Ramaswamy_Final_Submission

DEVELOPMENT OF HIGH-TEMPERATURE-SUPERCONDUCTING PROBE
TECHNOLOGY FOR NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
By
VIJAYKUMAR RAMASWAMY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2015

4
ACKNOWLEDGEMENTS
I am extremely grateful to Dr. Arthur Edison and Dr. William Brey for accepting me as
part of their research group and their mentoring through the years. I am thankful to both of them
for their constant encouragement and support through many highs and lows. The many years in
Florida have been a great learning experience for me, greatly enriched by both my mentors, and I
am grateful to them both for the opportunity. Additional thanks go to Dr. Thomas Mareci,
Dr. Joanna Long and Dr. Mingzhou Ding for serving on my supervisory committee and for their
helpful comments on my dissertation.
Thanks are also due Dr. Jerris Hooker at the National High Magnetic Field Lab for
helpful discussions and collaboration throughout the project. A special word of thanks is due to
Dr. Richard Withers and Robert Nast for their collaboration in the early parts of the project
during their time at Agilent Technologies, Inc. Their continued comments and discussions have
been very helpful and inspiring. I am very grateful to James Rocca at UF for the numerous hours
he spent patiently training me on the NMR spectrometer. The NMR testing of the probes have
been made possible with lots of assistance from Jim. I also extend my thanks to Robert Harker
and Ion Ghiviriga at the University of Florida, and Brendan Duggan and Anthony Mrse at the
University of California San Diego for their advice and assistance in using superconductive
probes.
My graduate school experience was greatly enriched by all the fellow passengers. I would
like to thank all colleagues and classmates, current and past, in Department of Biomedical
Engineering, in the Edison laboratory, and in the National High Magnetic Field Lab, for their
cooperation and friendship during my time here.
Funding for the probe development project was available from the NIH – NIBIB
R01EB009772 grant to Dr. Arthur Edison. A portion of this work was performed at the National

5
High Magnetic Field Laboratory, which is supported by National Science Foundation
Cooperative Agreement No. DMR-1157490 and the State of Florida. Thanks are due to Agilent
Technologies for making available instrumentation which was critical to the performance of this
project.
I would like to thank the administrative staff at the departments of Biomedical
Engineering (BME) and Biochemistry and Molecular Biology (B&MB) at the University of
Florida, and at the National High Magnetic Field Lab at Florida State University for their
assistance. Frequent travel between Tallahassee and Gainesville was essential for this project.
Thanks are due to Denise Mesa and Mary Desilets for their assistance with travel arrangements,
often at very short notice.
Finally, I would like to thank my family and friends for their continuous support through
all my endeavors. Many classmates from my school and undergraduate days deserve my thanks
for egging me on several occasions to go farther than I thought possible. I am also thankful to the
numerous new friends in Florida who helped create a home away from home.

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TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS.............................................................................................................4
LIST OF TABLES...........................................................................................................................9
LIST OF FIGURES .......................................................................................................................10
ABSTRACT...................................................................................................................................14
CHAPTER
1 GENERAL INTRODUCTION ..............................................................................................16
Introduction to NMR Spectroscopy........................................................................................16
Motivation for Cryogenic Microsample Probes .....................................................................18
Project Overview ....................................................................................................................20
2 TECHNOLOGY AND IMPACT OF HTS PROBES ............................................................23
Technology of HTS Probes ....................................................................................................23
Refrigeration and Vacuum Design ..................................................................................23
Initial designs ...........................................................................................................23
Dipping probes .........................................................................................................25
Closed-cycle cryocoolers .........................................................................................26
HTS Probe Technology ...................................................................................................28
Substrates and film-growth ......................................................................................29
Microwave surface resistance ..................................................................................30
HTS Resonators...............................................................................................................31
Helmholtz pair resonators ........................................................................................32
Racetrack resonator..................................................................................................35
Spiral resonator ........................................................................................................36
Faraday-shielded spirals...........................................................................................38
Counterwound spirals...............................................................................................38
Impact of HTS Probes ............................................................................................................39
1
H-optimized HTS probes ...............................................................................................39
13
C-optimized HTS probes ..............................................................................................39
Limitations of HTS Probes .....................................................................................................41
3 DESIGN OF DOUBLE-RESONANCE HTS COILS............................................................61
Introduction.............................................................................................................................61
Electromagnetic Simulation....................................................................................................61
Sensitivity........................................................................................................................61
B1 Homogeneity...............................................................................................................62
Sample Loading...............................................................................................................63
Development of Double-Resonance Coils..............................................................................65

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Orthogonal Coils .............................................................................................................65
Preliminary Design..........................................................................................................66
Optimization of Figure-8 Mode.......................................................................................67
Orientation of Spirals for Reduced E-field......................................................................67
Faraday Shield Integration ..............................................................................................68
Single-Sided Double-Resonance Design.........................................................................69
Conclusion..............................................................................................................................69
4 CONSTRUCTION AND EVALUATION OF 1
H-13
C DUAL-OPTIMIZED HTS
PROBE ...................................................................................................................................83
Introduction.............................................................................................................................83
Probe Construction .................................................................................................................83
HTS Coil Testing.............................................................................................................83
Coil Pair Testing..............................................................................................................84
Cryogenic preamplifier....................................................................................................86
Probe Evaluation.....................................................................................................................87
RF Tests...........................................................................................................................87
Initial measurements ................................................................................................87
B1 mapping ...............................................................................................................88
NMR Tests.......................................................................................................................89
B1 pulse length..........................................................................................................89
B1 homogeneity ........................................................................................................90
Signal-to-noise ratio .................................................................................................90
Lineshape .................................................................................................................91
Results and Discussion ...........................................................................................................91
B1 Pulse Length ...............................................................................................................91
B1 Homogeneity...............................................................................................................92
Signal-to-Noise Ratio ......................................................................................................92
Lineshape.........................................................................................................................93
Conclusion..............................................................................................................................94
5 IMPROVEMENTS IN MECHANISMS FOR FREQUENCY TUNING AND
IMPEDANCE MATCHING ................................................................................................109
Background...........................................................................................................................109
Moveable Tuning Loop .................................................................................................109
Moveable Matching Loop .............................................................................................111
Advantages and Drawbacks of Moveable Loops ..........................................................113
Alternate Tuning Mechanisms..............................................................................................114
Circuit Analysis of Resonant Tuning Circuit .......................................................................115
Moveable Resonant Tuning Loop .................................................................................119
Upward shift...........................................................................................................120
Downward shift......................................................................................................120
Fixed Coupling Loop with Variable Capacitors............................................................122
Upward shift...........................................................................................................122
Downward shift......................................................................................................123

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Fixed Coupling Loop............................................................................................................124
Simulation......................................................................................................................124
Implementation..............................................................................................................125
Conclusion............................................................................................................................127
6 CONCLUSIONS AND FUTURE DIRECTIONS ...............................................................147
Summary...............................................................................................................................147
Future Directions ..................................................................................................................148
LIST OF REFERENCES.............................................................................................................150
BIOGRAPHICAL SKETCH .......................................................................................................156

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LIST OF TABLES
Table page
2-1 Loss tangents of various substrates reported in the Theva datasheet.................................43
3-1 Simulation of effect of sample loading using finite dielectrics capability in
HyperLynx.........................................................................................................................71
3-2 Comparison of simulated metrics of performance for conventional single-resonance
designs and double-resonance designs...............................................................................71
4-1 Resonant modes observed on the dual-optimized probe alongside mode identification...96
4-2 Standard sensitivity test samples of some common nuclei................................................96
4-3 Measurements of 1.5-mm 1
H-13
C dual-optimized HTS probe...........................................96
4-4 Measurements of 1.5-mm 13
C-optimized HTS probe........................................................97
4-5 Comparison of pulse length and S/N values of microsample probes – 1.5-mm 13
C-
optimized probe, 1.5-mm dual-optimized probe, and 1.7-mm Bruker
MicroCryoProbeTM
............................................................................................................97

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LIST OF FIGURES
Figure page
2-1 Cryostat portion of cryogenic probe designed by Styles et al [5]......................................43
2-2 Schematic of dipping probe. ..............................................................................................44
2-3 Block diagram of Gifford-McMahon based refrigeration system .....................................45
2-4 Illustration of the complete setup for a single channel of HTS coils.................................46
2-5 Cross-section layout of a typical HTS cryogenic probe ....................................................47
2-6 Comparison of surface resistances of superconductors and copper as a function of
frequency............................................................................................................................48
2-7 DC magnetic field dependence of surface resistance of YBCO for various film
thickness.............................................................................................................................49
2-8 DC magnetic field dependence of YBCO surface resistance on magnetic field
direction .............................................................................................................................50
2-9 Parallel slits in YBCO to reduce effect of persistent currents in the resonator. ................51
2-10 Lumped element model of a Helmholtz pair of coupled resonators..................................52
2-11 Simulated current and magnetic field distribution at the two resonance modes of a
Helmholtz pair of coupled resonators................................................................................53
2-12 Racetrack resonator............................................................................................................54
2-13 Spiral resonator..................................................................................................................55
2-14 Spiral with Faraday shields................................................................................................56
2-15 Counterwound spiral coils .................................................................................................57
2-16 Cross-section of nested coil arrangement in the 1-mm HTS probe...................................57
2-17 Cross section of nested coil arrangement in the the 1.5-mm 13
C optimized probe............58
2-18 NMR spectra from mixtures of synthetic metabolites .......................................................59
2-19 13
C-13
C INADEQUATE spectrum of 1.1 mg natural abundance 13
C histidine.................60
3-1 Perspective view of the B1-shift test simulation setup.......................................................72
3-2 Plot of the component of the magnetic field in the transverse plane.................................72

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3-3 Perspective view of the dielectric shift test simulation setup ............................................73
3-4 Cross section of 1.5-mm probe utilizing double resonance coils. .....................................73
3-5 Preliminary double-resonance coil design using an I-bar and spiral resonators................74
3-6 Schematic of the orthogonal magnetic fields at the two resonance frequencies of the
double-resonance design....................................................................................................75
3-7 Figure-8 resonator formed using two racetracks ...............................................................76
3-8 Tapering of center strip in figure-8 coils for optimal homogeneity...................................77
3-9 Orientation of spirals..........................................................................................................78
3-10 E-field plots for spirals without Faraday shields ...............................................................79
3-11 E-field plots for spirals with Faraday shields. ...................................................................79
3-12 Double-resonance 1
H-13
C coil design................................................................................80
3-13 Photograph of double-sided 1
H-13
C HTS coil....................................................................81
3-14 Single sided double-resonance coil for 2
H/15
N channels...................................................82
4-1 Trimming plot of a 15
N coil for the v1 probe.....................................................................98
4-2 Mode splitting of a pair of coupled figure-8 resonators. ...................................................99
4-3 B1-mapping of 1
H channel of the 1
H-13
C dual optimized probe. .....................................100
4-4 B1 map of 13
C channel of the 1
H-13
C dual optimized probe.............................................101
4-5 Pulse length calibration for the 1
H channel of the dual-optimized probe........................102
4-6 B1 homogeneity of the 1
H channel of the dual-optimized probe. ....................................103
4-7 Signal-to-noise ratio of the 1
H channel of the dual-optimized probe. .............................104
C channel of the dual-optimized probe .............................105
C channel of the 13
C-optimized 1.5-mm probe. ................106
4-10 Lineshape spectrum of 1% CHCl3 in Acetone obtained using the 1
H-13
Cdual-
optimized 1.5-mm probe..................................................................................................107
4-11 Lineshape spectrum of 1% CHCl3 in Acetone obtained using the 13
C-optimized 1.5-
mm probe. ........................................................................................................................108

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5-1 Circuit model of a resonator and a moveable inductive tuning loop ...............................128
5-2 Tuning achieved using a shorted moveable tuning loop as a function of the coupling
between the loop and the resonator..................................................................................129
5-3 Estimated Q over the tuning range when tuned using a moveable loop..........................130
5-4 Experimentally measured Q over the tuning range using a moveable loop ....................131
5-5 Circuit model for a moveable matching loop ..................................................................132
5-6 Adjustment of moveable inductive loops affects the magnetic field homogeneity.........133
5-7 Experimentally measured Q-values of the 1
H channel in the 13
C-optimized probe.. ......134
5-8 Circuit model of a concept of resonant tuning circuit......................................................134
5-9 Circuit model of a resonant tuning circuit. ......................................................................135
5-10 Plot of X as a function of the tuning circuit frequency normalized to the desired
frequency..........................................................................................................................136
5-11 Plot of the tuning of the resonator as a function of coupling to a moveable resonant
tuning loop. ......................................................................................................................137
5-12 Plot of the Q over the tuning range with a moveable resonant tuning loop.....................138
5-13 Plot of the tuning of the resonator as a function of of coupling to a moveable
resonant tuning loop.........................................................................................................139
5-14 Plot of the Q over the tuning range with a moveable resonant tuning loop (Q1=200). ...140
5-15 Plot of the tuning as a function of the tuning circuit frequency for various levels of
coupling............................................................................................................................141
5-16 Plot of the Q over the tuning range when the resonator is tuned up with a fixed loop
tuning circuit for various levels of coupling....................................................................142
5-17 Plot of the tuning as a function of the tuning circuit frequency for various levels of
coupling............................................................................................................................143
5-18 Plot of the Q over the tuning range, when the resonator is tuned down with a fixed
loop tuning circuit for various levels of coupling............................................................144
5-19 Circuit simulation of tuning range with fixed inductive loop along with a variable
tuning capacitor................................................................................................................145
5-20 Plot of tuning achieved with a fixed inductive loop and variable capacitors ..................146

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5-21 Plot of the Q over the tuning range as an HTS resonator is tuned using a fixed
inductive coupling loop and variable capacitors..............................................................146

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Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DEVELOPMENT OF HIGH-TEMPERATURE-SUPERCONDUCTING PROBE
TECHNOLOGY FOR NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
By
Vijaykumar Ramaswamy
May 2015
Chair: Arthur S. Edison
Major: Biomedical Engineering
Nuclear magnetic resonance (NMR) spectroscopy is a very powerful technique to study
molecular structure and dynamics because of the rich chemical information it can extract.
However, its inherent low sensitivity is the Achilles’ heel of NMR, especially when compared to
other spectroscopic methods for metabolomics applications. Development of high-sensitivity
detection technology is critical in improving the state-of-the-art. NMR probes based on High
Temperature Superconductors (HTS) offer extremely high sensitivity and are particularly
suitable for small-sample applications.
Novel double-resonance HTS coils have been developed that are suitable for detecting
two different nuclei. The advantage of these coils is the opportunity to optimize the sensitivity
for two channels in the same probe. The double-resonance coils achieve this by placing two
resonators on the same substrate. Isolation between these two resonators is achieved by making
the magnetic fields from the resonators orthogonal to each other. Electromagnetic simulation was
used in the design and optimization of superconducting resonators. Using these novel double-
resonance HTS coil designs, a 1.5-mm probe optimized for detection sensitivity of 1
H and 13
C
nuclei at 14.1 T is being developed. The performance of this probe is characterized with RF tests

15
as well as NMR tests, and the performance is compared to a 1.5-mm 13
C-optimized probe built
previously by our group. Based on RF tests, a 60% improvement in 1
H sensitivity and a 25%
drop in 13
C sensitivity are expected compared to the 13
C-optimized probe. The measurements in
NMR tests show a 45% improvement for 1
H channel, while a 50% drop in sensitivity is seen for
the 13
C channel. The lineshape achieved with this probe is slightly lower compared to that
achieved with other HTS based probes.
Finally, this project addresses the problem of mechanical unreliability associated with the
moveable loop coupling and tuning mechanism. A fixed inductive coupling loop along with a
variable capacitive network is used to achieve frequency tuning and impedance matching. A
discussion of the various loss mechanisms in these inductive loops offers an insight into novel
strategies for optimal loop design. Incorporation of superconducting inductive loop for tuning
and matching will not only improve the reliability of HTS probes, but also provide
improvements in sensitivity achieved with HTS probes.

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CHAPTER 1
GENERAL INTRODUCTION
Introduction to NMR Spectroscopy
Nuclear magnetic resonance (NMR) is a physical phenomenon that facilitates the
observation of specific quantum mechanical magnetic properties of atomic nuclei. NMR
spectroscopy is a very powerful technique for the determination of molecular structure and
dynamics. This power arises from the wealth of information that can be obtained by the precise
manipulation of the nuclear spins in a molecule [1]. Nuclei which have non-zero spin exhibit
nuclear magnetic resonance.
When placed in an external magnetic field, the nuclear spins align in one of several
energy levels. In the simple case of spin one-half nuclei, there are two states - either parallel (α)
or anti-parallel (β) to the static magnetic field. The NMR signal arises from the transition
between the parallel and antiparallel states. The ratio of the number of spins aligned parallel to
the magnetic field to the number of spins aligned anti-parallel to it at thermal equilibrium is
given by the Boltzmann equation.
𝑁 𝛼
𝑁 𝛽
= 𝑒
∆𝐸
𝑘 𝐵 𝑇 , (1-1)
where 𝑁𝛼 and 𝑁𝛽 are the number of spins aligned in α and β states respectively, ∆𝐸 is the
difference in energy between the two states, 𝑘 𝐵 is the Boltzmann constant, and 𝑇 is the
temperature in K. The NMR signal arises from the transition of spins between the two states, and
therefore depends on the difference in population. The difference in energy levels of the two
nuclei depends on the magnetic field strength and is given by

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∆𝐸 =
ℎ𝜔0
2𝜋
. (1-2)
where ℎ is the normalized Planck constant, and 𝜔0is the resonance frequency or Larmor
frequency.
𝜔0 = 𝛾𝐵0 , (1-3)
where B0 is the strength of the external magnetic field, γ is the gyromagnetic ratio and 𝜔0 is the
resonance frequency in rad/s. The gyromagnetic ratio is intrinsic to each isotope. The
gyromagnetic ratios of some common nuclei are given in Table 1-1. Some common biological
nuclei of interest are 1
H, 2
H, 13
C, 15
N, 17
O, 31
P.
The difference in energy levels, even for large values of B0, is extremely small compared
to the average thermal energy 𝑘 𝐵 𝑇. Thus, from to the Boltzmann equation, the spin excess in the
parallel state to the antiparallel state is very small. The inherent low sensitivity of NMR,
especially in comparison to other spectroscopic techniques, arises from this low equilibrium
polarization.
An NMR probe is at the heart of an NMR experiment. The probe applies a secondary
magnetic field B1 in which is perpendicular to the direction of B0. The B1 is a radio-frequency
(RF) field at the Larmor frequency of the nuclei to be detected. The B1 field tips the
magnetization in to the transverse plane. The behavior of the magnetization after the B1 field is a
precession at the Larmor frequency. The precessing magnetization creates a time-varying
magnetic field at the Larmor frequency. The field detected by the receiver coil, referred to as the
free induction decay (FID), is the magnetic resonance signal. In solution spectroscopy, the high-
resolution spectrum of the detected signal provides the wealth of information sought for from the
sample.

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Motivation for Cryogenic Microsample Probes
The theoretical NMR signal strength is proportional to the 7/4th
power of the polarizing
magnetic field [2], and increasing the magnetic field should, in principle, provide
correspondingly higher sensitivity. However, several factors including the magnetic field
dependence of relaxation and technical limitations of providing the necessary uniformly strong
radiofrequency (RF) fields often lead to lower gains in signal-to-noise ratio (SNR) than are
predicted theoretically. Moreover, extremely high magnetic fields are very expensive and can be
difficult to site and maintain. Magnets made from currently used superconducting materials have
an upper limit of about 24 T, although new superconducting materials are being developed that
may in the future substantially increase the upper limit.
Increasing the amount of sample in the experiment also improves the observed SNR of
the NMR experiment. However, the amount of sample available in biological and biomedical
studies is often limited, especially in areas such as natural products chemistry or eukaryotic
proteins, where it may only be possible to collect or produce a small quantity of material.
Moreover, many proteins are concentration-limited, precipitating when the concentration limit is
exceeded. Mass-limited and concentration-limited scenarios are common and require different
solutions for optimal NMR performance.
The use of various hyperpolarization techniques such as dynamic nuclear polarization is
becoming more widespread and practical. Dynamic nuclear polarization (DNP) is one attractive
method for significantly enhancing NMR sensitivity [3]. It is worth noting that optimal probe
design is orthogonal to hyperpolarization methods, and combining an optimal probe with
hyperpolarization can produce multiplicative benefits.
Improvement in RF probe technology is often the most cost-efficient means to achieve
better SNR in an NMR experiment. This involves efficient detection of the available signal in a

19
low-loss low-noise environment in order to maximize the signal. Neglecting sample losses, the
effect of the features of the probe on the signal-to-noise ratio can be written as [4]
𝑆𝑁𝑅 ∝ √
𝜂𝑄
𝑇𝑐+𝑇𝑎
. (1-4)
where, 𝜂, the filling factor of the coil, is a measure of how much of the total RF field energy is
within the sample volume, Q is the quality factor of the coil, and Tc is the physical temperature
of the coil and Ta is the noise temperature of the preamplifier. Thus, the sensitivity of an NMR
probe may be improved by a number of methods.
Small volume. Smaller diameter probes with correspondingly small sample volumes
improve the filling factors of the coils [4]. While there is a decrease in the overall sensitivity due
to less material, the mass-sensitivity (defined as sensitivity per unit mass of sample) increases by
approximately 1/d, where d is the diameter of the sample volume.
Probe temperature. The sources of noise in a spectrometer are Johnson noise arising
from the coils, added noise from the preamplifier stage and from the sample under consideration.
Cooling the coils and preamplifiers down to cryogenic temperatures reduces the thermal noise in
the RF electronics substantially [5]. Biological samples usually have specific temperature
requirements and cannot generally be cooled.
Quality factor. The quality factor or Q of a resonant coil is the factor representing the
ratio of the total energy stored to the energy lost per cycle. Higher coil Q therefore leads to
efficient conduction of the induced signal in the receiver system. Matched Q of room-
temperature coils is not more than a few hundred. Cold normal metal coils can have Q up to
1,000. Coils made from high-temperature superconductors have Q in the range of 5,000-10,000.
Thus superconducting coils reduce loss is the coil to provide better sensitivity [4].

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Project Overview
The focus of this work is the development of high sensitivity NMR probes based on high-
temperature-superconductors (HTS) optimized for microsample applications. As mentioned
above, the small sample size has the advantage of an improved filling factor. Further, a
microsample makes it an ideal volume for many samples which may only be available in limited
quantities. This work on probe technology development uses a 14.1 T magnetic field strength,
since it is a commonly available high-field magnet in analytical laboratories.
Chapter 2 surveys the technology development and scientific impact of cryogenic probes
based on HTS materials. The specific focus of this work is to improve upon the design of HTS-
based NMR probes to maximize detection sensitivity on two channels simultaneously, while
improving their reliability and other performance parameters.
Firstly, the project develops novel coil designs for a dual-sensitive NMR probe for
optimized detection of 1
H and 13
C nuclei. Chapter 3 deals specifically with design considerations
in the development of HTS resonators that are used as detection coils in HTS probes. Double-
tuned resonators have been developed to optimize detection sensitivity of two channels in the
same probe. Chapter 4 details the construction of a dual-sensitive probe developed using these
double-tuned resonators. RF test results as well as NMR performance of the probe are presented.
With a 1.5-mm sample diameter and 20-μL active sample volume, this probe will be suitable for
analysis of mass-limited metabolites and natural products.
Further, the project aims to improve the design of HTS probes, which will impact the
manufacturability and reliability of these probes. A critical point-of-failure in HTS probe
technology is the coupling and tuning mechanism, which has had virtually no change in the state-
of-the-art in more than a decade and a half. In Chapter 5, strategies for novel coupling and tuning

21
of HTS resonators are discussed. Fixed coupling loops are used along with variable capacitor
network to achieve reliable tuning and matching.
The overarching intention of this work is to develop HTS technology-based NMR probes
for routine use. To this end, probes with larger sample volume that are more reliable are desired.
Both the double-resonance coil designs as well as novel tuning mechanism are aimed at enabling
this goal.

22
Table 1-1: Gyromanetic ratios of common NMR nuclei
Nucleus
Gyromagnetic ratio
𝛾 (rad/s/T)
Gyromagnetic ratio
𝛾 (MHz/T)
Natural abundance
(%)
1
H 267.5123 42.5759 99.98
2
H 41.0648 6.5357 0.02
7
Li 103.9679 16.5470 92.57
9
Be 37.5923 5.9830 100.00
10
B 28.7456 4.5750 18.83
11
B 85.8283 13.6600 81.17
13
C 67.2615 10.7050 1.11
14
N 19.3271 3.0760 99.64
15
N 27.1119 4.3150 0.37
17
O 36.2665 5.7720 0.04
19
F 251.6730 40.0550 100.00
23
Na 70.7612 11.2620 100.00
25
Mg 16.3740 2.6060 10.15
27
Al 69.7057 11.0940 100.00
29
Si 53.1432 8.4580 4.70
31
P 108.2970 17.2360 100.00
33
S 20.5209 3.2660 0.74
35
Cl 26.2134 4.1720 75.40
37
Cl 21.8152 3.4720 24.60
39
K 12.4847 1.9870 93.08
79
Br 67.0227 10.6670 50.57
81
Br 72.2503 11.4990 49.43

23
CHAPTER 2
TECHNOLOGY AND IMPACT OF HTS PROBES
This chapter provides an overview of the technology and impact of superconducting
cryogenic probes [6][7].1
Technology of HTS Probes
Refrigeration and Vacuum Design
Cooled NMR probes improve sensitivity by reducing both RF loss and decreasing
thermal noise. However, proximity to the RF coil or resonator, typically formulated as filling
factor, is also an important element in NMR sensitivity. Good cryostat design is crucial to the
success of cryogenic NMR probes, since is it necessary to minimize the gap between the RF
coils and the sample, and yet maintain good temperature stability for both. Since the RF
magnetic field must penetrate the cryostat efficiently, it is not possible to rely on use of metallic
radiation shields. Other important considerations are the length of time required to cool the
cryostat and the amount of cryogen that is consumed (for an open cycle system, which was
originally used).
Initial designs
The earliest implementation of a cryogenically cooled NMR probe reported by Styles et
al. in 1984 is considered a landmark development in NMR instrumentation [2]. This 13
C
1
Parts of this chapter are reprinted from the Encyclopedia of Magnetic Resonance, V.
Ramaswamy, J.W. Hooker, R.S. Withers, R.E. Nast, A.S. Edison, W.W. Brey, Microsample
Cryogenic Probes: Technology and Applications, Copyright 2013 with permission from John
Wiley & Sons, Ltd. and from Journal of Magnetic Resonance, 235, V. Ramaswamy, J.W.
Hooker, R.S. Withers, R.E. Nast, W.W. Brey, A.S. Edison, Development of a 13
C-optimized 1.5-
mm high temperature superconducting NMR probe, 58–65, Copyright 2013 with permission
from Elsevier Limited.

24
detection probe operated in a 4.3 T, 83-mm bore magnet. The 13
C receiver coil as shown in
Figure 2-1 was wound from hollow silver tubing, through which a stream of liquid helium was
pumped. The stream also cooled the inner conductor of a transmission line which connected the
receiver coil to adjustable tune and match capacitors. The transmission line served to
mechanically support the coil as well as to partly transform the coil impedance for optimal noise
performance of the preamplifier. A reentrant glass cap at the top of the probe allowed space for
the insertion of a room temperature 10-mm sample tube. The vacuum space between the receiver
coil and the wall of the glass cap provided thermal isolation between the coil and sample. The
silver tubing was also polished to reduce radiative heat transfer to the sample. To reduce its noise
figure, the 13
C preamplifier was immersed in liquid helium at the base of the cryostat. The 13
C
transmission and 1
H decoupling coils and sample spinner were not cooled but were part of the
room temperature assembly. The probe included a nitrogen-cooled radiation shield to reduce
consumption of liquid helium. A reservoir of liquid helium was held in the main part of the
cryostat.
This initial system was not practical for routine use but the authors later reported an
improved continuous flow system which did not require the liquid helium bath [8]. This second
version achieved an operating temperature of 15 K by means of a stream of liquid helium from
an external cryostat with a flow rate of 500 mL/hr. The authors reported that the system could
provide stable NMR results within an hour of starting the cool-down procedure. Efficiency was
improved by using return gas to cool the radiation shield and the transfer line. The probe fit into
a standard Bruker 360 MHz wide bore magnet. A drawback of the second system was that the
preamplifier was located outside the main cryostat and cooled by liquid nitrogen. Room
temperature cables between the probe and preamplifier reduced the sensitivity of the probe, but

25
still the authors reported 13
C sensitivity 3.9-x better than Bruker specified for a similar room
temperature probe.
The first use of superconducting coils for magnetic resonance applications was not for
NMR spectroscopy but for NMR microscopy. Black et al. in 1993 reported the development of
an HTS based probe [9]. Unlike the Styles system, vacuum gaps were maintained between the
walls of a quartz Dewar. This allowed the single 18-mm diameter HTS resonator to be cooled to
about 10 K by placing it in directly in a cold helium gas stream. The cold helium space was
surrounded by a vacuum gap, which was in turn surrounded by an annular vessel filled with cold
nitrogen gas to form a thermal shield. Another vacuum gap separated the nitrogen shield from
the outer vacuum wall. The sample was placed within a 10-mm diameter reentrant portion of the
cryostat and warmed by a stream of nitrogen gas. The 3-mm thickness of the double-walled
Dewar’s vacuum gap limited the proximity of the coil to the sample to about 5 mm, degrading
the filling factor and thus the gain in sensitivity achieved using superconducting coils.
Nevertheless, an improvement in SNR of a factor of ~10 was observed when compared to a
room temperature, 4-mm diameter solenoid. The authors noted that, because of the high quality
factor of the resonator, it was important to keep its temperature constant to maintain tuning.
Dipping probes
For testing, HTS coils are generally cooled with the use of a dipping probe such as shown
in Figure 2-2. This type of device secures the coil substrates as they are lowered into a Dewar for
the purpose of testing. The dipping probe has a number of design goals. The probe should
provide an RF shield to eliminate radiation loss. It also must provide a flexible and efficient
method to couple signal to and from the coil. Finally, the probe’s normal metal elements should
contribute minimal RF loss. While the dipping probe can be used with liquid nitrogen for HTS
materials with a transition temperature above 77 K, the dielectric constant of liquid nitrogen will

26
tend to shift the measured frequency. Additionally, bubbles generated in liquid nitrogen may lead
to an unstable resonance. Therefore, liquid helium is typically used, which has a very low
dielectric constant and so tends not to affect the resonance frequency. Another advantage of
liquid is that (unlike helium gas) it resists ionization when significant voltages are developed
across elements in the coils. Helium gas has a low breakdown electric field and so short transmit
pulses could probably not be sustained. To test self-resonant coils, it is convenient to couple the
RF energy inductively through small loops formed at the ends of coaxial cables. It is best to use
fairly small gauge wire for these loops, since they must be located fairly close to the HTS
resonators and so can be the source of eddy current loss. The main support tube and the coaxial
cables should be made from an alloy such as stainless steel, which has low thermal conductivity
to reduce heat flow from the external environment into the Dewar. The probe head, which holds
the device during testing, should have low thermal mass and high thermal conductivity so that it
will come to equilibrium with the cryogen quickly. There should also be a provision to ventilate
the coil chamber with dry gas while the probe warms, to avoid condensing water on the oxide
resonator. The mechanical robustness of the probe is also important. Should it become frozen in
place, it should be able to withstand some level of stress as it is freed without components
breaking or falling off into the Dewar.
Closed-cycle cryocoolers
All of the methods discussed above can be classified as “open-cycle,” relying on the
periodic addition of cryogen to keep the probe at operating temperature. It is naturally much
more convenient to utilize a “closed-cycle” system based on a refrigerator which operates
indefinitely on a single charge of cryogen. Such a system based on the Gifford-McMahon (GM)
refrigerator was demonstrated in 1996 by Kotsubo and Nast [10]. Current cryogenic systems for
commercial probes are similar to this design, shown in Figure 2-3. The primary component of

27
the GM-based refrigeration system is a compressor, used to pressurize room-temperature helium
gas. The compression heat is best removed with water or air near room temperature. The
compressed gas flows to and cools down within the GM coldhead upon expansion controlled by
a rotary valve and displacer piston operated in sync. Advantageously, in GM cryocoolers, the
compressor need not be operated in sync with the displacer. Further, the compressor may be sited
relatively far away from the coldhead.
A secondary flow loop, cooled by thermal contact to the thermal interface surfaces of the
GM coldhead, circulates a small amount of gas from the compressor. Typically, a GM coldhead
with two-stage cooling is employed. Only one stage is shown in Figure 2-3 for simplicity. The
gas in the secondary loop is precooled by counterflow heat exchangers using the returning cold
gas before encountering the coldhead. These counterflow heat exchangers included in the
secondary loop greatly reduce the thermal load requirements of the cryogenic system. The
secondary flow loop gas is contained in small capillary tubing at a pressure of around 200 psi.
The cooled gas in the secondary loop is used to cool a coldhead in the probe on which the
HTS coils are mounted. A single coldhead machined from copper provides a mounting surface
for the entire set of coils required in the probe. Sapphire is an ideal substrate for the HTS
resonators, due to its high thermal conductivity at cryogenic temperatures. It is convenient to
solder the superconducting coils to small metal mounting feet which can then be attached to the
coldhead with machine screws. This approach avoids thermally induced pressure of clamps,
which may tend to crack the brittle sapphire substrates. Provisions are typically made to allow
for coupling and tuning loops to penetrate through the coldhead as shown in Figure 2-4. Because
the coils and coldhead are in a vacuum, only a single-walled dielectric center tube is needed to
provide thermal isolation between the coils and the room temperature NMR sample. In

28
distinction to the reentrant cryostats used in earlier designs, the configuration shown in
Figure 2-4 allows for the flow of heated air across the sample in order to compensate for
radiative cooling and to regulate the sample temperature precisely.
A salient advantage of this system is that the coils are cooled by conduction to the cold
head and are not in direct contact with the cryogenic gas. This facilitates the use of a single
walled Dewar, instead of the double walled Dewar used by Black [9]. As a result, the coils may
now be placed closer to the sample, thereby improving the filling factor to gain detection
sensitivity. An additional advantage of this cooling system is the use of high pressure helium in
the cold circuit. This allows for cold helium flow over a long distance through small capillary
tubes which can be performed using vacuum insulated transfer line having very low thermal loss.
The overarching advantages of this system are convenience, reliability and cost-effectiveness,
which have enabled its commercial availability and current widespread use.
HTS Probe Technology
The essential design element of an HTS cryogenic NMR probe is a pair of self-resonant
superconductive loops or coils. Each coil is patterned and diced from a wafer of superconductive
oxide (usually YBCO) which has been epitaxially coated onto a dielectric substrate. The coils are
placed on both sides of the sample as shown in Figure 2-4 to provide a uniform B1 field
perpendicular to the plane of the coils and through the sample. A sample tube at room
temperature is placed in the center of the probe within a vacuum tube that provides thermal
isolation from the coils, which are maintained at cryogenic temperatures near 20 K. Additionally,
heated nitrogen gas is flowed over the sample tube to counter radiant heat loss. Orthogonal pairs
can be nested to provide channels for additional isotopes. Figure 2-5 shows the schematic of a
typical triple-resonance NMR probe in cross-section, with the coil pair closest to the sample,
yellow in Figure 2-5, providing the best RF performance. The coils of the various nuclei are

29
placed around the sample in the order of priority of detection sensitivity, with outer coils
primarily used for decoupling or lock.
Substrates and film-growth
The availability of high quality HTS films is crucial to their use in NMR probes. YBCO
and other oxide superconductors are highly anisotropic and conduct well only in the plane
perpendicular to the material’s c-axis. In a “bulk” material, such as wire used in NMR magnets,
the grains are randomly oriented and there is significant ohmic loss associated with RF current.
There may also be additional loss associated with the stabilizing conductor needed for quench
protection in magnet applications. In contrast, the HTS materials used for NMR resonators are
thin films of HTS material coated in an epitaxial layer onto dielectric substrates which match the
lattice constant and symmetry of the HTS crystal, so that the c-axis of the superconductive film
is perpendicular to the substrate surface. Although the superconducting layer is typically < 1µm
in thickness, its superconducting properties are those of a single crystal and so it is a nearly ideal
material for RF resonators.
High-quality films have been grown on a number of crystalline ceramic substrates. Early
success was achieved with lanthanum aluminate (LaAlO3), the substrate for the Black et al.
microscopy probe [9]. However, LaAlO3 has a number of disadvantages, including brittleness,
unstable crystal structure, and moderate RF loss. MgO is an excellent material from the
perspective of film growth, as its thermal expansion coefficient is close to YBCO, allowing for
growth of film up to about 3 µm without cracking. However, MgO is brittle and hygroscopic.
Sapphire is a much tougher and more stable material, and with the addition of a thin buffer layer,
allows for the growth of high-quality YBCO films up to about 350 nm. Sapphire can be obtained
in 4 different cuts (A-, C-, M-, and R-plane), depending on how the wafer is sliced relative to the
crystal lattice. R-plane sapphire with a CeO2 buffer layer is typically used in microwave

30
applications such as NMR probes because of the high quality of film which can be grown. The
fact that sapphire has an anisotropic dielectric constant that varies between about 9.4 and 11 does
not reduce its performance; but does make resonance frequency more difficult to predict
accurately. Additional advantages of sapphire include very low RF loss and very high thermal
conductivity at low temperatures [11]. Another advantage of sapphire is that it is only slightly
diamagnetic. Effects of the susceptibility of the dielectric substrate are mitigated by placing the
boundaries of the sapphire substrate outside the active region of the NMR experiment.
Useful YBCO films for NMR must satisfy a number of requirements. The film must have
a precisely controlled stoichiometry to provide a high critical current needed for transmit pulses
and to maintain a low surface resistance when operated in high magnetic fields. Because the film
will be patterned into a complex self-resonant structure, there must be no defects that would
affect the resonance frequency or current distribution in the patterned device. The film must
maintain these characteristics over dimensions of 15 mm. Such films are grown employing
reactive co-evaporation on wafers up to 4 in. and even larger [12]. These deposition systems
utilize a specialized substrate heater developed specifically for HTS film growth in which a
rotating disk holder physically separates the deposition zone from the reactive high oxygen
pressure zone in a surrounding high vacuum background [13]. Both single- and double-sided
films have been produced in this manner [14].
Microwave surface resistance
The intrinsic Q of the resonator is determined by the resistance of the material.
Superconductors exhibit zero resistance only at zero frequency (𝜔 = 0), but exhibit a finite
resistance at microwave frequencies. However, at the frequencies of interest in the NMR range,
surface resistance (Rs) of YBCO is several orders of magnitude lower compared to copper.
Figure 2-6 shows the experimentally measured surface resistance of superconductors and copper

31
as a function of frequency [15]. The crossover point for copper and YBCO surface resistance
occurs at several hundred GHz.
The microwave surface resistance of YBCO depends strongly on the quality of the
superconducting material, but also on a number of external factors. Nakagawa et al. have
investigated the dependence of Rs on temperature, static magnetic field and film thickness using
YBCO films thinner than the penetration depth λL [16]. A dielectric resonator method is well
known to measure the surface resistivity of low loss measurements [17]. Using this method,
Honma et al. studied the dependence of surface resistivity of YBCO in high dc magnetic fields
[18]. Figure 2-7 shows the dc magnetic field dependence of Rs for various film thicknesses when
the magnetic field is applied parallel to the c-axis of the YBCO. Further there is a strong
dependence of the direction of applied magnetic field in relation to the YBCO crystal [19]. As
shown in Figure 2-8, the surface resistance increases rapidly when the magnetic field is applied
parallel to the c-axis of the YBCO, however the effect is much smaller when the field is normal
to the c-axis. In the construction of NMR probes, the YBCO coils are placed with the c-axis
normal to the static magnetic field.
HTS Resonators
There are several types of HTS resonators that will be discussed below, but they all have
a number of characteristics in common. First, because of the highly anisotropic nature of the
YBCO crystal structure, all types must be operated with the substrate parallel to the strong B0
polarizing field of the NMR magnet. Persistent induced currents will then be limited to the
greatly reduced critical current density parallel to the c-axis of YBCO. If the coils are tilted with
respect to B0, two undesired effects will occur. First, persistent currents in the coil plane will
spoil the homogeneity of the magnet and broaden the NMR line. Second, the RF surface
resistance of the material will rise and the resonator’s quality factor will be depressed.

32
Fortunately in NMR, the coils can be aligned parallel to the polarizing B0 magnetic field,
allowing the coils to retain their high Q’s. However, HTS coils are not suitable for designs that
are tilted, for example at the magic angle.
The requirements on the homogeneity of the static polarizing magnetic field are
extremely stringent. An acceptable limit of homogeneity is generally 1 part per billion (ppb),
since a less homogenous polarizing field will produce NMR spectra with poor lineshapes. Even
with the resonator parallel to the magnetic field, the YBCO can distort the homogeneity of B0 in
the sample region. If the conductors are wide, then circulating currents are possible which
adversely affect the homogeneity. Fortunately, the effect can be largely mitigated by slitting the
coil into narrow wires or fingerlets parallel to direction of the current as shown in Figure 2-9,
which avoids any closed loops of YBCO that could support a persistent current [20].
Helmholtz pair resonators
In order to generate a uniform magnetic field in the sample region, HTS resonators are
used in a pair configuration similar to Helmholtz coil arrangement. When two resonators of the
same frequency, are brought close to each other, neither one will continue to resonate at its
original frequency. Two separate modes will then be seen, one above and one below the original
frequency. This counterintuitive phenomenon is a result of their mutual inductance, and can be
easily understood using a lumped circuit model. Shown in Figure 2-10 (A) are two resonators,
each modeled by a series LC resonator, such that resonance frequencies of each resonator
independently occur at
𝜔1 =
1
√ 𝐿1 𝐶1
, and (2-1)
𝜔2 =
1
√ 𝐿2 𝐶2
. (2-2)
The mutual inductance M between the two resonators is defined as

33
𝑀 = 𝑘√ 𝐿1 𝐿2 . (2-3)
where the coupling coefficient k varies between 0 to 1 depending on the geometry and proximity
of the resonators. The same circuit using the T-equivalence for the mutually coupled inductors is
shown in Figure 2-10 (B) and (C). The two resonant modes are caused due to the difference in
current flow, where the current in both the loops is in the same sense in (B), while the current is
in the opposing sense in each resonator in (C).
Consider the case when the current in both the resonators is in the same sense as shown
in Figure 2-10 B. The closed loop equation for one of the resonators can be written as:
𝐼1
𝑗𝜔𝐶1
+ 𝐼1 𝑗𝜔(𝐿1 − 𝑀) + 𝑗𝜔𝑀(𝐼1 + 𝐼2) = 0. (2-4)
1
𝑗𝜔𝐶1
+ 𝑗𝜔 (𝐿1 + 𝑀
𝐼2
𝐼1
) = 0. (2-5)
Equivalently, the loop equation for the resonator 2 can be written as
1
𝑗𝜔𝐶2
+ 𝑗𝜔 (𝐿2 + 𝑀
𝐼1
𝐼2
) = 0. (2-6)
The resonance condition occurs at
𝜔 =
1
√(𝐿1+𝑀
𝐼2
𝐼1
)𝐶1
=
1
√(𝐿2+𝑀
𝐼1
𝐼2
)𝐶2
. (2-7)
When the current in the inductors is in the opposite sense, as shown in Figure 2-10C, the
closed loop equation for each of the resonators can be written as
𝐼1
𝑗𝜔𝐶
+ 𝐼1 𝑗𝜔(𝐿1 − 𝑀) + 𝑗𝜔𝑀(𝐼1 − 𝐼2) = 0 (2-8)
1
𝑗𝜔𝐶1
+ 𝑗𝜔 (𝐿1 − 𝑀
𝐼2
𝐼1
) = 0 (2-9)
Equivalently, the loop equation for the resonator 2 can be written as
1
𝑗𝜔𝐶2
+ 𝑗𝜔 (𝐿2 − 𝑀
𝐼1
𝐼2
) = 0 (2-10)
The resonance condition occurs at

34
𝜔 =
1
√(𝐿1−𝑀
𝐼2
𝐼1
)𝐶1
=
1
√(𝐿2−𝑀
𝐼1
𝐼2
)𝐶2
. (2-11)
As can be seen in Equations 2-7 and 2-11, two distinct resonance frequencies result
depending on the direction of the current in the resonators.
If the two resonance frequencies of the two resonators are significantly different, an
imbalance in the current may result, thereby causing the magnetic field to be significantly
weaker and less homogeneous. Typically, the two resonators are made identical in order to avoid
any imbalance in the currents, such that 𝐿1 = 𝐿2 = 𝐿, 𝐶1 = 𝐶2 = 𝐶 and |𝐼1| = |𝐼2| = 𝐼. Further,
𝜔1 = 𝜔2 = 𝜔0 =
1
√ 𝐿𝐶
(2-12)
𝑀 = 𝑘𝐿 (2-13)
The two resonance frequencies then occur at
𝜔 =
𝜔 𝑜
√(1±𝑘)
(2-14)
The difference in frequency between the upper and lower mode is determined by the
magnitude of the mutual inductance, and the spectrum of the coil pair will show two modes
around the individual coil resonance. Electromagnetic simulation from a pair of resonators is
illustrated in Figure 2-11. The current in both coils flowing in the same sense results in the lower
resonance frequency as shown in A. Currents flowing with the opposite sense in each coil results
in the higher resonance frequency of the pair as shown in B. The lower mode is responsible for
generating the uniform magnetic field used in NMR experiments as shown in C. The upper mode
generates a magnetic field as shown in D with a null in the sample region and is unusable for
NMR.

35
Racetrack resonator
A very commonly used resonator in HTS probes is the racetrack. The principal advantage
of this design is the reduction in the fringing electric field from the coil penetrating the sample
region [21], and is suitable as a detection coil for high frequency channels such as 1
H. Since the
electric field is contained very close to the coil, the racetrack can be operated in close proximity
to the sample region. The electric field of the coil is contained within its capacitive elements
which are distributed into a number of capacitors in series. The characteristic design feature of
the resulting ‘racetrack’ coil design is then the number of capacitors.
The racetrack coil typically has either 4 or 2 interdigital capacitors which are distributed
along the length of the coil and are arranged in series with each other. A 4-capacitor racetrack
along with its lumped-element equivalent is shown in Figure 2-12. In an N-capacitor design, the
capacitance per unit length is made N2
times the capacitance of a single-capacitor design for the
same frequency. Due of this, the voltage on the coil is lower by a factor of N2
, thus producing a
much smaller electric field. The large interdigital capacitance required is achieved by the use of
fine feature size for the conducting fingers and gaps between the fingers. Therefore, the upper
limit on the number of capacitors that may be used in a coil is determined by the availability of
high-quality defect-free film deposition and the resolution of the photolithographic process.
Another constraint is the minimum gap width required between the digits of the capacitors to
avoid arcing between the fingers.
A racetrack coil is not suitable for lower resonance frequency because of the high
interdigital capacitance required. A 50% periodicity of finger to gap-width ratio maximizes the
capacitance [22]. However, a periodicity of finger to gap-width ratio of approximately 75% is
generally employed in order to accommodate the high current carrying capacity needed for short

36
B1 pulse lengths. At the coil dimensions of the 13
C coils for 1.5-mm probes, racetrack coils
would only be suitable for approximately 250 MHz and higher.
Coil designs have been described where the capacitive regions are separated from the
current carrying parts of the racetrack [23]. The idea is that the capacitive region can follow the
50% finger-to-gap width ration required to maximize the capacitance, whereas the current
carrying regions will require the parallel slits only in order to avoid the magnetization of
superconductors. Appropriate use of this idea may enable a racetrack with low enough
frequency.
Spiral resonator
Due to the unsuitability of the racetrack at low frequencies, the commonly used resonator
for lower frequency channels is the spiral. The schematic of a spiral is shown in Figure 2-13 A.
Its relatively long, continuous conductor allows it to produce lower frequencies than the
racetrack. The current distribution on a spiral resonator resembles a vibrating string, with nodes
on each end as the boundary condition. At its fundamental resonance frequency, the current
distribution of a spiral resonator has nulls only at the ends and a single maximum near the
longitudinal center of the conductor.
Spirals also produce higher-order resonances, with additional current nulls along the
length of the conductor, and have a number of current maxima equaling the mode number [24].
Simulated current distribution showing the resonance behavior for the first three modes is shown
in Figure 2-13.
Due to the interaction of the adjacent turns, the resonance behavior of spirals is not
harmonic. In other words, the nth
mode is not n times the fundamental frequency. Even though
the resonant mode spectrum of a spiral is still linear, it is observed that both the slope and y-
intercept of the spiral vary from those of a harmonic resonator. This non-harmonic behavior of

37
spirals is demonstrated in Figure 2-13 B. An empirical expression has been formulated recently
to accurately predict the fundamental and higher-order resonance frequencies of planar
Archimedean spiral resonators in a uniform medium [25]. The deviation from the harmonic
spectrum relates most closely to the ratio of inner to outer radii. D is defined as a factor of
deviation from harmonic, which can be calculated as
𝐷 = − ((0.29 + 0.043𝐹) (
𝑟 𝑖
𝑟 𝑜
) + 0.22) ((𝐹 − 0.5) (2.65 (
𝑃
𝑟 𝑜
+ 0.03)) + 1). (2-17)
where, ri, ro are the inner and outer radii, P is the pitch of the Archimedean spiral. The resonance
frequency is calculated as
𝑓𝑛 =
𝑣
2𝐿
(0.24𝑁−0.46
+ 0.95)(𝑛 + 𝐷), (2-18)
where, fn is the nth
mode, v is the velocity of the electromagnetic waves in the surrounding
uniform medium, N is the number of turns of the spiral, and L is the length of the spiral. It will be
useful to extend this empirical approach to model resonance behavior of oblong shaped
resonators on sapphire dielectric substrates that are common in NMR applications. The
advantage of this non-harmonic behavior of spirals is that the higher-order modes can be moved
away from the resonance frequency of another channel in the probe using simple design steps.
The disadvantage of this simple spiral resonator design is the relatively large stray
electric field produced by the coil, which fringes into the sample region. This makes the spiral
susceptible to electrical loading by the sample, and therefore, unsuitable for high sensitivity
detection. Thus, spiral resonators are traditionally used only on decoupling or lock channels,
which are relatively far away from the sample.

38
Faraday-shielded spirals
Spirals can be tuned to low frequencies, but produce a large fringing electric field.
Withers described the use of electric field shields with spiral coil designs in order to approach
this problem [26]. The shield assembly consists of a series of HTS strips placed directly across
from the entire coil windings, preferably on the other side of the substrate. The strips are oriented
at right angles to the windings as shown in Figure 2-14. The Faraday strips reduce the
conservative portion of the electric field. They have negligible effect on the RF magnetic field.
Counterwound spirals
Another approach to reduce the electric field involves two spirals counter-wound on the
opposite sides of the substrate [27]. Counterwound spirals were originally introduced as MRI
coils to achieve lower frequencies than would be possible with just the single spiral [28]. The
counterwound design utilizes both sides of a sapphire substrate, with spirals on either side of the
substrate having opposite handedness when viewed from the same remote point. The resonance
mode occurs with the current in both the spirals flowing in the same sense (clockwise or counter-
clockwise), thus developing opposite voltages across both spirals. It is observed that the
resonance frequency of the counterwound pair is lower than would be achieved with only the
effect of mutual inductance between the two spirals. The winding of the spirals in opposing
directions results in capacitive coupling between the two spirals, which reduces the resonance
frequency further. This capacitive coupling helps the counterwound spiral contain most of the
electric field within the substrate between the two spirals, thereby reducing the electric field in
the sample region. It is important to note that the counterwound spirals are used in NMR probes
as a ‘pair of pairs’ such as shown in Figure 2-15.

39
Impact of HTS Probes
1
H-optimized HTS probes
Brey, et al. previously reported a 1-mm HTS probe with 1
H, 2
H, 13
C, and 15
N channels for
spectroscopy at 600 MHz based on Bruker Cryoprobe components [29]. The orthogonal coil
nesting arrangement used in this probe is shown in Figure 2-16. With a 7.5-µL sample volume,
the 1-mm probe demonstrated a record setting mass-sensitivity on the 1
H channel. The
applications of this probe include introduction of single-animal extraction analysis [30] and
analysis of previously unanalyzable fractions of marine natural products [31].
Bruker Biospin has since commercialized a 1.7-mm triple resonance probe based on HTS
technology. With a 30 µL sample volume, the MicroCryoProbeTM
claims the highest
commercially available 1
H mass-sensitivity [32]. The work of Hilton, et al. demonstrated the
performance and limits of detection of this probe [33]. The authors noted that with this probe,
just a 1 mg sample is sufficient to determine the full structure and stereochemistry of strychnine,
a compound that originally took 150 years to fully characterize.
13
C-optimized HTS probes
In contrast to 1
H detection, carbon detection in NMR has been much less common
because of relatively low sensitivity and only 1.1% natural abundance of the NMR active 13
C
isotope. However, 13
C detection has several advantages over 1
H detection for biomolecular
studies. First, whereas the diamagnetic chemical shift range for 1
H is only about 12 ppm, for 13
C
it is over 200 ppm, providing much greater chemical shift dispersion and less overlap. Second,
for compounds at natural abundance, with 1
H decoupling, 13
C resonances are narrow singlets, in
contrast to the rather complicated multiplet patterns seen in 1
H spectra. Third, biological
molecules are based predominantly on carbon scaffolds [34], and correlations between 13
C atoms
provide much more direct information for small molecule structure elucidation than the many

40
combinations of 1
H-based correlations that are more commonly used. Finally, many
macromolecular studies rely on partial deuteration to remove the line-broadening influences of
protons, and in this situation direct 13
C detection provides the only way to detect a signal since
the protons are not there [35].
Even with all of the advantages that direct 13
C detection provides, it remains rarely used
in biomolecular studies because of its low sensitivity at natural abundance. Isotopic labeling may
provide higher abundance, but can be too expensive for some types of samples or impossible
with organisms that cannot be cultured.
It is well known that RF sample losses limit the sensitivity gain which can be achieved
with cryogenic probe [36]. We note that RF loss increases strongly with frequency, so species
such as 13
C with lower gyromagnetic ratio have greater potential for sensitivity improvement
than 1
H. Sample loading scales as the 4th
power of sample diameter and so should be minimal
with the 1.5-mm samples [37].
A 5-mm 13
C-optimized probe using HTS coils was offered by Varian/Agilent under the
trade name XSens owing to the sensitivity of the directly detected 13
C nuclei [38]. Being the
most sensitive probe for 13
C detected experiments, this probe had 10x the sensitivity of a room-
temperature broadband probe, offering a 100-fold reduction in acquisition time. Scientific
applications on this probe include the study of natural products [39][40][41][42], polymers [43]
and synthetic chemistry [44][45].
Our group has recently designed a 13
C-optimized 1.5-mm triple resonance probe using
HTS coils [7]. The coil nesting arrangement is shown in cross section in Figure 2-17. The 13
C
coils are placed closest to the sample for maximizing the sensitivity of this channel. The 13
C
mass-sensitivity of this probe is twice that of the XSens probe, enabling 13
C based metabolomics

41
and natural products studies. Figure 2-18 shows spectra obtained from metabolic mixture using
this probe. The advantage of a wider chemical shift axis in a 13
C spectrum is useful to analyze
metabolomics. Figure 2-19 shows an INADEQUATE spectrum on 1.1 mg of histidine was
collected in 48 hours, which would have taken nearly 2 weeks on any other probe to obtain the
same SNR. This spectrum demonstrates the feasibility of recording the direct 13
C-13
C
correlations in a natural product type sample. Metabolic analysis with natural abundance 13
C
spectra collected using this probe have reported improved metabolite identification and
separation of biologically distinct groups [46].
Limitations of HTS Probes
HTS probes with remarkable gains in sensitivity have been reported. However, a few
unresolved issues including manufacturability and unsatisfactory field homogeneity inhibit the
widespread acceptance of this technology. Some of the barriers to this technology may be
summarized as follows:
Sensitivity. Due to the high quality HTS thin films available, HTS probes achieve
exceptional Q-values and therefore significant gains in sensitivity. However, due to the planar
fabrication limitation, the geometric filling factor around the sample is less than optimal. A
triple-resonance HTS probe with a 2
H lock is accomplished by orthogonal nesting of four pairs
of HTS resonators. Hence, the detection sensitivity of only one channel may be optimized in an
HTS probe. Further, the small sample volume limits the sensitivity improvements to only mass-
sensitivity, and not the overall sensitivity, as is desirable for concentration-limited samples.
Magnetic field homogeneity. Solution-state NMR with high spectral resolution using
small sample volumes places a stringent requirement on static magnetic field homogeneity of
1 ppb or less. HTS materials are strongly diamagnetic, and are thought to significantly disturb B0
homogeneity when placed close to the sample, resulting in broadening of spectral lines. The

42
difficulty, or in some cases inability, to achieve satisfactory narrow lineshape using HTS probes
continues to remain the most significant barrier to this technology. In the case of aqueous
solvents, this effect is further aggravated due to incomplete water suppression.
Moveable Loops. Tuning and matching achieved using moveable wire loops are
convenient to build and adjust. However, moveable parts present some challenges including
vibration and mechanical unreliability. The RF loss in the moveable loops changes when their
position is changed, and consequently the Q of the probe changes as tuning is adjusted. Since the
position of the loops is not precisely known at all times, it is not possible to model them in
simulation. The movement of inductive loops within the probe has also been identified as
adversely affecting magnetic field homogeneity, requiring frequent shimming. Since the tuning
mechanism is not compatible with that used in normal-metal cryogenic probes, it is difficult to
incorporate HTS coils into more conventional probes.

43
Table 2-1. Loss tangents of various substrates reported in the Theva datasheet [11]
Substrate Maximum size Buffer layer εr
tan δ
(1GHz,
77K)
Maximum
film
thickness
LaAlO3 3” CeO2 23.6 10
-5
1.0 μm
MgO 3” or 70x70 mm
2
--- 9.7 2×10
-6
> 3 μm
YSZ
(ZrO2:Y) 100 mm
Y2O3 or
CeO2 27 10
-3
1.5 μm
Sapphire 200 mm CeO2 11.6/9.4 < 10
-6
350nm
SrTiO3 1” CeO2 2000 10
-3
1.0 μm
NdGaO3 2” CeO2 23 3×10
-4
1.0μm
YAlO3 2” CeO2 15.5 2×10
-6
< 500 nm
LSAT 2” CeO2 22.7 2×10
-4
1.0μm
Figure 2-1. Cryostat portion of cryogenic probe designed by Styles et al [5]. The receiver coil
was constructed from a hollow silver tube, which was cooled by pumping cold helium
gas through it. (Figure reproduced with permission from Elsevier Ltd.)

44
Figure 2-2. Schematic of dipping probe used to test the self-resonant coils before incorporating
them into a NMR probe. The coil is placed at the head of a long tube that is dipped
into a liquid helium Dewar. The coil is coupled to an inductive loop (not shown), and
its position is adjusted using a micrometer for impedance matching.

45
Figure 2-3. Block diagram of Gifford-McMahon based refrigeration system. The GM coldhead is
cooled by controlled expansion of helium gas. A secondary loop cools the NMR
probe by circulating a small amount of helium gas.

46
Figure 2-4. Illustration of the complete setup for a single channel of HTS coils, including the
sample isolation tube, an RF coupling loop and a tuning loop. Tuning and matching is
adjusted by varying the positions of the tuning and coupling loops respectively. The
coils are maintained at 20K, while the sample is vacuum isolated and maintained at
room temperature by flowing nitrogen gas.

47
Figure 2-5. Cross-section layout of a typical HTS cryogenic probe. The coils are placed in a
vacuum space (shown in blue) surrounding a center tube. The sample region (shown
in orange) remains near room temperature, while the coils are cooled to about 20 K by
conduction heat transfer.

48
Figure 2-6. Comparison of surface resistances of superconductors and copper as a function of
frequency. In the frequency range of interest for NMR, the surface resistance for
YBCO is several orders of magnitude lower than copper, and the crossover point
occurs at several hundred GHz [15]. (Figure reproduced with permission from
Springer.)

49
Figure 2-7. DC magnetic field dependence of surface resistance of YBCO for various film
thickness [18] when the applied magnetic field is normal to the plane of the substrate.
(Figure reproduced with permission from Elsevier BV)

50
Figure 2-8. DC magnetic field dependence of YBCO surface resistance when the applied
magnetic field is parallel to the substrate (Rs(p)) and normal to the substrate (Rs(n))
[19]. In NMR, the substrate is positioned such that the static magnetic field is parallel
to the plane of the substrate.

51
Figure 2-9. Parallel slits in YBCO to reduce effect of persistent currents in the resonator. The
YBCO coils are slit parallel to the direction of the RF current such that no closed
loops are formed.

52
Figure 2-10. Lumped element model of a Helmholtz pair of coupled resonators (A). Two coupled
resonators are modeled each by an inductance and a capacitance. The mutual
inductance between the two resonators is denoted by M. Two modes are seen
depending on whether the current in the pair of resonators is (B) in the same sense in
the two coils, or (C) in the opposing sense in each coil.
A
B
C

53
Figure 2-11. Simulated current and magnetic field distribution at the two resonance modes of a
Helmholtz pair of coupled resonators. The current in the two resonators are (A) in the
same sense at the lower frequency and (B) in the opposite sense at the higher
frequency. (C) The magnetic field at the lower resonance frequency is uniform in the
sample region, while (D) at the higher resonance frequency, the magnetic field goes
through a null. Only the lower mode is suitable for use in NMR.
A B
C D

54
Figure 2-12. Racetrack resonator (A) Schematic of a 4-capacitor racetrack resonator. (B)
Lumped element model of a racetrack resonator
A B

55
Figure 2-13. Spiral resonator (A) Schematic of a multi-turn spiral resonator (B) Mode plot of
spiral resonator showing non-harmonic behavior in contrast to harmonic behavior of a
uniform transmission line. Simulated current distribution of spiral showing
fundamental resonance (C), the second mode (D) and the third mode (E).
A B
C D E

56
Figure 2-14. Spiral with Faraday shields. Electric field from the spiral fringing into the sample
can be minimized by incorporating shielding wires that are perpendicular to the
direction of electric current.

57
Figure 2-15. Counterwound spiral coils (A) A Helmholtz pair of counterwound spiral coils is
shown in (A). The simulated electric field plot in (B) shows that most of the electric
field is contained within the substrates making them suitable as low-frequency
detection coils.
Figure 2-16. Cross-section of nested coil arrangement in the 1-mm probe. The 1
H coil was placed
closest to the sample for optimal sensitivity, while 2
H was placed next in order to
obtain adequate lock sensitivity using a very small sample volume. 13
C and 15
N
channels were used for decoupling only.
A
B

58
Figure 2-17. Cross section of nested coil arrangement in the the 1.5-mm 13
C optimized probe.
The 13
C coils are placed closest to the sample for maximizing the sensitivity.

59
Figure 2-18. Mixtures of synthetic metabolites with concentrations ranging from approximately 1
to 5 mM (40-200 nmol). The 13
C 1D spectrum (A) was collected in 2 hours using a
60° 13
C pulse, an acquisition time of 0.8 sec, a recycle delay time of 0.1 sec, and 1
H
decoupling during the entire experiment to build up an NOE. The 1
H 1D spectrum (B)
was collected in 3.5 min using a 90° 1
H pulse, acquisition time of 2.28 sec, a recycle
delay of 2 sec, and 32 scans. Resonances from one of the components (isoleucine at
about 3 mM) are indicated. (NMR spectra acquired by Chaevien Clendinen)

60
Figure 2-19. 13
C-13
C INADEQUATE spectrum of 1.1 mg natural abundance 13
C histidine. The
1D spectrum on the top is a 13
C spectrum collected for 27 minutes. The
INADQUATE spectrum was collected for 48 hours using the Agilent
“INADQUATEAD” pulse sequence, which utilizes an adiabatic 13
C 180° pulse. The
dotted lines and circles indicate the correlations in the INADEQUATE spectrum,
which allows a complete assignment of the 13
C backbone. The traces below are single
slices from the maxima of the INADQUATE spectrum. (NMR spectrum acquired by
Chaevien Clendinen)

61
CHAPTER 3
DESIGN OF DOUBLE-RESONANCE HTS COILS
Introduction
The design of double-resonance HTS coils is imperative to the development of HTS
probe that are optimized for sensitive detection of two nuclei. As previously described, the
principal requirement of an HTS resonator to be used in an NMR probe is that it should resonate
at the correct frequency and generate a strong and uniform magnetic field across the sample
region. Double-resonance coils must resonate at two distinct frequencies generating strong and
uniform magnetic fields at both frequencies. For optimal NMR performance, these resonators
must also minimize the electric field fringing into the sample. The design of double-resonance
coils suitable for 1
H and 13
C detection is described in detail in this chapter.
Electromagnetic Simulation
Electromagnetic simulation is an important tool in the design of HTS resonators [47]. A
commercial simulation software HyperLynx (previously available as IE3D) was used to simulate
the resonator designs. Apart from the prediction of fundamental and higher order resonance
frequencies, HyperLynx simulation tests have been developed to predict the performance of HTS
resonators. Simulation techniques for sensitivity, B1 homogeneity, and dielectric sample loading
are described in the following sections.
Sensitivity
The test for sensitivity of candidate coils in simulation is based on a method described by
Fuks and Anderson [48]. Their approach is a perturbation method in which a small test body is
moved inside the coil. The resulting shift in resonance frequency is used to map the RF magnetic
field. The setup used in simulation is shown in Figure 3-1. A small, metallic cylinder, much
smaller than the sample dimensions, is inserted in the sample region [49][50]. For a constant

62
coil-Q, the ratio of the resulting upward shift in frequency to the resonance frequency is
proportional to the square of the B1 field in the sample region.
𝐵1 ∝ √
𝑓𝛿
𝑓0
⁄ (3-1)
where f0 is the resonance frequency in the absence of the metal cylinder and fδ is the shift upon
insertion of the cylinder. Since sensitivity varies directly as the B1,
Sensitivity ∝ √
𝑓𝛿
𝑓0
⁄ (3-2)
This method is incorporated into our simulations to quantify and compare the sensitivity of the
candidate coil designs
B1 Homogeneity
The next important criterion in the selection of resonator design is the homogeneity of the
RF magnetic field. The near-field distribution of the electric and magnetic fields can be
calculated using HyperLynx simulation. In order to estimate the homogeneity of the coils, we
need to evaluate the magnetization over the entire sample region. The signal Si contributed by
each point i following an RF pulse applied for time t is described by
𝑆𝑖(𝑡) ∝ 𝐵1𝑖 𝑠𝑖𝑛(𝛾𝐵1𝑖 𝑡), (3-3)
where, 𝐵1𝑖 is the 𝐵1 field strength at each data point i and 𝛾 is the gyromagnetic ratio. The
overall signal detected is the summation from each data point.
𝑆(𝑡) ∝ ∑ 𝐵1𝑖 𝑠𝑖𝑛(𝛾𝐵1𝑖 𝑡)𝑖 (3-4)
For a reasonably uniform B1, 𝑆(𝑡) typically resembles a decaying sinusoid. The first
maximum corresponds to a 90° pulse, the second maximum corresponds to a 450° pulse, and the
third maximum corresponds to an 810° pulse. To carry out the homogeneity prediction, the

63
magnetic field values in the sample region are determined using the near field calculations
capability in HyperLynx. This field calculation is fed into equation 3-2 to calculate the signal
intensity as a function of time. A sample plot of 𝑆(𝑡) is shown in Figure 3-2. For the present
purposes, arbitrary units can be used for both the signal intensity and time step. Ratios of the first
three maxima then provide the predictions for the expected 450/90 and 810/90 values.
Sample Loading
The loss in an NMR experiment originates from the thermal noise in the coil and sample.
The signal-to-noise ratio in NMR may be written as [37]
𝑆𝑁𝑅 ∝
𝑀0 𝐵1
√(𝑇𝑎+𝑇𝑠)𝑃𝑠+(𝑇𝑎+𝑇𝑐)𝑃𝑐
(3-5)
where M0 is the magnetization, B1 is the RF magnetic field strength, Ta is the noise temperature
of the preamplifier, Ts and Tc are the physical temperatures of the physical temperature of the
sample and coil respectively. Ps and Pc are the power absorbed in the sample and coil
respectively. In a cryogenic probe, where the coil and preamplifier are maintained at extremely
low temperatures compared to the sample, the importance of minimizing the power absorbed in
the sample is clear from the above equation.
The power absorbed in the sample is determined by the electric field (E) over the sample
volume [37].
𝑃𝑠 =
1
2
∫ 𝜎𝐸2
𝑑𝑉, (3-6)
where, σ is the RF conductivity of the sample including dielectric loss. Thus improvements in
probe design to localize the E-field away from the sample region are imperative to improving the
SNR. It is well known that Ps is proportional to the sample resistance Rs and Pc is proportional to
the coil resistance Rc. The loss in the sample reflects as a change in Q of the coil when the
sample is loaded into the probe. Some straightforward relationships as follows may be defined.

64
Ignoring radiation loss and loss due to eddy currents in the normal metal elements in the
probe, the total power PT can be represented as
𝑃𝑇 = 𝑃𝑐 + 𝑃𝑠. (3-7)
The power components may be represented in terms of the coil-Q values with and without the
effect of the sample loading.
𝑃𝑇 ∝
1
𝑄 𝐿
, 𝑃𝑐 ∝
1
𝑄 𝑈
, and 𝑃𝑠 ∝
1
𝑄 𝑆
. (3-8)
where, QU and QL are the unloaded and loaded Q, and QS is the sample Q which can be
calculated as
1
𝑄 𝑠
=
1
𝑄 𝐿
−
1
𝑄 𝑈
. (3-9)
Using these substitutions, Equation 3-5 may be rewritten as
𝑆𝑁𝑅 ∝
𝑀0 𝐵1
√ 𝑃 𝑇√ 𝑄 𝐿√(𝑇𝑎+𝑇𝑠)
1
𝑄 𝑠
+(𝑇𝑎+𝑇𝑐)
1
𝑄 𝑈
(3-10)
This expression allows a direct comparison of sample loading effect in the candidate coil
designs based on the simulated change in Q.
For the sample loading simulations, the sample is modeled as a finite planar dielectric
with a finite conductivity. A 100 mM NaCl sample, with a dielectric constant of 78 and
conductivity of 1.2 S/m, is used as the lossy sample. The sample tube is modeled with a
rectangular cross section of equal area, since HyperLynx is not capable of solving arbitrary
shaped dielectric structures. M0 is neglected from the equation since all candidate coils will be
operating the same static magnetic field. The coil Q is limited by the microwave surface
resistance and quality of the film, and is thought to be independent of the resonator design.
Therefore QU is generally assumed with a high value (~10,000), which is typical of HTS
resonators. The loaded Q value obtained from simulation is normalized to this assumption. The

65
B1 in the sample for a known input power PT is also obtained from the same simulation. Thus,
the loading simulation using the finite dielectrics capability in HyperLynx is used to obtain a
reasonable estimation of sensitivity of the candidate coil. A sensitivity factor L introduced by
Kelly et al. [51] is calculated for candidate coil designs as,
𝐿 =
𝑆𝑁𝑅 𝐿
𝑆𝑁𝑅 𝑈
(3-11)
where, SNRU is the sensitivity estimated for a lossless sample and SNRL is the sensitivity
estimated for a lossy sample.
Development of Double-Resonance Coils
Orthogonal Coils
The limitation of patterning the YBCO films only on planar sapphire substrates restricts
the coils to planar designs. This eliminates the potential of high filling factors achievable only
with curved coils designed to snugly fit around the sample. The nested Helmholtz pair
arrangement causes only one channel, the one placed closest to the sample, on the probe to be
highly optimized. The simplest coil design to obtain double-resonance is to pattern two
resonators on opposite sides of the substrate. However, the problem with this arrangement is the
shielding of the higher frequency magnetic field by the lower frequency coil when the magnetic
fields generated by them are parallel to each other [52].
Hence, the ideal approach to optimizing the sensitivity of two channels simultaneously is
to design the channels with minimum magnetic interaction. To this end, the two resonators are
made to have magnetic fields orthogonal to each other. This is achieved by making one of the
resonators as a figure-8 with the magnetic field parallel to the substrate, whereas the other
resonator has a conventional resonance with magnetic field perpendicular to the substrate [53].
Bottomley et al. have described similar double resonance surface coils for MRI applications [54].

66
These coils are not self-resonant; instead, they are made to resonate at the appropriate
frequencies with the use of capacitors. These coils utilize two loops resonating at the two
different frequencies, which produce magnetic fields orthogonal to each other. Boskamp et al.
have used a ‘loop plus butterfly’ design to construct a quadrature detection coil [55]. In this case,
the two coils produce orthogonal magnetic fields but at the same frequency.
Preliminary Design
Preliminary double resonance coils resonating at 1
H and 13
C frequencies for 14.1 T were
designed with mutually perpendicular fields in order to minimize the magnetic interaction as
shown in Figure 3-5 [52]. The design incorporates a spiral on one side of the substrate, and an
I-bar on the opposite side of the substrate. At the 13
C frequency, the current flows almost entirely
in the spiral similar to the fundamental mode, with very little interaction from the I-bar. The
magnetic field generated is perpendicular to the substrate. Capacitive coupling between the I-bar
and the spiral plays an important part in establishing the 1
H resonance. At the 1
H frequency, the
current flows along the center strip of the I-bar, and returns along the wires of the spiral in the
form of a figure-8. The magnetic field generated is parallel to the substrate. Figure 3-6 shows the
schematic of the orthogonal magnetic fields at the two resonance modes.
While the double-resonance effect is demonstrated using this design, there are a number
of practical challenges in using this design. Primarily, independent frequency tuning of the two
channels is impossible using this design. The 13
C mode, being a simple spiral fundamental
resonance, behaves in a relatively predictable manner, and produces a satisfactorily homogenous
field. However, in the 1
H mode, the homogeneity was very poor. The large E-field generated by
the spiral fringing into the sample is another challenge that needs to be addressed.

67
Optimization of Figure-8 Mode
In order to achieve independent tuning of the two resonance frequencies, the figure-8 coil
is modified to be self-resonant. Since the figure-8 mode is for the higher frequency 1
H channel,
two racetracks placed adjacent to each other are used. This design is shown in figure 3-7. Both
racetrack coils are chosen to be 4-capacitor design.
To counter the poor homogeneity of the figure-8 mode, the center strip of the I-bar was
made broader at the middle and tapered at the ends in order to balance the current density
distribution. Figure 3-8 shows the modified design with improved magnetic field homogeneity.
Orientation of Spirals for Reduced E-field
The spiral structure exhibits chirality, such that right- and left-handed spirals may be
defined. The only difference between right- and left-handed spirals is that the turns move in
either the clockwise or anticlockwise sense when moving from the inside to the outside. The E-
field generated by a single spiral follows the direction of the RF current, i.e., if the current flows
from the inner turn to the outer turn, the E-field fringes from the inside of a spiral to the outside.
In effect, the only difference between the right- and left-handed spirals is the phase of the E-field
produced corresponding to the same B-field.
When used individually, spiral resonators have properties independent of chirality.
However, when used as a pair, the helicity of the spirals in the pair needs to be considered.
Shown in Figure 3-9 are two different pairs of spirals. In A, the two spirals have the same
helicity. Since one spiral is flipped over to be placed on the opposite side of the sample, this set
is referred to as a flipped pair of spirals. In B, the two spirals are mirror images of each other,
and hence are referred to as a mirrored pair of spirals in this discussion.
Figure 3-10 shows the simulated E-fields from two pairs of spirals described above. The
figure shows the cross section at the center of the long axis of the coil. The flipped pair of spirals

68
has the E-field directed from one spiral to the other, passing through the sample as shown in A.
In the case of mirrored pair of spirals, the E-field has a null near the center of the sample as
shown in B.
Shown in Figure 3-11 are the E-fields from the same pairs of spirals, when Faraday
shielding elements are added for each spiral. The direction of the residual E-field is seen from
the figures. The Faraday shields are more effective for the mirrored pairs of spirals with E-field
suppression of nearly 30 dB over the entire sample space.
Sample loading with a finite dielectric was simulated for each of the spiral orientations
with and without the inclusion of Faraday shields. The results from the sample loading tests are
tabulated in Table 3-1.
Faraday Shield Integration
If the Faraday shield wires are included as an additional layer, a three-layer coil design
results. For fabrication convenience, the Faraday shield wires for the 13
C channel have been
integrated into the 1
H coil layer. Furthermore, the wires of the 1
H figure-8 coil themselves act as
shielding elements to suppress the electric field from the 13
C spiral infringing into the sample.
This coil design is shown in Figure 3-12.
A photo of a double-sided 1
H-13
C HTS resonator is shown in Figure 5-13. A salient
feature of this design is that the two resonators as well as the Faraday shields are included in only
two YBCO films, without the need for a third layer. Patterning this design on a single substrate
with double-sided YBCO deposition eliminates the need for gluing together any substrates.
Another advantageous feature of this design is that, even though it is double-sided, there
is little overlap between the front and back sides. Thus, laser trimming can be performed with
negligible risk of backside damage. The 1
H resonator trimming was performed on the distal arms
of the figure-8. 13
C resonator trimming was performed on the fingers parallel to the long axis of

69
the coil. In this approach, only a few fingers of Faraday shield may be damaged which has
negligible effect on the overall performance of the coil. This is in contrast to the counterwound
spiral designs, where laser trimming poses a significant risk of backside damage to the spiral on
the opposite side.
Single-Sided Double-Resonance Design
Single sided double-resonance coils have been designed by making the two coils slightly
different in size. One such design for a 2
H/15
N coil is shown in Figure 3-14. There is no provision
made to contain the electric field from these coils. However, since these are coils are for the 2
H
lock and 15
N decoupling, they are much further from the sample and thus a higher electric field is
acceptable. The advantages of single-sided coils are the simpler patterning process and the ease
of handling.
Conclusion
In conventional HTS coils for NMR, the coil for only one nucleus is patterned on a single
sapphire substrate. Two such coils are used as a Helmholtz pair on either side of the sample in
order to achieve reasonable homogeneity. Four such pairs of substrates are employed in order to
realize the four channels of the triple resonance probe, i.e. 1
H, 13
C and 15
N, and the 2
H lock
channels.
In the ‘double resonance’ coil embodiment, coils for two different nuclei are included
with only two pairs of substrates. This enables us to improve the filling factor of the coils, and
hence, their detection sensitivity. The sensitivity tests predict about 63% increase in 1
H
sensitivity when compared to the conventional designs. A slight reduction of about 10% in 13
C
sensitivity is predicted compared to the conventional designs. Both the changes are in accordance
with the change in the relative distances of the coils from the sample.

70
An additional advantage of double-resonance coils is that four channels can be included
with only two pairs of substrates. The requirement of fewer nested substrates in the probe
simplifies the construction of the probe significantly.

71
Table 3-1. Simulation of effect of sample loading using finite dielectrics capability in
HyperLynx.
Coil
Unloaded
Lossless
SNR
Loaded SNR with
Sample
Loss
Sensitivity
Factor (L)QU
B1
(A/m)
QL QS
B1
(A/m)
Flipped 12000 384 356 3974 5942 248 145 40.73%
Mirrored 12000 384 356 234 239 56 30 8.42%
Flipped
shielded
12000 381 353 6237 12989 322 207 58.64%
Mirrored
shielded
12000 381 353 11009 133425 372 317 89.80%
Table 3-2. Comparison of simulated metrics of performance for conventional single-resonance
designs and double-resonance designs.
Probe 13
C-optimized probe Dual-optimized probe
Channel 1
H 13
C 1
H 13
C
810/90 (%) 83% 82% 75% 84%
B1 Shift 2.42 MHz 1.20 MHz 6.50 MHz 0.96 MHz

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