Coplanar RF probe coil arrangement for multifrequency excitation

[0002] This invention relates to the field of nuclear magnetic resonance apparatus and particularly to radio frequency (rf) probe structures utilizing high temperature superconducting coils.

[0003] Nuclear magnetic resonance (NMR) spectrometers first became available in 1946. In 1950 observations of “shifted” resonances in nitrogen spectra by W. G. Proctor & F. C. Yu, Phys. Rev. 77, 717, (1950) stimulated efforts to improve the homogeneity and stability of magnets used in the experiments and led to the observation of chemically shifted resonances in proton spectra by J. T. Arnold, S. S. Dharmatti, and M. E. Packard, Jour. Chem. Phys. 19, 1608, (1951). This marked the beginning of high resolution NMR and its application as an analytical tool for chemistry, and sparked rapid growth in the development of NMR spectrometers. This development continues today at a pace limited only by the availability of relevant technology. Recent work is predicated upon improvements in rf probe performance incorporating receiver coils made from recently available high temperature superconducting (HTS) materials.

[0004] Nuclei of most isotopes of the elements have non-zero spin and exhibit gyromagnetic properties. They behave like microscopic spinning bar magnets and possess a coupled nuclear magnetic moment. In the absence of an externally applied magnetic field the nuclear moments of an ensemble of non-zero spin nuclei are randomly oriented in their atomic or molecular environment. When a static homogeneous magnetic field B is applied, the magnetic moments interact with the field and become oriented with respect to it. The spins are then said to be “polarized” by the field. Only certain orientations are allowed in accordance with well known quantum mechanical principles as described in “Nuclear Magnetic Resonance—Principles and Theory”, R Kitamaru, eds. Elsevier Science Publishers, 1990, Chap 2, pp. 25-36. As a consequence of the interaction of the field with the nuclear spin system, the nuclear energy level splits into multiple discrete levels corresponding to the different allowed orientations. Nuclei with spin equal ½ are the most suitable and most frequently used for high resolution NMR experiments. For simplicity and without loss of generality with respect to this present work, spin equal ½ nuclei will be assumed hereinafter. The split into two energy levels, corresponds to magnetic quantum numbers +½ and −½ for a spin ½ nucleus. The separation of the energy levels is proportional to the intensity of the magnetic field at the nucleus and to a proportionality constant γ called the magnetogyric ratio. In thermal equilibrium in the static field, a Boltzmann distribution of energies is maintained. There are more spins in the lower energy state than in the higher energy state. This difference is called the Boltzmann excess.

[0005] When an ensemble of nuclei are simultaneously subjected to both a static magnetic field and an appropriate rf magnetic field of frequency ν such that the energy of a quantum of radiation hν, where h is Planck's constant, is equal to the energy difference between the two spin energy levels, transitions can occur with equal probability from one state to the other. Due to the Boltzmann excess there is a net absorption of energy by the nucleus from the rf field. This transfer of energy is a necessary condition for obtaining a NMR signal.

[0006] In the aggregate, large ensembles of nuclei such as would be present in practical size samples obey the laws of classical dynamics. For convenience of visualization and ease of understanding, a classical vector model of the NMR phenomenon is hereinafter described.

[0007] With the static magnetic field applied, individual nuclei align themselves to the field, some with their microscopic magnetization vector substantially in the direction of the field, which is the low energy state corresponding to spin equal +½. Also, some nuclei align with their magnetization vector substantially in the direction opposite to the field, which is the high energy state corresponding to spin equal −½. In accordance with the Larmour Precession Theorem the individual nuclei precess about the direction of the field with an angular frequency ω_L=γB, where γ is the aforementioned magnetogyric ratio for each of the isotopic species, and B is the local field at the nuclei. More nuclei align in the direction of the field than in the direction opposite to the field, the difference being equal to the Boltzmann excess. Therefore, collectively the ensemble of nuclei exhibits a net macroscopic nuclear magnetization vector in the direction of the applied polarizing field B.

[0008] To generate a NMR signal, rf excitation is applied to the sample by a rotating magnetic field in the plane perpendicular to the direction of the polarizing field thereby enabling a transfer of energy to the spin system. The rotating field is provided by an alternating current in an excitation coil having its axis of symmetry perpendicular to the direction of the polarizing field. A linear oscillating magnetic field is generated along the x- axis of the excitation coil as shown in FIG. 1a. The linear oscillating field can be decomposed into two counterrotating components, one of which, usually called the B₁field, rotates in the direction of rotation of the aforementioned ensemble of nuclear spins, as shown in FIG. 1b. When the angular frequency ω of the two rotating magnetic field components 20 and 22 is equal to ω_L, the angular frequency of precession of the ensemble of nuclei 23, a resonance condition exists and, as shown in FIG. 1c, the net magnetization vector 8 tilts away from the z-axis 24 which is the direction of the static polarizing field 12 and precesses about it. As the magnetization vector 8 precesses about the polarizing field, it intersects the turns of a receiver coil, thereby generating a NMR signal. At resonance the angular frequency ω in the vector description equals 2πν, where ν is the frequency of excitation which produces transitions between spin states in the quantum description of the phenomenon.

[0009] The broad general utility of NMR as a tool for determining the chemical structure of compounds is due to the influence of the molecular environment on the local magnetic field at the nuclei. The local magnetic field at the nucleus of a particular nuclear species at a particular site in a molecule is the vector addition of the externally applied field, altered slightly by the magnetic influence of its molecular environment. By way of example, circulation of electrons about the nucleus caused by the applied field results in an induced field at the nucleus which in some instances opposes the applied field (diamagnetism), and in some instances augments it (paramagnetism). By way of further example the local field at the nucleus can be additionally modified, taking on multiple values or “splitting” due to interactions with other non-zero spin nuclei in the molecule. As discussed hereinafter, these two effects, known as “chemical shift” and “spin-spin coupling” respectively are major sources of the fine structure seen in NMR spectra as described in “Introduction To NMR Spectroscopy”, R. Abrahms.; J Fisher, P. Loftus, pubs. J Wiley & Sons, 1993, chap. 2, pp. 13-33, chap. 3, pp. 34-53. NMR spectra which are characterized by resonance lines that are narrower than the shifts in resonance caused by chemical shift and spin-spin coupling are known as high resolution spectra and are primarily made possible by the application of an extremely homogeneous polarizing field.

[0010] An NMR spectrometer is comprised of: 1) a D.C. magnet which provides said stable homogeneous magnetic field for polarizing the spins, 2) an rf system which provides a suitable rf excitation signal, 3) a coil or a plurality of coils for coupling the rf excitation to the spins and for receiving the NMR response signal, 4) a detection system for detecting the NMR response signal, 5) a signal processing system for processing the detected NMR response signal, and 6) an output device for displaying the NMR signal. For high resolution NMR studies, the compound under investigation is usually dissolved in or mixed with a suitable solvent and is in liquid form contained in a sample tube which is typically 5 mm in diameter. The sample is held in a sample holder portion of a probe which positions it in the most homogeneous region in the magnetic field. The coil or coils for coupling the rf excitation to the sample and for detecting the NMR signal are mounted on the probe.

[0011] NMR is an inherently insensitive technique. Sensitivity is strictly defined in terms of the minimum concentration of a test material required to produce a signal that is just detectable above the level of noise. For practical purposes however, the signal to noise ratio, S/N, is generally considered a good measure of sensitivity and the terms sensitivity and S/N ratio will be used interchangeably hereinafter.

[0012] The NMR signal is small for two fundamental reasons and numerous practical considerations. The first fundamental reason is that the energy changes involved in NMR transitions are small, and the second is that the net absorption of energy by an ensemble of nuclei is proportional to only the excess in population of the lower of the two energy states involved in the transition (i.e. the Boltzmann excess), rather than the total population. Specifically, the ratio of the number of spins in the higher energy state to the number in the lower energy state is (1−hν/kT) where k is the Boltzmann constant. Therefore this excess population is very small, a typical value being of the order of 1 part in 10⁵. Other reasons for the small signal include the need to use dilute solutions of the species being observed, either because of limited availability of sample material or to prevent spectra being complicated and rendered unreproducible by the effects of intermolecular coupling.

[0013] As further discussed hereinafter, the dominant source of noise which enters into the determination of sensitivity is generally thermal noise originating in the receiver coil of the spectrometer.

[0014] In early continuous wave (CW) spectrometers, sample resonances were excited one at a time by a continuous sweep of the rf excitation or static magnetic field.

[0015] In modern NMR spectrometers one or more high intensity rf excitation pulses of short duration are applied and the NMR response of the spin system to the excitation is received and recorded as the spin system relaxes back towards its equilibrium state. The receiver is off during the excitation pulse. Then when the transmitter is switched off, the receiver is switched on to record the NMR response. Since one is off when the other is on, the excitation and receive functions can time share the same coil. Alternately, separate coils can be used for excitation and reception. When the rf excitation is removed the magnetization vector relaxes and precesses about the static field. As it precesses and intersects the turns of the receiver coil, an NMR time domain response signal called a Free Induction Decay, FID, is generated. The terminology “Free Induction Decay” derives from the characterization of the signal as being induced by a magnetization vector “free” of the influence of the rf excitation, while it is “decaying” back to equilibrium. The time domain FID signal is then converted to a frequency domain spectrum, by means of a Fourier Transformation. Instruments operating in this manner are called Pulsed FT NMR Spectrometers.

[0016] In a pulsed FT spectrometer all frequencies in the spectral band of interest are excited simultaneously and the resulting FID, when Fourier transformed, yields a spectrum over the entire band of interest. The time for acquiring data in a pulsed spectrometer is therefore greatly reduced and as a consequence, time averaging of FID's from multiple scans can be done in a reasonable time prior to Fourier transformation of the data. This results in an improvement in the signal to noise ratio, S/N, on the order of the square root of the number of scans. Time averaging is one of many methods and techniques that are routinely used to improve the sensitivity of NMR spectrometers.

[0017] Continued improvement in sensitivity has been a constant objective in the development of NMR spectrometers. Increasing signal strength, reducing noise, and improving signal processing methods have all contributed. Many of the factors that influence the attainable signal to noise ratio are treated in “A Handbook of Nuclear Magnetic Resonance ”, R. Freeman, pubs, Longman Scientific & Technical, 1988, pp. 216-229 which is hereby incorporated herein by reference. As discussed hereinafter, the signal to noise ratio can be further improved by cooling the receiver coil to a very low temperature while maintaining the sample at or near room temperature to reduce Johnson noise.

[0018] The available signal is proportional to both the nuclear magnetization and to the resonance frequency. Since the nuclear magnetization is proportional to the resonance frequency, the available signal for a given species is proportional to the square of the resonance frequency. Noise considerations however reduce the dependence of sensitivity on the resonance frequency to ω^{{fraction (3/2)}} Largely because of this strong dependence of sensitivity on frequency, the trend has been toward higher and higher magnetic field strength and correspondingly higher values of NMR frequencies. Most modern NMR spectrometers utilize superconducting magnets capable of providing fields as intense as 18 tesla which are homogeneous over suitable sample size volumes. 17.6 tesla corresponds to an NMR frequency of 750 Mhz for protons.

[0019] Most modern NMR spectrometers have three separate transmitter channels: one to provide for a conventional field-frequency lock system, a second to provide the signal for observing the nucleus under study, and a third to provide 2D and decoupling capability. A block diagram of a typical modern pulsed spectrometer is shown in FIG. 2.

[0020] The probe is a critical component in an NMR spectrometer. For a given static magnetic field strength and a given sample size, the performance of the probe defines the sensitivity of the spectrometer. An important consideration in probe design is the coupling efficiency ζ of the receiver coil to the sample. ζ is the ratio of effective inductance to total inductance of the receiver coil. Any portion of the inductance of the receiver coil that does not contribute towards the detection of the NMR signal, such as coil leads by way of example, results in a loss of sensitivity proportional to ζ^½. Another important consideration is the quality factor Q of the receiver coil which affects sensitivity by a factor of Q^½ since signal voltage is proportional to Q and noise voltage is proportional to Q^½. Q represents the ratio of energy stored in the receiver coil resonant circuit to the energy dissipated through resistive losses in the circuit. Another important consideration in probe design is the receiver-coil filling factor ξ which, for a fixed coil- volume, influences the signal strength and the sensitivity directly. In the simple case of a cylindrical coil with diameter d_cwrapped around a cylindrical sample with diameter d_s, ξ would be approximately (d_s/d_c)². ξ is a measure of the energy stored in the transverse magnetic field coupling to the sample, compared to the total magnetic energy stored in the receiver coil resonant circuit. Filling factor ξ, coupling efficiency ζ, and quality factor Q should all be as large as possible for maximum sensitivity.

[0021] In many cases it is desirable, to simultaneously irradiate an NMR sample with several rf fields, each with a different frequency, without strong interaction occurring between the circuits producing the irradiating fields and the circuits detecting the responses. It is known in the art that transmitter drive can be largely decoupled from receiver coils by positioning the transmitter and the receiver coils on the probe at right angles to each other. This so called quadrature-coil configuration minimizes flux coupling between the coils. By making the mutual inductance between the coils very small the coupling of the strong irradiating signal to the sensitive receiver circuit can be largely eliminated.

[0022] Modern spectrometers use superconducting magnets. The cylindrical sample is positioned coaxially with the D.C. magnet. The transmitter and receiver coils can be a saddle coil as shown in FIG. 3aor a split formed-wire coil as shown in FIG. 3b. Either are ordinarily shaped to couple closely to the sample while providing the required B₁field orthogonal to the static field B. Using high temperature superconducting (ITS) materials, coils have been fabricated by depositing a thin layer of superconductor on a flat dielectric substrate 45. A pair of such coils forming a magnetically coupled system, a Helmholtz pair, are shown in FIG. 4a, placed on opposite sides of a sample is in the prior art. Also in the prior art, a second pair of similar HTS coils is shown positioned orthogonal to the first pair as shown in FIG. 4bto simultaneously provide a field-frequency lock signal. HTS coils can have high currents induced therein which can drive the coil normal and destroy the Q or significantly reduce the Q resulting in loss of detection sensitivity.

[0023] Best results are obtained with HTS coils when the superconductor is lattice matched to the substrate, i.e. grown epitaxially. The substrate 45 should be a thermally conductive material to facilitate cooling of the coil and should have low magnetic susceptibility to avoid degrading the homogeneity of the magnetic field. Acceptable substrate materials include sapphire, lanthanum aluminate, and magnesium oxide. A preferred HTS material is YBa₂Cu₃O_7-δ(YBCO), which has a critical transition temperature T_cof approximately 87° K. A coil made of this material is described in “HTS Receiver Coils For Magnetic Resonance Instruments”, R. S. Withers, B. F. Cole, M E. Johansson, G. C. Liang, G. Zaharchuk, Proc. SPIE, 2156, 27-35, (1994).

[0024] For proper performance HTS coils must be maintained at a temperature significantly below their transition temperature T_c. Joule-Thomson and Gifford-McMahon closed cycle refrigerators are known which cool the coils to 25° K. The coils are thermally isolated from the samples in this equipment and the samples can be maintained at or near room temperature if desired.

[0025] High resolution NMR probes using HTS coils can provide higher sensitivity than probes with non-superconducting coils. For a given sample volume the sensitivity of a coil is proportional to (ξQ/T)^½ where T is the coil temperature and ξ and Q are the aforementioned filling factor and quality factor respectively. A superconducting coil may have a Q of 20,000 compared with 250 for a room temperature coil and can operate at 25° K. With the geometry appropriate for a 5 mm. sample tube, and allowing for the loss of filling factor required for thermal isolation of the sample from the coil, the potential sensitivity gain can approach a factor of 10.

[0026] Any of the aforementioned coil configurations can be used to provide excitation and to detect NMR responses at more than one frequency by tuning the probe coil circuit to resonate at more than one frequency. However, since inductive elements are used to provide the frequency separation, multiple tuning degrades performance of the probe compared to a single tuned probe because of the inevitable reduction in the aforementioned coupling coefficient ζ. Combining the use of multiple tuning of probe coil circuits and orthogonal coil disposition, any of the aforementioned prior art probe arrangements can provide rf excitation and reception of NMR responses at several different frequencies. Disadvantages of the prior art probe when used in this way include the aforementioned reduction in sensitivity due to lower coupling coefficient as well as high cost of fabrication. Additionally it is difficult to perform adjustments to minimize mutual coupling between orthogonal pairs.

[0027] We have provided an improved high sensitivity rf probe for NMR spectrometers utilizing planar high temperature superconducting coils. Multiple coil pairs are used to provide for simultaneous multiresonance excitation including excitation for field-frequency lock, spin-spin decoupling and other signal enhancement and spectra simplification objectives. The coil pairs on the probe can all be superconductors, or alternatively some can be superconductors and others normal conductors. The planar coils comprising one half of each coil pair are either substantially coplanar or on closely spaced parallel planes, with individual coil pairs having either common axes of symmetry or different axes of symmetry that form a small angle with respect to the axes of symmetry of the other coil pairs. The symmetry axes of all coil pairs are arranged to intersect at the center of the sample region. An advantageous feature of the invention is the flexibility afforded to adjust the spacing between coils and coil pairs to obtain a net mutual coupling of zero or near zero between coil pairs.

[0028] An object of this invention is to provide a NMR probe with improved sensitivity.

[0029] Another object of this invention is to provide a high sensitivity NMR probe with a plurality of coil pairs for multifrequency excitation of a sample.

[0030] Another object of this invention is to provide a high sensitivity probe with a plurality of coil pairs wherein the net mutual coupling between coil pairs is zero or near zero.

[0031] Another object of this invention is to provide a high sensitivity probe with a plurality of coil pairs wherein a method is provided for adjusting the net mutual coupling between coil pairs to zero or near zero.

[0032] Another object of this invention is to provide a high sensitivity NMR probe which utilizes high temperature superconducting HTS coils made of a thin layer of HTS material deposited on a flat substrate.

[0033] Another object of this invention is to provide a high sensitivity NMR probe which utilizes a plurality of HTS coil pairs.

[0034] Another object of this invention is to provide a high sensitivity NMR probe which utilizes one HTS coil pair and a plurality of total coil pairs.

[0035] Another object of this invention is to provide a high sensitivity NMR probe which utilizes one or more HTS coil pairs wherein the temperature of the superconducting coils can be maintained suitably low as to retain their superconducting property while the sample temperature is maintained at or near room temperature.

[0036] FIG. 1ais a vector diagram of a linear oscillating magnetic field.

[0037] FIG. 1bis a vector diagram showing the counter rotating components of the linear oscillating field of FIG. 1a.

[0038] FIG. 1cis a vector diagram illustrating the nuclear magnetic resonance condition.

[0039] FIG. 2 is a block diagram of a Pulsed FT NMR Spectrometer.

[0040] FIG. 3ashows a prior art saddle type probe.

[0041] FIG. 3bshows a prior art split wire probe.

[0042] FIG. 4ais a schematic drawing of a pair of HTS coils with an input-output coupling loop.

[0043] FIG. 4bis a schematic drawing of an orthogonal pair of HTS coils.

[0044] FIG. 4cis a section view A—A of FIG. 4a.

[0045] FIG. 5ais a schematic drawing of two nested HTS coil pairs with common axes of symmetry according to the invention.

[0046] FIG. 5bis a schematic drawing of two overlapping HTS coil pairs with common axes of symmetry according to the invention.

[0047] FIG. 5cis the equivalent circuit of the coil pairs of FIGS. 5aand 5b.

[0048] FIG. 6ais a schematic drawing of two nested coil pairs with an LC trap in one according to the invention.

[0049] FIG. 6bis the equivalent circuit of the coil pairs in FIG. 6a.

[0050] FIG. 7 is a schematic drawing of two overlapping coil pairs with non common axes of symmetry according to the invention.

[0051] FIG. 7ais a schematic drawing of a Faraday shield according to the invention.

[0052] FIG. 7bis a schematic drawing showing Faraday shields positioned between coils according to the invention.

[0053] FIG. 8 is a graph of mutual inductance vs. coil spacing.

[0054] FIG. 9 is a graph of total mutual inductance vs. coil spacing.

[0055] FIG. 10 is a schematic drawing of two non-overlapping coil pairs with non common axes of symmetry according to the invention.

[0056] FIG. 11 is a schematic drawing of three non-overlapping coil pairs with non common axes of symmetry according to the invention.

[0057] With reference to FIG. 1a, a linear oscillating rf magnetic field 14 is shown applied in the x-y plane 16 along the x axis 18. With reference to FIG. 1b, clockwise rotating component 20 and counter clockwise rotating component 22 of the linear oscillating magnetic field 14 are shown rotating about the z axis 24. The clockwise rotating component 20 is the rf B₁excitation field. With reference to FIG. 1c, when the angular frequency ω of the excitation field 20 equals the Larmour frequency ω^L, the net magnetization vector 8 tilts away from the direction of the field 12 and simultaneously begins to precess about it. When the excitation field 20 is removed the magnetization vector 8 continues to precess about the field 12, generating a free induction decay signal in a receiver coil disposed with its axis or a projection of its axis of symmetry in the x-y plane 16.

[0058] With reference to FIG. 2, a block diagram of a modern Pulsed FT NMR Spectrometer is shown. Three separate transmitter channels provide for simultaneous multifrequency excitation to the probe, an observe channel 26, a field/frequency lock channel 28, and a decoupler channel 30. The field-frequency lock signal uses either a rapidly pulsed or a CW rf field. Other inputs to the probe are gated on and off by timing gates 32 under the control of computer 34.

[0059] FIG. 3ashows a prior art saddle type probe coil 36 and FIG. 3bshows a prior art split formed-wire probe coil 37. Both are cylindrically shaped to maximize the filling factor for a cylindrical sample. Multiple frequency excitation can be provided with these probe coils by multiple tuning of the probe coil circuit, at the cost of reduced coupling efficiency. The parts of the coil are physically arranged so that the currents in the wires produce opposite canceling fields except for certain wires that aid. With respect to FIG. 3b, the field from current in 38 is largely canceled by the field from current in 38i. Similarly the field from current in 38bis canceled along the sample axis by the field from current in 38f. In contrast the field from current in 38ais aided by the field from current in 38eand the field from current in 38gis aided by the field from current in 38c. The direction of the fields remaining are illustrated by the vector B₁arranged to be directed primarily parallel to the x-y plane and to pass through the center of the sample space. The coils on the opposite side,s of the sample space each define a magnetic field and the resultant field produced by the pair of coils defines a magnetic field having a symmetry plane which passes through the center of the sample space.

[0060] With reference to FIG. 4a, a pair of prior art planar HTS probe coils 40, forming a Helmholtz coil pair, is shown disposed on opposite sides of a cylindrical sample 42. FIG. 4cshows the substrate supporting coils 40, but in all other drawings the substrate is not shown and is assumed. With reference to FIG. 4b, a second pair of HTS coils 44, is shown disposed orthogonally to the first pair 40 to provide for simultaneous multifrequency excitation. The orthogonal disposition of the coil pairs minimizes their mutual coupling. These coils are excited by coupling to a loop antenna 41″ which is connected by a transmission line 41 to an rf source. The coupling antenna for the second coil pair 44 is not shown.

[0061] With reference to FIG. 5a, an embodiment of our invention is shown having two sets 46 of nested substantially coplanar HTS proton (¹H) coils 48 and deuterium (²H) field-frequency lock coils 50. Each set is preferably mounted on a single substrate (not illustrated) The two sets of coils are positioned on opposite sides of the normally cylindrical sample (not shown), the long axis of the sample being disposed in the direction of B_o, the static magnetic field 51. Each pair of coils is excited by loop antennae which are not shown to avoid clutter but are assumed.

[0062] With reference to FIG. 5b, another embodiment of our invention is shown having two sets 52 of overlapping substantially coplanar HTS proton (¹H) coils 54 and deuterium (²H) field-frequency lock coils 56. The two sets of coils are positioned on opposite sides of the normally cylindrical sample (not shown), the long axis of the sample being disposed in the direction of the magnetic field 51.

[0063] Similar coils on opposite sides of the sample constitute a coil pair. The nested coil pairs 48, 50 have a common axis of symmetry 57 which passes through the center of the sample. Similarly the overlapping coil pairs 54,56 have a common axis of symmetry 58 which passes through the center of the sample. As a practical matter, the nested coils 48,50 are more easily fabricated from single HTS films than the overlapping coils 54,56. The latter requires two electrically isolated films deposited on separate thin substrates or alternatively separate films deposited on opposite sides of a single substrate. The equivalent circuit 59 applicable to both the nested coils 48,50 and the overlapping coils 54,56 is shown in FIG. 5c. Mutual inductance 60 between the coil pairs needs to be made as small as possible to minimize both the ratio of currents I₂/I₁when at the proton frequency and the ratio of currents I₁/I₂when at the field-frequency lock frequency.

[0064] Small mutual inductance is achieved by the placement of the conductors of the two coils. The mutual inductance between two coils can be obtained from the equation $M=\frac{\mu }{4\pi }\oint \oint \frac{\cos \theta d{s}_{1}d{s}_2}{r}$

[0065] where μ is the permittivity of free space (47π×10⁻⁷H/m), ds₁, and ds₂increments along the conductors of coils 1 and 2 respectively, r the distance between ds₁, and θ is and 6 is the angle between the two increments. The double integral is taken along the path of each conductor. From this formula one observes that there is no contribution to the mutual inductance from regions where ds₁and ds₂are perpendicular to each other, and the mutual inductance is minimized by keeping regions where the two conductors are parallel as far from each other as possible. Thus by centering the small coil of FIG. 5awithin the larger coil one reduces their mutual inductance. In FIG. 5bthe two coils can be made with comparable self inductance, however by spacing the coil sections where the conductors are parallel the mutual inductance between them is minimized.

[0066] An analysis of the equivalent circuit 59 gives resonant frequencies of

[0067] ω_high²=ω₁²{1+α²/[N(P−1)]}/(1α²/N)

[0068] ω_low²=107₂²{1−Pα²/[N(P−1)]}/(1−α²/N)

[0069] where ω₁²=1/(L₁C₁), ω₂²=1(L₂C₂), α=M/L₁, N=L₂/L₁, and P=L₂C₂/L₁C₁. We assume that P>>1, [For deuterium, P=1/(0.1535)²=42.4], and that α²/N<1.

[0070] At the proton frequency the ratio of currents in the deuterium coil 50, 56 to that in the proton coil 48, 54 is

[0071] I₂/I₁=−(α/N) [P/(P−1)]≈−α/N=−M/L₂for deuterium

[0072] At the field-frequency lock frequency, the ratio of currents in the proton coil to that in the deuterium coil is

[0073] I₁/I₂=α/(P−1)=(M/L₁)/(P−1)

[0074] For the nested coils of FIG. 5a, values of (M/L₁)=0.5 to 0.6 are achievable, and if the inductance L₂of field-frequency lock coil 50 is made three times the inductance L₁of proton coil 48, then M/L₂≈⅙. Under these conditions the current ratios I₂/I₁and I₁/I₂in the aforementioned equations would be acceptable for some applications.

[0075] With reference to FIG. 6a, an LC trap 62 at the proton frequency could be added to the field-frequency lock coil 50 by bridging part of its inductance 63 with a capacitor 64 to further reduce the lock current at the proton frequency. FIG. 6bshows the modified equivalent circuit 66 with the addition of the trap 62. The trap 62 reduces the lock current at the proton frequency by a factor β=(L₃/L₂)/(1−ω²L₃C₃). The trap in effect increases the inductance of the lock coil from L₂to (β+1) L₂at the proton frequency. The trap 62 is most effective when its resonant frequency is the same as the proton frequency, but it has a substantial impedance even when its resonance is slightly off the proton frequency. With the trap resonance 0.5% above the proton frequency, β=100L₃/L₂and with L₃=L₂/4 by way of example, the lock current is reduced by a factor of 25.

[0076] As heretofore described, the nested HTS coil pairs 48,50 and the overlapping HTS coil pairs 54,56 have common axes of symmetry 57,58 respectively, which axis are positioned to pass through the center of the sample (not shown) in the space between the coils. The fields produced by the coil pairs 48,50 have the same symmetry axis 57 and the fields produced by the coil pairs 54,56 have the same symmetry axis 58. Although each of the two sets of nested coils 46 and overlapping coils 52 may be mounted on individual close spaced thin substrates there is no way in these embodiments of the invention to reduce the mutual inductance of the coil pairs to zero without destroying their symmetry axes after the individual coils are made.

[0077] With reference to FIG. 7, another embodiment of the invention is shown which overcomes the aforementioned problem. The two coils 70, 72 are configured to have overlapping region 74 and non overlapping regions 75 like the coils 54,56 in FIG. 5b. However in this alternative the symmetry axes 76, 78 of coil pairs 70, 72 respectively are not coaxial but instead their axes intersect at the center 80 of the sample region (sample not shown). By adjusting the distances 82, 84 that separate the planes of each coil from its mate, and the coil spacing 86 between the symmetry axes of coils on each side of the sample region, it can be shown that a net mutual coupling near zero can be obtained.

[0078] The mutual inductance between coils 70 and 72 can be analyzed by considering separately the mutual inductance between each wire segment of coil 70 with each wire segment of coil 72. To illustrate this the four segments of each coil are lab-led by the letters n, e, s, and w (north, east, south, and west) as indicated in FIG. 7. Since segments labeled n and s are perpendicular to segments labeled e and w there is no contribution to the mutual inductance from these pairs. Specifically there is no mutual inductance between the following pairs: 70nand 72eor 72w; 70eand 72nor 72s; 70sand 72eor 72w; 70wand 72s.

[0079] In summing the mutual inductance from the remaining coil segment pairs the relative signs of the various contributions must be considered. This is easily done by considering the direction of the conductors in each coil to have the same sense of rotation. The direction of the coil segments of FIG. 7 is taken as clockwise. The coils are symmetric to a reflection in the Z=0, i.e. the horizontal plane. With these conditions the mutual inductance contribution between segments 70nand 72nis equal to the contribution between 70sand 72sand is positive. The contribution by 70nand 72sis equal to the contribution by 70sand 72nand is small and negative. The contribution by 70eand 72eand by 70wand 72ware positive and large when the horizontal coil spacing, Y₀is small and the contribution rapidly decreases with increasing spacing. The contribution by 70wand 72eis generally small and negative. The contribution by 70eand 72wis small and negative for small horizontal coil spacing Y₀, and becomes large and negative as these two conductors approach each other. By selecting the spacing Y₀between these coils and therefore the spacing between the two conductors 70eand 72w, the total mutual inductance can be made positive, zero or negative.

[0080] If the measurements of the lengths and spacing of the conductors are made in units of centimeters (cm) and the mutual inductance M expressed in units of nanoHenrys (nH), the formula for the mutual inductance takes the form $M=\oint \oint \frac{\cos \theta d{s}_{1}d{s}_2}{r}nH$

[0081] By way of example the double integral has been analyzed for two coils shown in FIG. 7 with the following dimensions: Lengths 70e=70w=72e=72w=2 cm. Lengths 70n=70s=72n=72s=1 cm. Spacing between the planes of the two coils X₀=0.1 cm. The distance between the coil centers =Y₀. FIG. 8 shows the relative value of mutual inductance as a function of Y₀. With these dimensions the mutual inductance goes from positive for values of Y₀less than approximately 0.82 cm. to negative for values of Y₀larger than approximately 0.82 cm. The mutual inductance is near zero at Y₀=0.82 cm.

[0082] The contribution to mutual inductance of the coil pair 71 and 73 on the other side of the crossover point 80 of FIG. 7 must also be considered. Since these coils are identical to coils 70 and 72, the mutual inductance between them will also change in the same way with spacing Y₀Coils 70 and 71 are tuned to the same frequency and have essentially the same electrical current. Coils 72 and 73 are also tuned to the same frequency, but a different frequency from that of coils 70 and 71. The mutual coupling between segments of coil 70 and coil 73 must be considered. The spacing between coils 70 and 73 is largely independent of Y₀and depends only on the distance X₁between the planes containing coils 70 and 73.

[0083] In this example the distance X₁between the planes containing coils 70 and 73 is chosen to be 1 cm. Carrying out the analysis for the mutual inductance between coils 70 and 73 gives a value of 2.56 nH. Adding this value to the mutual coupling between coils 70 and 72 yields the total mutual coupling of coil 70 to the two coils 72 and 73. FIG. 9 is a graph showing the total mutual inductance between coil 70 and the combination of coils 72 and 73 vs. Y₀. By symmetry the total mutual inductance between coil 71 and the combination of coils 72 and 73 is the same as that of coil 70. As noted from FIG. 9 the total mutual inductance is approximately zero when Y₀=0.91 cm.

[0084] Making the total mutual inductance between coils 70 and 71 and the combination of coils 72 and 73 zero, insures that currents in the coil pair 70, 71 do not induce currents into coils 70 and 73. However there may also be electric fields due to the voltages on these coils and any residual capacitive coupling between the coil pairs may cause undesired coupling. It is well known that capacitive coupling between coils can be greatly reduced or eliminated by the use of a Faraday shield. In this case a Faraday shield 77 can be made of a number of parallel conductors 79 that are electrically connected at one end as illustrated in FIG. 7a. The conductors may be fabricated from HTS materials in the same manner that coils are fabricated. Shields 77 can then be placed between coils 70 and 72 and between coils 71 and 73 as illustrated in FIG. 7b.

[0085] As noted in FIG. 9 there is another value of Y₀that leads to zero total mutual coupling to coil 70 from the two coils 72 and 73. In this example the other value of Y₀that gives zero total mutual coupling is approximately 1.24 cm. In this case, using the value of 1.24 cm. for Y₀there is no overlap of the coil conductors, permitting the coils to be in the same plane as shown in FIG. 10. However with the coils in the same plane, i.e. X₀=0 instead of X₀=0.1 cm. as in the above example, but with all other coil dimensions the same, the values of mutual inductances between coil segments change slightly requiring therefore a slightly different value of Y₀to yield zero total mutual coupling. Repeating, the analysis with X₀=0 but with all other dimensions the same yields a total mutual inductance of approximately zero when Y₀=1.265. The coils 90 and 92 of FIG. 10 are in one plane and therefore both coils can be fabricated on one side of a single substrate. Their mating coils, 91 and 93, can similarly be fabricated on one side of a second substrate. As the graph of FIG. 8 indicates, the mutual inductance between coils 90 and 92 of FIG. 10 is negative whereas the mutual inductance between coils 90 and 93 of FIG. 10 is positive, the sum of the two therefore yielding a total mutual coupling of zero when Y₀=1.265.

[0086] With reference to FIG. 11, the coil arrangement of FIG. 10 may be extended to 3 coil pairs 94 and 95, 96 and 97, 98 and 99. This arrangement may be particularly useful in 2D or 3D experiments where short high power pulses are applied to determine molecular structure or molecular confirmation. The coil pair 96 and 97 may be made of HTS materials to provide high sensitivity for receiving the weak NMR responses, and the coil pairs 94 and 95, 98 and 99, may be made of copper or other normal conductors to provide the high power pulses. With this coil arrangement a near zero coupling condition of the coil pairs 94 and 95, 98 and 99 from the coil pair 96 and 97 may be obtained. Coupling between the two coil pairs 94 and 95, 98 and 99 may be of no consequence. Coil pairs 94 and 95, 98 and 99 may be placed on planes somewhat farther from the sample region than the coil pair 96 and 97, and if desired Faraday shields may be appropriately placed on separate planes between them to reduce or eliminate capacitive coupling as previously described and illustrated in FIGS. 7aand 7bfor the case of two overlapping coils. As in the aforementioned case the Faraday shield may be made of HTS material to minimize rf losses. In this multiple coil arrangement the coils may be in different planes and may or may not be overlapping. The multiple coil arrangement with overlapping coils is not shown.

[0087] Although specific HTS coil shapes and aspect ratios and only simple resonant circuit configurations are used herein for illustrative purposes, it is not intended that the invention be restricted to them but rather that it be applicable to all HTS planar thin film coil structures. Although specific applications utilizing multifrequency excitation are cited including field-frequency lock and spin-spin decoupling, it is not intended that the invention be restricted to these applications but rather that it be applicable to all applications utilizing multifrequency excitation. Also, though reference herein is limited to ¹H, ²H, and ¹³C nuclei, it is not intended that the invention be restricted to them but rather that it be applicable to other spin active nuclei as well, particularly including important nuclei such as ¹⁴N, ¹⁵N, ¹⁹F, ³¹P and ³⁵Cl. In accordance with these considerations the scope of the invention should be (construed in view of our claims.