Plasma and Fusion Research: Regular Articles

Volume 14, 3405060 (2019)

Study on Configuration of Conductor Samples for 13 T - 700 mm
Test Facility∗)
Shinsaku IMAGAWA1,2) , Tetsuhiro OBANA1,2) , Suguru TAKADA1) ,Shinji HAMAGUCHI1) and Hirotaka CHIKARAISHI1)
1)

2)

National Institute for Fusion Science, NINS, 322-6 Oroshi, Toki, Gifu 509-5292, JapanSOKENDAI (The Graduate University for Advanced Studies), 322-6 Oroshi, Toki, Gifu 509-5292, Japan(Received 23 December 2018 / Accepted 19 February 2019)

A 13 T test facility with a 700 mm cold bore has been utilized for the research of high-field and high-current
superconductors for magnets of fusion reactors. Studies on configuration of a conductor sample have been carriedout for simplification of the conductor sample and its supporting structure. Since sideways force and rotational
moment are induced by an asymmetric current component of the sample, the route of feeders and the configurationof terminals of the sample must be optimized. The sample is set at the coaxial position in the center plane of theexternal field coil because a vertical or radial shift of the sample induces vertical or radial force. According to
the structural analysis of the sample chamber, the allowable sideways force of the sample is estimated at 44 kN.
Considering the electromagnetic force and the magnetic field at the terminals, representative configurations ofone-turn samples are proposed. Concerning the number of turns of the conductor sample, a one-turn or rewoundcoil is preferred for a fast ramp rate of the sample current.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: joint, high current conductor, high magnetic field, Nb3 Sn, superconducting magnet, test facility
DOI: 10.1585/pfr.14.3405060

1. Introduction
High current superconductors are needed for magnets
of fusion reactors to suppress the high voltage during shutoﬀ due to the coil quench. Degradation of critical currentsof Nb3 Sn conductors for the ITER magnets was observedin cyclic loading test [1–3]. The degradation should be
more serious in the higher field and the higher current conductors. Therefore, a 13 T test facility with a 700 mm cold
bore [4] and with 50 kA current leads has been prepared
for the research of high-field and high-current superconductors. In order to attain suﬃcient length of testing region
and to apply electromagnetic hoop stress on the superconductors, we propose a coil-shaped conductor sample of few
turns, as shown in Fig. 1.
Study on configuration of a conductor sample has
been carried out to simplify the sample itself and its supporting structure. Since an asymmetric current componentof the sample induces sideways force and rotational moment, the route of feeders and the configuration of terminals of the sample must be optimized. The sample is set
at the coaxial position in the center plane of the external
field (EF) coil because a vertical or radial shift of the sample induces vertical or radial force. In addition, the electromagnetic coupling between the EF coil and the coil-shaped
sample must be considered to prevent excess current inauthor’s e-mail: imagawa@nifs.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

duced by the rapid change of the other coil current. In thispaper, four types of configurations of one-turn samples areproposed, and their electromagnetic force and the magnetic
field at the terminals are compared. In addition, the restriction on number of turns of the sample is discussed.

2. Four Types of Sample
Configurations
A coil-shaped testing sample is set at the center planeof the EF coil, as shown in Fig. 1. The conductor iswound inside a mechanical supporting ring to withstandlarge electromagnetic hoop force by itself. Their assemblyis hung from a top plate of the cryostat, and installed in
the sample chamber, which is evacuated for thermal insulation. The conductor sample is cooled with supercriticalhelium, and the supply gas temperature can be varied from
4.4 K to 50 K. The current leads for the sample are cooledwith the same coolant, and their outlets are connected to
the room temperature recovery line of the helium refrigeration system [5]. Since the sample is hung from the top
plate, the sideways force induced by an asymmetric current component mainly at the feeders must be minimized,
and the residual sideways force on the sample must be supported from the sample chamber. The allowable sideways
force is discussed in Section 3.
Four types of one-turn samples are proposed as shownin Figs. 1-3. Their three-dimensional views and nominaltransverse magnetic fields are shown in Figs. 4 and 5, re-3405060-1

c 2019 The Japan Society of Plasma
Science and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles

Volume 14, 3405060 (2019)

Fig. 1 Setup of the test facility with a 13 T external field coil anda conductor sample (Type-A).

Fig. 3 Configuration of samples Type-C (a) and Type-D (b).

spectively. The minimum bending radii and electromagnetic forces are summarized in Table 1. In the case of thesample current in the co or counter direction to the current of EF coil, the vertical shift of the sample from thecenter plane of the EF coil induces attractive or repulsive
force toward the center plane, and the radial shift induces
repulsive or attractive force toward the center axis. At thesample position where radius r of 0.3 m and vertical position from the center plane z of 0, the gradient of nominal
vertical field dBz /dr is 5.3 T/m, and the nominal radial field
Br is given by
Br = 5.25z + 34.5z2 .

Fig. 2 Configuration of a conductor sample Type-B.

(1)

In the case of one-turn sample with the current of 50 kA,
a radial shift of 5 mm, for example, induces the sideways
force of 1.25 kN, and a vertical shift of 50 mm induces thevertical force of 32.9 kN. Since the vertical force of thesample is supported with four M16 rods, the allowable tension force of which is 62 kN with considering the safety
factor of 2, the vertical shift must be controlled within this3405060-2

Plasma and Fusion Research: Regular Articles

Volume 14, 3405060 (2019)
Table 1 Dimensions and electromagnetic forces of the one-turnsamples of Type-A to Type-D.

Fig. 4 Three-dimensional view of four types of samples.

Fig. 5 Transverse magnetic field at the conductors and terminalsof the samples of Type-A to Type-D.

range.
In the case that the joint length at the terminal is longer
than 300 mm, Type-A, where both feeders are pulled up
and connected to copper busbars, is preferred because thedepth of the sample chamber from the center of the EF
coil is limited to 429 mm. The sideways force is relatively
strong because the current loop is not closed against theexternal field at the feeders. In addition, rotational moment
is induced by the horizontal forces at the testing region andat the feeders, and vertical force is induced in the feeders
inclined against the axis.
Type-B is the simplest one-turn coil with straight terminals shorter than 300 mm, as shown in Fig. 2. Both terminals are clamped with a set of plates and bolts. Relatively weak sideways force is induced by the small diﬀerence of vertical magnetic field between the testing region
and the terminals. The bending radius of the conductor
near the terminal is around 110 mm, which can be elon-

gated by shortening the length of terminals or by shifting
the position of the terminals toward the center.
Type-C adopts special shape of terminals. Since thehorizontal length of the straight section of the terminalis 200 mm, the minimum bending radius is elongated to150 mm. The rotational moment is small because of thesymmetric configuration of the sample against the center
plane of the EF coil. In Type-B and Type-C, the terminals are located at the highest field area. In order to avoid
normal transition from there, the temperature of the terminals should be kept lower than the testing region during
measurement of critical currents or current sharing temperatures. The temperature gradient can be realized by preparing a heater on the inlet of coolant for the testing region andtwo outlets of coolant in front of the terminals, as shown inFigs. 2 and 3.
In Type-D, the terminal is pulled away from the center
plane to reduce the transverse magnetic field at the feeders
and to elongate the minimum bending radius. In the caseof incline of 45 degrees, as shown in Fig. 3 (b), transverse
magnetic field at the terminal can be reduced to 70% of
the testing region, and the minimum bending radius can beelongated to 220 mm. The Type-D is considered to be reasonable in the case of short joint length less than 300 mm.

3. Structural Analysis of Sample
Chamber
Structural analyses of the sample chamber have been
carried out to estimate the allowable sideways force fromthe sample by using Autodesk Inventor Professional 2010.
The sample chamber consists of a top flange, upper cylinder, middle plate, lower cylinder, and bottom plate. Theirthicknesses are 50 mm, 8 mm, 18 mm, 4 mm, and 12 mm,respectively. Tetrahedral solid elements are adopted for allparts. Since the thick top flange is firmly fixed to the top
plate of the cryostat with bolts, displacement of the upper surface of the upper cylinder is fixed as a constraint
condition of structural analysis. The longitudinal elastic
modulus is set at 190.3 GPa, and Poisson’s ratio is 0.305.
Figures 6 (a) and 6 (b) show the original and deformed
shapes, respectively, in the case of sideways force of
100 kN from the sample. The maximum displacement is
6.85 mm, and the highest Mises stress of 393 MPa is in-3405060-3

Plasma and Fusion Research: Regular Articles

Volume 14, 3405060 (2019)

Fig. 6 Original shape (a) and deformed shape (b) of the sample
chamber in the case of the sideways force of 100 kN.

Fig. 7 Electric circuits for a conductor sample and the EF coil.
Table 2 Coil inductances and specifications of PS systems.

duced at the corner between the middle plate and the lower
cylinder. In order to suppress the displacement less than
3 mm which is the average gap between the lower cylinder
and the EF coil, the allowable sideways force is 44 kN. In
this analysis, the sideways force is applied by uniformly
distributed force with the height of 50 mm and the lengthof arc of 650 mm, which is 30% of the circumference ofthe lower cylinder, for avoiding peak stress there. In orderto estimate the actual local stress at the contact point of thesample, a contact stress analysis is necessary.

4. Consideration on Number of Turns
The electric circuits of the EF coil and the conductor sample are shown in Fig. 7, and inductance of the coils
and specifications of the power supply (PS) systems arelisted in Table 2. Since both PS systems have bypass lines
with diodes for protection of the coil, negative inductive
voltage induces increments of the coil current. In the caseof a one-turn sample with the same direction of current
flow as the EF coil, the EF coil current is increased by
3.6 A at the highest ramp rate of the sample current of 999 A/s. The equivalent current decay time constants of
the Nb3 Sn and NbTi coil of the EF coil is estimated at 4.9 s
and 15.1 s, respectively, with the quench simulation [6].
Since mutual inductance between the one-turn sample andNb3 Sn/NbTi coil is 2.07/2.34 mH, the induced voltage ofthe sample during the shut-oﬀ of the EF coil is estimatedat 0.44 V. Since the induced voltage is almost proportional
to the number of turns of the sample, 10 turns are allowable
under the restriction of moderate ramp rate of the sample
current around 100 A/s. In the case of the faster ramp rate,a rewound sample, as shown in Fig. 8, or a one-turn sample
is preferred.

5. Summary
Four types of conductor samples for the 13 T - 700 mm
test facility are proposed. From the viewpoints of the mag-Fig. 8 Configuration of a rewound coil composed with two
Type-B conductor samples.

netic field at the terminals and the minimum bending radius, Type-D is considered to be reasonable in the case ofa short terminal within 300 mm. In the case of a longer terminal, Type-A is suitable. According to the structural analysis of the sample chamber, the allowable sideways forceof the sample is estimated at 44 kN. Since this force corresponds to the length of 70 mm of the current of 50 kA
at 12.5 T, the feeders must be as close as possible to eachother. Concerning the number of turns of the conductor sample, 10 turns are allowable under the restriction ofmoderate ramp rate of the sample current around 100 A/s.
In the case of the faster ramp rate, a one-turn or rewoundcoil is preferred.

Acknowledgments

3405060-4This work was performed with the support of thePlasma and Fusion Research: Regular Articles

Volume 14, 3405060 (2019)

NIFS Collaboration Research program (UFAA001 andUFAA006).
[1] A. Devred et al., Supercond. Sci. Technol. 27, 044001(2014).
[2] A. Devred et al., IEEE Trans. Appl. Supercond. 23, 6001208(2013).

[3] T. Hemmi et al., IEEE Trans. Appl. Supercond. 22, 4803305(2012).
[4] S. Imagawa et al., Plasma Fusion Res. 10, 3405012 (2015).
[5] S. Hamaguchi et al., Plasma Fusion Res. 10, 3405020(2015).
[6] S. Imagawa et al., IEEE Trans. Appl. Supercond. 22,4803305 (2012).

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