Teflon, Rexolite 1422, or polystyrene that is compatible with the experimental environment (temperature, etc.) and that does not have an interfering EPR signal. Differential temperature coefficients of expansion, and cracking upon thermal cycling, limit use of some plastic materials, and impurity signals prevent use of most ceramic or oxide materials, especially for cryogenic operation. The Bruker “split ring” implementation of the LGR solves this problem by incorporating the return flux region and the sample region into one structure that can be supported by the outside rim. This is analogous to a 3-loop-2-gap LGR, in one mode of which two of the loops provide the return flux path for the third loop (Wood et al., 1984). For some reentrant LGR designs no separate support is required (Sotgiu, 1985; Sotgiu and Gualtieri, 1985; Quine et al., 1996).

Hyde and Froncisz (1989) reviewed several resonator topologies, pointing out designs intended for applications such as ENDOR and ELDOR. Several examples are sketched in Figure 2. Additional examples are sketched in some of the patents on LGRs, USA patents 4,435,680, 4,446,429, 4,453,147, 4,480,239, and 4,504,788. In a multi-purpose resonator, whose resonant element is sketched in Fig. 2d, the sample goes into the larger, center, loop, and the smaller loops are for the return flux. A different choice was made for a 2-loop-1-gap resonator for Q-band (Froncisz et al., 1986) and an X- band LGR designed for continuous and stopped flow studies of small amounts of samples (Hubbell et al., 1987). Putting the sample in the smaller loop increases the at the sample for a fixed incident microwave power, since the integral of the power over the cross section must be equal in the two loops. The 2-loop-1-gap resonator has been found to have advantages over the 1-loop-1-gap resonator in terms of thermal and mechanical stability (Hubbell et al., 1987).

The resonator component that contains the loops and gaps has to be shielded, coupled to the transmission line, and mechanically supported in an assembly that mates to the rest of the spectrometer. One example of a full assembly is shown in Fig. 3. Another full assembly is shown in Hyde et al. (1985).

Figure 2. Some LGR topologies that have been proposed. This figure is derived from several figures that show even more possible arrangements of loops, gaps, and locations of wires for RF coils for ENDOR. a, b, and c are three views of a 1-loop-2-gap resonator (Froncisz and Hyde, 1984; Hyde and Froncisz, 1989). The charges near the gaps denote regions of high electric field, and the large black dots in c label the points of minimum electric field. These are locations at which ENDOR or modulation coils can be placed with minimal effect on the microwave distribution. Sketch d is a 3-loop-2-gap resonator of the type (Wood et al., 1984) used in a resonator designed to be the analog of the “multipurpose” rectangular cavity resonator (Hyde et al., 1989). Inductive coupling is shown in a, and capacitive coupling is shown in e. Resonator f is a 2-loop-1-gap LGR for very small samples, which are placed in the small loop (Hubbell et al., 1987; Froncisz et al., 1986).