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Designs and Tests of Compensation Coils to
Reduce Screening Currents Induced in HTS Insert
Coils for NMR Magnet
Kazuhiro Kajikawa, Member, IEEE, Gwendolyn V. Gettliffe, Yong Chu, Daisuke Miyagi, Thibault P. Lécrevisse,
Seungyong Hahn, Juan Bascuñán, and Yukikazu Iwasa
Abstract—Two types of compensation coils are focused on to
reduce screening currents induced in solenoid coils wound with
high temperature superconducting (HTS) tapes. One is a pair
of copper compensation coils located coaxially inside and outside
the HTS coil to apply an AC magnetic field in the axial direction.
The other is an HTS compensation coil with notch located only
outside the HTS coil to minimize the radial components of local
AC fields applied to windings of the HTS coil as small as possible.
It is found that the copper compensation coils yield the allowable
amount of power dissipation in liquid helium. The effectiveness of
the HTS compensation coil to reduce screening-current-induced
fields (SCFs) generated by another magnetized HTS coil is also
validated experimentally in liquid nitrogen using a commercially
available coated conductor with narrow width.
Index Terms—AC magnetic field, compensation coils, HTS
wires, screening current.
I. I NTRODUCTION
IGH temperature superconducting (HTS) wires with
long length such as Bi-2223 Ag-sheathed wires and
coated conductors based on either Y-123 or RE-123 have been
developed and become commercially available. These HTS
wires are in the form of a tape with the width of several
millimeters. Although the Bi-2223 Ag-sheathed tape has a
multifilamentary structure, its filamentary region whose cross
section has the aspect ratio of about 20 behaves like a bulk
superconductor due to an electromagnetic coupling between
the filaments [1]. The coated conductor also includes a very
thin superconducting (SC) layer with the thickness of a few
micrometers, so that its aspect ratio becomes more than 1000.
When these HTS tapes with large aspect ratios are wound as
windings for nuclear magnetic resonance (NMR) or magnetic
resonance imaging (MRI) magnet, the magnetic fields generated by screening currents induced in HTS tapes significantly
H
Manuscript received August 12, 2014. This work was supported by JSPS
KAKENHI Grant Number 24360110, and was also supported by the National
Institute of Biomedical Imaging and Bioengineering and the National Institute
of General Medical Sciences, both of the National Institutes of Health under
Award Number R01RR015034.
K. Kajikawa was with the Francis Bitter Magnet Laboratory, Massachusetts
Institute of Technology, Cambridge, MA 02139 USA. He is now with the Research Institute of Superconductor Science and Systems, Kyushu University,
Fukuoka 819-0395 Japan. Phone: +81-92-802-3836; fax: +81-92-802-3829;
e-mail: kajikawa@sc.kyushu-u.ac.jp.
G. V. Gettliffe is with the Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology, Cambridge, MA 02139 USA.
Y. Chu, D. Miyagi, T. P. Lécrevisse, S. Hahn, J. Bascuñán, and Y. Iwasa
are with the Francis Bitter Magnet Laboratory, Massachusetts Institute of
Technology, Cambridge, MA 02139 USA.
degrade the field homogeneity in the central part of the
magnet [2]–[7]. Therefore, the reduction of the screeningcurrent-induced fields (SCFs) is one of very important key
technologies to realize HTS magnets for NMR/MRI.
A useful method to eliminate the effect of the screening
current in the HTS tape has been proposed [8], [9] on the basis
of the abnormal transverse-field effect [10]–[13] or the vortex
shaking effect [14]–[16]. In this method, an AC magnetic
field is provisionally applied to the HTS tape in the direction
parallel to its wide surface or along with its wire axis. After
this treatment, the distribution of the screening current is
changed and the direction of magnetization becomes parallel
to the AC field, so that the initial screening current induced
in the wide surface of the HTS tape finally disappears. The
proposed method has also been validated experimentally by
using an HTS coil wound with a Gd-based coated conductor
and a pair of copper coils located coaxially inside and outside
the HTS coil to generate the AC magnetic field [8], [9].
In this study, an HTS insert and copper compensation coils
are designed to assess the possibility of removal of screening
currents induced in HTS tapes wound for full-scale NMR
magnet. Another type of compensation coil wound with HTS
tapes is also designed and fabricated to suppress the power
dissipation in liquid helium, and the decays of SCFs are
experimentally observed by using the HTS compensation coil.
II. D ESIGNS OF HTS I NSERT AND C OPPER
C OMPENSATION C OILS
A low temperature superconducting (LTS) insert coil for a
500-MHz NMR magnet developed previously [17] is considered to be replaced by a coil wound with a coated conductor.
The main part of the original 500-MHz NMR magnet consists
of the LTS insert, an LTS main coil, and two sets of LTS
correction coils cooled at 2.3 K using liquid helium under
subatmospheric pressure, and the operating current of 108.1 A
generates the central magnetic field of 11.71 T. When the
combination of these coils except for the LTS insert is cooled
at 4.2 K using liquid helium under atmospheric pressure,
the operating current of 87.1 A can generate the central
field of 7.05 T corresponding to the resonance frequency of
300 MHz [3], [18]. It is assumed that an HTS insert coil to
be replaced generates the central field of 2.35 T (100 MHz)
inside the 300-MHz LTS background magnet at 4.2 K.
Tables I and II summarize the specifications of HTS insert
and copper compensation coils, respectively. Since the HTS
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50
Parameter
Value
Tape size (width × thickness)
Thickness of SC layer
Inner/outer diameter of HTS insert
Height of HTS insert
Number of turns of HTS insert
Current applied to HTS insert
Central magnetic field
Minimum local Ic (and load factor)
Maximum local Ic (and load factor)
Maximum full penetration field
4.05 mm × 0.3 mm
0.2 µm
82.2 mm/118.2 mm
399 mm
60 × 80 turns
160.3 A
2.35 T
186 A (0.863)
314 A (0.510)
49.4 mT
Critical current density, Jc (MA/cm2)
TABLE I
S PECIFICATIONS OF D ESIGNED HTS I NSERT
40
30
20
5T
10
10 T
0
0
30
60
90
120
Field angle, θ (deg.)
TABLE II
S PECIFICATIONS OF D ESIGNED I NNER /O UTER C OPPER C OILS
Value
1 mm
2 layers/2 layers
78.2 mm/118.2 mm
82.2 mm/122.2 mm
399 mm
68.8 mT
60 Hz
0.531 nΩ·m@RRR = 30, 4.2 K
1.50 mm
40 W/60 W
3.81 W
200
7.5
8
7
200
250
80
85
150
z (mm)
Parameter
Thickness of copper tape
Number of layers of coil
Inner diameter of coil
Outer diameter of coil
Height of coil
Amplitude of AC magnetic field
Frequency of AC magnetic field
Resistivity of copper
Skin depth, δ
Wattage of Joule heating
AC loss of HTS insert
Fig. 1. Approximated curves for experimental results of critical current
densities at 4.2 K in 4-mm-wide coated conductor with SC layer of 1.1 µm
in thickness [19].
300
100
8.5
9
50
7
(b)
(c)
8 7.5
90
0
40 45 50 55 60 40 45 50 55 60 40 45 50 55 60
r (mm)
r (mm)
r (mm)
(a)
insert has to be sandwiched by a pair of compensation coils
to reduce screening currents induced in the HTS windings,
their total size is almost identical to the original LTS insert.
The coated conductor has the width of 4 mm and the thickness
of 0.25 mm, and it is surrounded by an electrical insulator of
25 µm in thickness. The HTS insert is composed of 80 single
pancake coils with 60 turns of the coated conductor, and the
operating current of 160.3 A generates the central field of
2.35 T. The inner and outer compensation coils are wound
with a rectangular copper wire of 1 mm in thickness, and the
number of layers is two for each coil. The heights of the HTS
insert and copper compensation coils are identical.
The local distribution of critical currents inside the HTS
insert is numerically estimated by taking into account their
dependence on the magnitudes and orientations of local magnetic fields, B. Fig. 1 plots the experimental results of critical
current densities at 4.2 K in a 4-mm-wide coated conductor
with the SC layer of 1.1 µm in thickness as a function of field
angle θ in the fixed external fields of 5 T and 10 T [19]. The
angle θ = 0◦ means that the external field is perpendicular to
the wide surface of the coated conductor, whereas the angle
θ = 90◦ is parallel. In this study, these experimental results
are approximated by means of the least-square technique in
the range of 0◦ ≤ θ ≤ 90◦ for the equations
Jc (|B|, θ) = √
−Γ
α |B|
[ π ( θ )m ]
[ ( )m ] ,
2
cos 2 90◦
+ γ12 sin2 π2 90θ◦
(1)
Fig. 2. Profiles of (a) field magnitude (T), (b) field angle (deg.), and (c) critical
current (A) inside upper half of HTS insert combined with LTS background
magnet. The total central field is 9.40 T.
[
m = ln
2
π
√
]
(
2
arcsin 4(γ3γ2 −1) / ln 1 −
γ = p + q |B| ,
θ0
90◦
)
,
(2)
(3)
where (2) ensures that the off-axis double Ic [19], which
represents the angle off the ab-plane axis at which the critical
current Ic becomes twice the Ic in the perpendicular orientation, is constant for the fixed field magnitude |B| under the
assumption of (1). A set of fitting parameters is obtained for Jc
(A/m2 ) and B (T) as α = 3.43×1011 , Γ = 0.717, θ0 = 21.3◦ ,
p = 2.20, and q = 0.346. The approximated curves are drawn
as thick solid lines in Fig. 1, and thin lines are for 6 T to 9 T
at even intervals of 1 T.
Figs. 2(a) and (b) show the profiles of magnitudes and
angles of local magnetic fields inside the HTS insert having
the transport current of 160.3 A (2.35 T) combined with the
LTS background magnet generating the central field of 7.05 T.
The profiles for only the upper half of the HTS insert are
given for the sake of symmetry. By using Figs. 2(a), (b),
and (1), the distribution of critical currents inside the HTS
insert is also calculated in Fig. 2(c), where the thickness of
SC layer is assumed to be 0.2 µm as listed in Table I. The
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minimum local critical current is estimated as 186 A around
the middle of uppermost pancake coil, which is larger than
the operating current. On the other hand, the maximum local
critical current is 314 A around the middle of outermost layer,
which corresponds to the full penetration field of 49.4 mT.
If the residual resistivity ratio (RRR) of copper in high
magnetic field is assumed to be 30 [20], its resistivity at 4.2 K
is 0.531 nΩ·m [21]. In this case, the skin depth δ of 1.50 mm
for the frequency of 60 Hz is larger than the half thickness of
copper tape. Therefore, the major part of power dissipation for
copper windings might be the Joule heating, which could be
estimated as 40 W and 60 W for the inner and outer copper
compensation coils, respectively, if the AC field amplitude of
68.8 mT, which is 1.39 times larger than the maximum full
penetration field, is generated by these compensation coils. On
the other hand, if the both sides of the coated conductor have
copper stabilizing layers including very thin silver overlayers
with the total thickness t of 99.5 µm each in addition to
that for the other components of 51 µm [22], the maximum
temperature can be estimated as less than 250 K for the heating
duration time of 3 s on the basis of a theory for thermal
runaway under an adiabatic condition [23].
If an AC field with the amplitude Hm is applied to an SC
infinite slab of d in width with the direct transport current I,
the hysteresis loss Wh per unit volume per cycle under the
assumption of the Bean model [24] is given by [25]–[27]
{
1 3
k ,
Hm ≤ Ht
2
)
(
)
Wh = 2µ0 Hp × (3
, (4)
1 + i2 k − 32 1 − i3 , Hm > Ht
where Hp = Jc d/2, k = Hm /Hp , i = I/Ic , and Ht =
Hp (1 − i). The eddy-current loss We per unit volume per
cycle for two metal plates with the thicknesses t and the gap
2g is also given by [28]
We =
2π
3
2
∆2 {1 + 3g/(2t)} ,
µ0 Hm
∆ ≪ 1,
(5)
where ∆ = t/δ. By using (4) and (5), the hysteresis loss in the
SC layer and the eddy-current loss in the copper stabilizing
layers are estimated as 0.34 W and 3.47 W, respectively.
The abnormal transverse-field effect [10]–[16] can exponentially decay the magnetization due to a screening current
induced by an external DC field if an external AC field larger
than the full penetration field is applied perpendicular to the
DC field. The characteristic number of cycles, Nc , which is
defined by the AC cycle required for the magnitude of the
magnetization to fall to 1/e of its initial value, is given by [16]
Nc = A /(8.02 k) ,
(6)
where A is the aspect ratio of cross section of SC layer and
equals 20000 here. When k = 1.39 is used in (6) for the
windings around the middle of outermost layer in the HTS
insert, the characteristic number of cycles is estimated as
Nc = 1790, which corresponds to the period of 29.8 s for the
frequency of 60 Hz under consideration. Since the latent heat
of evaporation of liquid helium is 2.59 kJ/L, the total heating
of 104 W for 29.8 s consumes 1.20 L of liquid helium.
The axial magnetic field BSCF at the origin generated by
the radial magnetic moment loop of mr per unit length located
at the position (r, z) can be expressed by
{ (
)5/2 }
BSCF = 3µ0 mr r2 z / 2 r2 + z 2
.
(7)
Let us consider a single pancake coil wound in the pitch of
p using an SC strip with the width of 2w and the thickness
of d, which could be approximated by an infinite slab with
the width of 2w. If the Bean model [24] is used, the full
penetration field of the approximated infinite slab, Bp , is given
by Bp = µ0 λJc w with λ = d/p. When the radial magnetic
field Br and the transport current I are simultaneously applied
to one of strips under consideration in the pancake coil, the
magnetic moment mr per unit length can be expressed as

0 ≤ Br < B i
Br (i − 1) ,
2ap  Bp 2
Br2
×
, (8)
mr =
2 i + 2Bp − Br , Bi ≤ Br < Bp

µ0
)
 Bp ( 2
Br ≥ Bp
2 i −1 ,
where Bi = Bp i. When an SCF in the HTS insert is calculated using (7) and (8), it could be underestimated somewhat
because the end effect is ignored and the minor contribution
from a few turns in both the innermost and outermost is not
taken into account [29]. The SCF just after the energization of
the HTS insert and the LTS background magnet is estimated
as −1.88 mT, whose magnitude corresponds to 200ppm of the
central field of 9.40 T. After that, the application of the AC
magnetic field to the HTS insert for 180 s using the copper
compensation coils leads to the SCF of −3.08 µT (0.33ppm),
and it evaporates about 7 L of liquid helium.
III. D ESIGN AND T ESTS OF HTS C OMPENSATION C OIL
In order to avoid the excess energy dissipation in the copper
compensation coils and keep the inside bore wide for NMR
system, a new type of compensation coil is discussed here.
The compensation coil is wound using another HTS tape and
located only outside an HTS coil intended for the reduction
of induced screening currents. The HTS tape with a narrow
width might be used for the compensation coil because the
SCF caused by this HTS compensation coil itself after the AC
operation should be suppressed as small as possible. Since
a few layers for the HTS compensation coil are enough to
generate an AC magnetic field larger than the full penetration
field, the contribution to the SCF is expected to be slight.
An HTS compensation coil is designed and fabricated as
shown in Fig. 3 and Table III. The existing HTS insert has
been wound with Bi-2223 Ag-sheathed tapes of 3.1 mm in
width and 0.25 mm in thickness [18], [30]. The HTS insert is
comprised of 50 double pancake coils, and the total number
of turns is 7200. The inner and outer diameters of the HTS
insert are 78.2 mm and 120.3 mm, respectively, and its height
is 327.6 mm. On the other hand, the HTS compensation coil
is wound with three pieces of coated conductors of 2.01 mm
in width and less than 0.1 mm in thickness. Their critical
currents at 77 K in self-field are 53 A to 56 A. The inner
diameter and height of the HTS compensation coil are 130 mm
and 360 mm, respectively. The number of layers is two,
and the second layer has the notched length h of 300 mm.
Hence, the number of turns of the first layer is 164, whereas
the number of turns of the second layer is 14 × 2. This
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4
Compensation coil
h
LTS magnet
HTS insert
Fig. 3. Schematic illustration of HTS insert, HTS compensation coil, and
LTS magnet. The LTS magnet is used to induce the screening currents in the
windings of the HTS insert.
TABLE III
S PECIFICATIONS OF HTS C OMPENSATION C OIL
Parameter
Value
Tape width
Tape thickness
Critical currents of tapes at 77 K in self-field
Inner diameter of coil
Height of coil
Number of layers of coil
Notched length in 2nd layer, h
Number of turns of 1st layer
Number of turns of 2nd layer
Critical current of coil at 77 K in self-field
2.01 mm
92, 95, 92 µm
54, 53, 56 A
130 mm
360 mm
2
300 mm
164
14 × 2
45 A
Screening-current-induced field (mT)
5
±40 A@1.5 A/s
±40 A@15 A/s
±30 A@15 A/s
±5 A@15 A/s
4
3
2
1
0
0
20
40
60
80
100
Cycle
Fig. 4. Experimental results of decay property of SCFs for number of cycles
of applied AC magnetic field.
type of notched solenoid is expected to minimize the radial
components of local magnetic fields applied to the windings
of the HTS insert. There are no electrical insulations for the
coated conductors, so that insulated 40 AWG gauge nichrome
wires and 1-mil-thick polyimide sheets are used for turn-toturn and layer-to-layer insulations, respectively. Although the
total length of winding is about 80 m, the piece lengths of
the coated conductors are limited around 35 m. Therefore,
three pieces of the coated conductors are soldered in series
to wind the HTS compensation coil. Several samples with
the configuration of lap joint are prepared in advance, and
their joint resistances and critical currents in liquid nitrogen
are evaluated experimentally. The last sample made from the
53-A coated conductor shows the joint resistance of 52 nΩ for
the joint length of 136 mm and the critical current of 52.3 A
for the criterion of 1 µV/cm. The critical current of the HTS
compensation coil is also measured as 45 A in liquid nitrogen.
The HTS insert and HTS compensation coil are located
coaxially and immersed in liquid nitrogen. This HTS insert
is magnetized in advance to induce the screening currents
inside it by using an LTS magnet with larger clear bore. The
LTS magnet is firstly charged up to 1.25 T and discharged
down to 0 T. The inactive period of about 15 min is spared
until the decay of the screening currents due to flux creep
becomes negligible. After that, the SCFs in the axial direction
are measured using a Hall probe located in the center of the
HTS insert. Fig. 4 shows the experimental results of the decay
property of SCFs for the number of cycles of AC magnetic
field generated by the HTS compensation coil. A bipolar power
supply is connected to the HTS compensation coil and outputs
trapezoidal currents to it. Two different sweep rates of currents
of 1.5 A/s and 15 A/s are used in this experiments. The
amplitude of current is also fixed at 40 A, 30 A, or 5 A. The
conversion factor of current to the central magnetic field is
analytically estimated from the specifications of the fabricated
HTS compensation coil as 0.55 mT/A. It can be seen in Fig. 4
that the SCF for the case of 15 A/s to ±40 A decays with
increasing the number of cycles and becomes one tenth of the
initial value in 66 cycles. It is also found that the change of
sweep rate scarcely affects the decay property of SCFs, which
is almost determined by the number of cycles of AC field
as plotted in Fig. 4. On the other hand, the decrease in the
current amplitude leads to the slow decay of SCF. The Bi2223 tapes used for the HTS insert have the 77-K self-field
critical currents of 60 A to 84 A [30], which correspond to
the full penetration fields of 12 mT to 17 mT. This means
that the field amplitude for the current of 30 A applied by the
HTS compensation coil is roughly close to the full penetration
fields of the Bi-2223 tapes for the HTS insert. Therefore, the
significant decays of SCFs can be expected for the cases of
the applied currents larger than 30 A.
IV. C ONCLUSION
The HTS insert wound with the RE-123 coated conductors
were designed as well as a pair of copper compensation coils
to reduce the screening currents. The total power dissipation
during the AC operation was estimated as 104 W, and several
liters of liquid helium were evaporated within a few minutes.
The HTS compensation coil was also designed and fabricated
to suppress the power dissipation. The SCFs of another HTS
insert wound with the Bi-2223 tapes in the previous research
project were successfully reduced by applying the AC magnetic fields using the fabricated HTS compensation coil.
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