Proceedings of ITC/ISHW2007

Conceptual Design of Magnets with CIC Conductors for LHD-type
Reactors FFHR2m.
S. Imagawa, A. Sagara, and Y. Kozaki
National Institute for Fusion Science, 322-6 Oroshi, Toki, GIFU 509-5292, Japan

LHD-type reactors have attractive features for fusion power plants, such as no need for current drive, a wide
space between the helical coils for the maintenance of in-vessel components. One disadvantage was considered anecessarily large major radius to attain the self-ignition condition or to secure a sufficient space for blankets.
According to recent reactor studies based on the experimental results in LHD, the major radius of plasma is set to14 to 17 m with the central toroidal field of 6 to 4 T. The magnetic stored energy is estimated at 120 to 130 GJ.
Both the major radius and the magnetic energy are about three times as large as ITER. We intend to summarize
requirements for superconducting magnets of the LHD-type reactors and to propose a conceptual design of themagnets with cable-in-conduit (CIC) conductors based on the technology for ITER.
Keywords: cable-in-conduit conductor, fusion reactor, helical coil, LHD, superconducting magnet.

1. Introduction
Superconducting magnets for fusion reactors needhigh mechanical strength, high reliability, and low costs aswell as sufficient current densities in the high field. Cablein-conduit (CIC) conductors have been developed for large
pulse coils, and they are adopted for all magnets of ITER
[1-3]. Major features of the CIC conductors are a large
current up to 100 kA, high strength with thick conduits,
small AC losses, and high cryogenic stability. One
disadvantage is that they need circulation pumps forforced-flow cooling. The maximum length of a cooling
path is about 500 m that is determined by the pressure drop
for the required mass flow against the nuclear heating The
CIC conductor will not be the best for magnets of a helical
reactor that is operated with a constant current. However,technology related to CIC conductors will be strongly
improved through the construction of ITER, especially in acost and in the winding technique. Then, we study thehelical winding with CIC conductors on the engineeringbase of ITER as a conventional option.

2. Magnet Systems of LHD-type Reactor
A magnet system of an LHD-type reactor consists of apair of continuous helical coils and more than one pair ofpoloidal coils [4]. The position of the poloidal coils isdetermined by the dipole magnetic field, the quadruple
magnetic field, the stray field, the position of ports, and soon. At least one set of poloidal coils is necessary to adjust
the major radius of the plasma, the quadruple field, andauthor’s e-mail:imagawal@LHD.nifs.ac.jp

the stray field. In this case, the magnetic field around themachine center is fairly high, and the magnetic storedenergy is large. Two pairs of poloidal coils are appropriate,
because they can reduce the total weight of supporting
structures with reduction of the magnetic stored energy.
Also, the position of plasma axis can be controlled without
increase of the stray field. The position of the coils is notdetermined uniquely with the restrictions as above
because of the rest of the degrees of freedom. The coilposition can be adjusted to attain the space for the blanket,
the mechanical support, and ports. In this study, we adopt
two additional restrictions that aIV=aOV and ZIV=ZOV,
where a is the distance from the major radius circle of thehelical coil, and Z is the height, as shown in Fig. 1.
The lead angle of the helical coil is defined as thepitch parameter  = (mac)/(lRc), where l, m, Rc, and ac are
the pole number, the pitch number, the coil major radius,
and the coil minor radius, respectively. Figure 2 shows
the normalized stored energy of the LHD-type reactors
with two sets of poloidal coils. Since the poloidal coils
cancel the vertical field by the helical coils, the stored
energy is the larger with the longer distance of thepoloidal coils. Furthermore, it is the larger with the higher because the toroidal field area increases.
The coil current density, j, is very important for thedesign of superconducting magnets. Although the highdensity is useful to enlarge the space for blankets and forthe maintenance, it is restricted by cryogenic stability,
mechanical strength, and the maximum field. Considering
the space for the structural materials inside the winding, jis set approximately 25 A/mm2 in this study. The highest
magnetic field is also important for the superconducting
magnets. It depends mainly on the ratio of height of thehelical coil to the minor-radius [5]. The highest magnetic
field is set less than 13.5 T that is the same as the highest
field of the ITER-CS coils.
The necessary magnetic field and size can be
determined by the scaling low for the plasma
confinement and the necessary space for blankets. The
scaling law of ISS04 [6] for the energy confinement timeis adopted in this study. At first, we have studied thenecessary size under the condition of the enhancement
factor of energy confinement of 1.12 to the ISS04 scaling.
Since LHD has attained the factor of 0.93, the required
further improvement is 1.2 that will be achieved in thenear future. Table 1 shows examples of the design
parameters of LHD-type reactors, FFHR2m2, under theconditions: the parabolic distribution of both the plasma
density and temperature, the minimum space for blanketsof 1.1 m, the helical coil current density of 27.5 A/mm2,
helium ash ratio of 3%, oxygen impurities ratio of 0.5%,
and alpha particle heating ratio of 90%. The plasma
density was set to just the density limit of the Sudoscaling [7]. The central temperature was adjusted to makethe average , the ratio of plasma pressure to the central
magnetic pressure, at 5%. The plasma shape is assumed
to be similar as that of LHD at the inward shift mode, inwhich the best plasma confinement has been achieved.
In the conditions as above, the smallest major radius
is determined mainly by the space for blankets than thehighest magnetic field. The plasma major radius around
15 m is necessary for a reactor similar to LHD. Since thehigh-density operations elongate the energy confinement
time of the ISS04 scaling, the enhancement factor is lesswith the higher  operation in which the larger fusion
power is produced.

Stored Energy, W/WHC only, 1.15

Proceedings of ITC/ISHW2007

10.9

=1.15, 1-d=1.20, 1-d=1.25, 1-dLHD

1-d: R0/Rc=3.6/3.9

0.8

Bleak(2.5 Rc) < 0.5 mT)
aIV =aOV, ZIV =ZOV

0.7
0.1

0.15

0.2
0.25
(aPC-ac)/Rc

0.30.35

Fig. 2. Stored energy of magnets of LHD-type reactors with twopairs of poloidal coils under the condition of the sameheight and the same minimum distance from the helicalcoil in the poloidal cross-section.
Table 1.

Case study of LHD-type reactors FFHR2m2-j27.5.
1.15
1.2
1.25
Polarity / Field periods, l/m
2/10
2/10
2/10
Coil pitch parameter, 
1.15
1.20
1.25
Coil major radius, Rc (m)
15.68
16.52
17.53
3.61
3.97
4.38
Coil minor radius, ac (m)Coil center line length (m)
150
162
176
14.47
15.25
16.18
Plasma major radius, R0 (m)
1.75
2.24
2.83
Plasma minor radius, ap (m)
877
1516
2559
Plasma volume, Vp (m3)
5.53
4.95
4.49
Central magnetic field, B0 (T)
12.1
12.1
12.2
Max. field on coils, Bmax (T)Coil current, I (MA)
40.0
37.7
36.3
27.5
27.5
27.5
Coil current density, j (A/mm2)
1.1
1.1
1.1
Blanket space, d (m)Magnetic energy, W (GJ)
128
124
125
34.9
26.3
20.5
Density, ne(0) (1019 m-3)
16.9
17.9
18.9
Ion temperature, Ti(0) (keV)
55
5
Average beta, <>Fusion power, PF (GW)
3.9
4.2
4.8
1.65
2.01
Energy confinement time, E (s) 1.33
Enhancement factor to ISS04
1.12
1.12
1.12

3. Helical Coil with CIC Conductors

Fig. 1. Magnets and supporting structures of LHD-type fusion
reactor.

Main specifications of helical coils for an LHD-type
reactor, FFHR2m are as follows: the magnet-motive force
of about 40 MA, the magnetic energy of 120 to 130 GJ, acoil center line of 150 to 175 m, and average coil current
density of 25 to 30 A/mm2. Design criteria for CIC
conductors based on the ITER magnets are summarized inTable 2. Since the length of the coil center line of thehelical coil is five times as long as the TF coil, some ideas
are necessary in addition to adopting a large current ofalmost 100 kA. Parallel winding is a practical solution toshorten the cooling length within about 500 m.
Two types of mechanical structure are known for CIC
conductors. One is a thick conduit type, in which
rectangular conductors are simply wound with being
wrapped by insulating tapes. Fairly high stress is induced

Proceedings of ITC/ISHW2007
in the insulators by summed up forces. The other is aninternal plate type, in which the conductor is wound in thegrooves of the internal plate. The stress in the insulation isreduced. Besides, the force for winding is relatively small
because of thin conduits. Its disadvantage is complicatedmanufacturing process of the internal plates. However, its
technology will be improved through the construction of
ITER-TF coils. Internal plates with grooves are suite forparallel winding, because CIC conductors are just put inthe grooves as shown in Fig.3. In this concept, react andwind method is preferred to use conventional insulator andto prevent huge thermal stress. Nb3Al is a candidate for thesuperconducting strands of the conductor because of its
good tolerance against mechanical strain. A method of"react and wind" can be adopted by managing strain duringwinding within about 0.5%.
The magnetic field in the helical coil is the highest in
the first layer, and it is lower in the higher layers. Therefore,
the average current density of the superconducting strands
can be increased by grading the conductors in the case oflayer winding. Non-copper current density of Nb3Sn isgiven as [8],jc = 1 (1 jc1 +1 jc0 )(1)()
j = C (1- (T T ) ) B (1- B B )B = B (1- (T T ) )(1- T 3T )B =B(1- a )T = T (1- a )jc0 = j0 1- (T Tc0 )22 2

c10c2c20c20c20m

-0.5

c0c2

2c0

1.7

1.7 0.333

c0c0m

c0(2)
2(3)
(4)
(5)

Table 2. Design criteria for CIC conductors based on ITER.
Items
Design criteria
ITER-TF
Max. cooling length (m)
< 550
390
Current (kA)
< 100
68
Maximum field (T)< 1311.8< 300273
Non-Cu current density (A/mm2)
< 30
20.3
Coil current density (A/mm2)
Nb3Sn
SC material for HC
Nb3Al (*1)

Fig. 3. Concept of helical winding with CIC conductors.
Table 3. Increase of non-copper current densities of SC strandsof helical coil conductors by grading.
Jc at Bmax
Av. Jc by grading (A/mm2)
Bmax
2(T)
(A/mm )
3 grades4 grades 5 grades
11.0
361
514
534
543
11.5
304
449
468
477
12.0
254
391
409
417
12.5
209
338
355
363
13.0
170
290
306314(6)where j, T, B, and  are the current density, the temperature,
the magnetic field, and the strain, respectively. For ITER
conductor j0=33.51 kA/mm2, Tc0m=18 K, Bc20m=28 T,
a=1250 for tensile, 900 for compressive, and C0=1150[3]. Table 3 shows the non-copper current density of thestrands for the various magnetic field at 7 K with the strainof -0.5%. In the case of Bmax of 12 T, the average current
density can be increased by 60% by adopting four gradesof conductors.
The typical design parameters of the helical coil are
listed in Table 4, compared with the ITER-TF coils. Byadopting large conductors of about 90 kA and the parallel
winding of five-in-hand, the length of a cooling path iswithin 530 m including the case of =1.25 in Table 1. By
increasing the number of quench protection circuits, themaximum discharge voltage can be managed less than 10
kV in spite of the larger inductance and the shorter
discharge time constant than ITER-TF coils. Consequently,
the helical winding is expected to be realized with small
extension of the technology for ITER.

Table 4. Specification of helical coil with CIC conductors.
HC_1.15 HC_1.20 ITER-TF
Maximum field (T)
12.1
12.1
11.8
Magnetic energy (GJ)
128
124
41
Number of coils
2218
Turn number per coil
30*14
30*14
134
Conductor current (kA)
95.2
89.8
68.0
Length of a cooling path (m)
450
486
390
Number of parallel winding
55
1
27.5
27.5
20.3
Current density (A/mm2)
Cu ratio of strand (–)
11
1
400
273.4
Non-Cu current density (A/mm2) 400
Ratio of Cu strands in area (–)
0.452
0.452
0.360
Central tube diameter (mm)
12.0
12.0
8.0
Void fraction (–)
0.340.34
0.34
Cable outer diameter (mm)
43.5
42.3
40.2
Conduit outer diameter (mm)
46.7
45.5
43.4
Total length of conductor (km)
126
136
82.2
Total weight of SC strands (ton)
481
490
351
Total weight of Cu strands (ton)
442
450
206
151
151
128.7
Cu current density (A/mm2)
Discharge time constant (s)121215
Inductance (H)
28.2
30.6
17.7
Number of coil blocks
3535
9Max. voltage (kV)
6.4
6.6
8.9

Proceedings of ITC/ISHW2007
A winding method is a critical issue for the helicalcoil. In the case of LHD, a special winding machine wasdeveloped. The conductors from a rotating bobbin wereplastically formed into the helical shape by the shaping
head near the winding guide. This method will not becompatible with the "react and wind" method, because theallowable strain is in the range of 0.5% for Nb3Al strands.
A candidate of winding method is as follows:(1) Conductors are heated for reaction of Nb3Al on abobbin the circumference of which is same as the length of
one pitch of the helical coil.
(2) The conductors are transferred to a reel of a windingmachine. The reel revolves through the helical coil asshown in Fig. 4.
(3) The conductors are pulled aside by a set of winding
guides and wound in grooves of the inner plate with being
wrapped with glass tapes.
(4) After winding the whole turns in a layer, the next innerplate are assembled.
The torsion strain r in winding is given asr =r  tan 12 a c 4

can be adopted, and these coils are expected to be realizedwith the same technology for ITER.
Table 5. Specification of poloidal coil with CIC conductors for
FFHR2m2_1.20_j27.5.
OV coil IV coil ITER-PF3
Radius of coils (m)
21.5
11.5
11.97
Number of coils
22
1
Coil current per coil, I (MA)
19.6
12.1
8.46
15.3
16.8
15.26
Current density (A/mm2)
Maximum field (T)
6.6
6.3
4
Turn number per coil
14*28 10*20
11.75*16
Conductor current (kA)
50.1
60.4
45
Length of a cooling path (m)
473
361
441.9
Number of parallel winding42
2
Cu ratio of strand (–)
22
1200
230
Non-Cu current density (A/mm2) 200
Ratio of Cu strands in area (–)
00
0.24
Central tube diameter (mm)
12.0
12.0
12.0
Void fraction (–)
0.34
0.34
0.34
Cable outer diameter (mm)
40.1
43.7
34.5
Conduit height*width (mm)55.1*55.1 58*58
52.3*52.3
Total length of conductor (km)
106
28.9
14.1
Total weight of SC strands (ton)
653
215
41.4
Total weight of conductor (ton)
2140
641
258

(7)

where r and  are the radius of the conductor and the leadangle of the helical coil. In the case of FFHR2m2 in Table
1, the strain is estimated at about 0.3%. Since the effect ofthe torsion strain on the properties of superconducting
strands is not known, the feasibility study is needed.

5. Summary
CIC conductors can be adopted for large helicalwindings by adopting layer winding and parallel winding
method. Since "react & wind" method is preferred for large
magnets, Nb3Al is a candidate for the helical coilconductor because of its good tolerance against mechanicalstrain. It is necessary to demonstrate the feasibility of its
winding method. In addition, structural analyses of thewinding area are needed in order to confirm themechanical feasibility of the helical coil with the highcurrent density of 25 to 30 A/mm2. This conceptual design
is expected to be a conventional option that can be realizedby small extension from the ITER technology.

References[1]

ITER Final Design Report, Magnet Superconducting Design
Criteria, IAEA, Vienna, 2001.

Fig. 4. Concept to wind a helical coil with CIC conductors.

[2]
[3]
[4]
[5]

4. Poloidal Coil with CIC Conductors
The poloidal coils of LHD-type reactors are circular,same as the poloidal field coils of ITER. The typical design
parameters of the poloidal coil of the FFHR2m2 are listedin Table 5, compared with the largest poloidal field coil ofITER, PF3 coil. Since the radius of the larger coil, OV coil,is almost twice as large as the ITER-PF3 coil, parallel
winding is also necessary. Although the coil current is huge,
the highest magnetic field can be lowered than 7 T by
decreasing the coil current density. Therefore, NbTi strands

[6]
[7]
[8]

N. Mitchell et al., Fusion Eng. Des. 66-68, 971 (2003).
A. Ulbricht et al., Fusion Eng. Des. 73, 189 (2005).
A. Sagara et al., Nuclear Fusion 45, 258 (2005).
S. Imagawa and A. Sagara, Plasma Science & Technology
7, 2626 (2005).
H. Yamada et al., Nuclear Fusion 45, 1684 (2005).
S. Sudo et al., Nuclear Fusion 30, 11 (1990).
J. G. Weisend II, Handbook of cryogenic engineering(Taylor & Francis, 1998) p. 326.