J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

SCONE code: Superconducting TF coils design codefor tokamak fusion reactor
Hiroyasu UTOH, Takaaki ISONO, Mitsuru HASEGAWA1), Kenji TOBITA and Nobuyuki ASAKURA
Japan Atomic Energy Agency, Naka, Ibaraki 311-0193 Japan1)

Mitsubishi Electric Cooperation, Chiyoda, Tokyo 100-8310 Japan(Received: 29 October 2009 / Accepted: 12 March 2010)

For fusion reactor design study, a maneuverable design tool of superconductor (SC) TF coils, SCONE code, hasbeen developed. The code was originally developed to apply reactor conceptual design where a baseline design of
TF coils is required rather than the detailed one. The code consistently solves heat balance, electromagnetic stressand magnetic field at the TF coil system, and eventually provides the maximum field of the coil system and the
optimal material composition of the conductor consisting of SC strand, stabilizing copper, support structure, etc. It
was confirmed that the calculated result was reasonable in comparison with existing coil design.
Keywords: Superconducting coil, TF coil design, reactor design

1. Introduction

Bi-2212 is a HTS with the chemical composition of
Bi2Sr2CaCu2Ox, and Nb3Al (RHQT) represents the Nb3Al
wire processed by rapid-heating, quenching andtransformation (RHQT), which is high Jc (~1000A/mm2)
at 16T and 4.2K [5]. Nb3Al can employ react and wind(R&W) method. In the R&W method, a furnace size iscompact, suitable for large coil fabrication. Bi-2212 wire
has high critical current density of more than 1000A/mm2
at 20T and 4.2K [6]. The conductor design by HTS has
been reported [7,8].
Considering these situations, the SCONE code
encompasses the physical and electromagnetic property
data of Nb3Sn, Nb3Al and Bi-2122, and find an optimalcoil design along the same design methodology.

In tokamak fusion reactor, the TF coils are one of themost important components affecting the power densityof reactor. In addition, since the TF coil system accounts
for a significant fraction of the total mass of the reactor,
the design of the TF coil system has a large impact on theconstruction cost of the reactor. This means that the TF
coil design is one of the most important processes in theconceptual design of fusion reactors. However, theconceptual design requires only a rough picture of the TF
coils. This is why we have developed a concise andversatile design code of the TF coils, named SCONE(Superconducting coil evaluation).
The SC material used in the existing or abuilding
tokamaks are NbTi and Nb3Sn as shown in Table 1. In
fusion reactors beyond ITER, candidate SC materials will
be Nb3Sn, Nb3Al and high temperature SC (HTS) from apoint of view of critical current density in the highmagnetic field regime as shown in Fig.1. In the figure,Tab. 1 Superconducting strand and Bmax on existing or abuilding machines and fusion reactor designs.
KSTAR
JT-60SAITER
PPCS model A [1]Demo-CREST [2]
SlimCS [3,4]SC strand
Nb3Sn
NbTi
Nb3Sn
Nb3Sn
Nb3Al
Nb3Al

Bmax
7.4T
5.65T
11.8T
~13T
~16T
~16T

Fig. 1

Critical current density versus magnetic fieldauthor’s e-mail: uto.hiroyasu@jaea.go.jp

304©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

H. Utoh et al., SCONE Code: Superconducting TF Coils Design Code for Tokamak Fusion Reactor

3. Description on SCONE code

3.1 Basic concept
The main input parameters of the code are:(i) choice of SC strand material(ii) coil size(iii) operation conditions of SC
Choice of superconducting strand are NbTi, Nb3Sn, Nb3Al
and Bi-2212. The coil size parameters are the height (H),the width (D), the number of TF coils (Nt), the conductor
thickness (tc), the outer radius of central solenoid (CS)coils (Rcs) and the thickness of coil case (din & dout), as
shown fig.2. The conductor area is given by tc, Rcs and dout.
The magnetic field in TF coils is determined at the TF coil
inner leg RTF (=Rcs + dout + tc). The operation conditions
include the conductor current (I0), the operation
temperature To, the strain (ε), the terminal voltage (Vterm),
temperature limit up on a quench (Ta) and the design
stress (Sm).
Figure 3 shows the flowchart of the SCONE code.
Using input parameters, the operation current density ofsuperconducting wire (Jop) and the number of turns (N) arecalculated. The amount of stabilizer is given by solving theheat balance at the conductor area. From the amount ofstructure material, the von Mises stress caused byelectromagnetic force is calculated. When the stress given
by calculation does not meet the design conditions, thecalculation starts over N-1. When the code finds a
consistent solution satisfying all the conditions, key design
parameters, such as Bmax, Jop and N are output.

Fig. 3

Flowchart of SCONE code

3.2 Calculation of operation current density
The critical current density (Jc) of thesuperconducting wires is given by the magnetic field (B),the temperature (T) and the strain-state (ε). Jc of thesuperconducting wires is calculated by using the scaling
law for these parameters dependence of Jc [9].

[]J c (B,T, ε ) = A(ε ) Tc (ε )(1− t 2 )×[ Bc (T, ε )]

n− 3

b

p−1

2

(1− b)

q(1)

where, A (ε) is single strain-dependent parameter, andb = B Bc (T, ε ) and Bc (T, ε) is the upper critical field,which
is parameterized by€v(2)
Bc (T, ε ) = Bc (0, ε )(1− t )
and
T
(
ε
)
is
the
criticaltemperature.
Here,
t
=
T
T
(
ε
)
€
c
c
These parameters A (ε), Bc (T, ε) and Tc (ε) are dependent€ on the strain, and have the following relationship:⎛ A(ε ) ⎞1 u ⎛ B (0, ε ) ⎞1 w T (ε )€⎜⎟ = ⎜ c⎟ = cTc (0)⎝ A(0) ⎠⎝ Bc (0,0) ⎠(3)
Bc (0, ε )2
3
4= 1+ c2ε + c3ε + c4ε
Bc (0,0)A (0), Bc (0, 0), Tc (0), c2, c3 and c4 depend on not only
Fig. 2 Input data regarding TF coil geometry in SCONE
type of superconducting strand, but also the fabricationcode€ process and the manufacture. In the code, the suitablevalues for reactor design employed the present database.
On ITER TF coil design, Jop is determined inconsideration of temperature margin ΔT (Top=5.2K, ΔT

305

H. Utoh et al., SCONE Code: Superconducting TF Coils Design Code for Tokamak Fusion Reactor

operation current density Jop. It is the product of thenumber of TF coils Nt, number of turns N and conductor
current I0.
The heat balance calculation considers the detection
delay time. The Joule heating term of equation (4) and (5)is written as follows.
2⎛ t − t ⎞⎞
∞ ⎛
∞ 2
td
2
d
I
dt
=
I
dt
+
I
exp
−
⎜
⎟
∫0
∫0 0
∫td ⎜ 0 ⎜⎝ τ ⎟⎠⎟ dt
⎝
⎠
(6)
⎛
⎞
2
τ
= I 0 ⎜ t d + ⎟
2 ⎠
⎝

=0.5K). Figure 4 shows the temperature dependence of Jc
on Nb3Sn. When ΔT is considered as operation temperature
margin, Jc (Top + ΔT) becomes less than Jc (Top), and thedifference is also understood to be a Jop margin.

800
J marginJc(Top)600
Jc (A/mm2)

Jop

Jc(Top+ΔT)

400

€

200

0

Fig. 4Top

Here, Lt is the inductance in the TF coil system and Vterm isthe terminal voltage.

ΔT

€
4

4.5

5

5.5
T (K)

6

6.5

7

(

∞

3.4 Stress calculation
To calculate the stress of the TF coil inboard leg, thefollowing simple method is adopted in the conducting
area. The amount of structure material in the conductor isdetermined by the area of structure material Ast.

Temperature dependence of Jc on Nb3Sn.

3.3 Heat balance calculation
In superconducting coils, a stabilizer are required forthe quench protection. In the SCONE code, the area of
stabilizing copper is determined by the balance of Joule
heating and heat capacity of materials in the conductor, as
the follows
Nb;
T A
∞
(4)
∫ 0 I 2 dt = ∫Topa ρCu γ SM CSM ASM + γ Cu CCu ACu dT
Cu

Bi;

(8)
Ast = A − ASM − ACu − Ain − Acl
where, Ain is the area of insulator given by 0.1A, and Acl is
the area of cooling channel given by 0.49(ASM+ACu). From
the area of structural materials, the von Mises stress of TF€ coils at a cylinder formed by inboard legs are calculatedby the following equation:2)€∫ I dt
2

(5)
⎛ A
Ta
A ⎞
= ∫T ⎜⎜ Ag + SM ⎟⎟ ⋅ γ SM CSM ASM + γ Ag C Ag AAg + γ PbC Pb APb dT
op⎝ ρ Ag ρSM ⎠()

where ρCu, ρAg and ρSM are the resistivity of copper, silver€
and superconducting material, ASM, ACu, AAg, γSM, γCu, γAg€,€ γ , C , C , C and C are the area, the density and the
Pb
SM
Cu
Ag
Pb
specific heat capacity of superconducting material,stabilizing copper, silver and lead, respectively. Each ofthese parameters has a dependence of temperature. I is
the conductor current, Top is the operation temperature
and Ta is the maximum allowable temperature at
conductor area. Although γCu is dependent on T and B, thedata at B=16T is assumed in the code. The dependence on
B is little at the considered temperature range. At very €low temperature, γCu reduces to one-eighth, but the effecton heat calculation at the quench is little. ASM is €determined by the quotient of total magneto motive It and

€
306

2

(σ − σ ) + (σ − σ ) + (σ − σ )
=
t

r

r

z

z

2

t

(9)
2
where, σt, σr and σz are the toroidal, radial and axial
stresses, respectively. These are approximately
determined using the ratio ηst of Ast to conductor area A22( = π (Rout − Rin ) ) and the area of coil case Acase22( = π (Rout + din ) − A − πRcs ), as follows.

σ mises0€

where, td is the detection delay time and τ is equivalentdischarge time constant given by
Lt
τ=
(7)
Vterm
N⋅
I0

∗

σt =

2A
2
A
+ Acase1− 1− ηst

σr =

2A
2
A
+ Acase1− 1− ηst

σt

σr

∗

(10)

2

µ0
It
R
n 2
8π ηst A + Acase
R1ηst = Ast Aσz =Rin = Rcs + dout
Rout = Rcs + dout + t c

R1 = Rin + tc 2
R2 = R1 + D
where, σt* and σr* indicate the average stress in the

H. Utoh et al., SCONE Code: Superconducting TF Coils Design Code for Tokamak Fusion Reactor

conductor area.

2∗
pRout ⎛ Rin ⎞⎜
σr = −
1− 2 ⎟⎟
2
2 ⎜
r ⎠
Rout − Rin ⎝22∗
pRout ⎛ Rin ⎞⎜σt = −
1+ 2 ⎟⎟
2
2 ⎜
r ⎠
Rout − Rin ⎝

Tab. 2 ITER TF coil parameters

2

2

2

Number of TF coilsµ 0 j0 t cµ 0I t=2
66π 2 Rout
Here, p is the equivalent pressure of pinch strength atinner leg of TF coils. The membrane stress σmembrane isdefined as an arithmetic average of the von Mises stressesof TF coils at the six radial positions (Fig.5).

where,

rk = Rcs + dout +

€

€

€
€

6

(

)

k − 1 tc
5(12)~0.77%Height of TF coils

14m

9m

Magnetic energy in TF coils

41GJ

Terminal voltage

3.55kV

134

Allowable stress

Equivalent discharge time const.
(13)

5.2K

Operation strain

Number of turns

667MPa15s

parameters of ITER TF coils. A comparison on the coilparameters [11] are shown in Table 2. ITER consists of 18
TF coils, a CS, six poloidal field (PF) coils and 18
correction coils (CCs). The TF coils are operated at the
maximum field of 11.8T. The conductor is a circular Nb3Sn
cable-in-conduit with a central cooling channel, cooled bysupercritical helium. The winding uses one-in-handconductor with a double pancake configuration.
The ITER-TF coil parameters and the calculation
result from SCONE code are shown in Table 3. A
reasonable agreement is seen between the SCONE result
and the design parameters of ITER. Both “total magneto
motive force” and “number of turns” have a little
deviation compared to ITER parameters. The difference of“magnetic energy in TF coils” Et and “equivalentdischarge time const.” τ are caused by the difference of
coil shape definition. In SCONE code, the coil D-shape isapproximated by,

k = 1,⋅⋅⋅,6
The maximum primary stress σprm is defined as a
maximum the von Mises stresses.
σ prm = max{σ rk ,mises , k = 1 → 6}
(14)
The allowable stress criteria are:σ membrane ≤ S m and σ prm ≤ 1.5S m

68kA

Width of TF coils

6

σ membrane = k=1

Operation current in TF coils

11.8T

Operation temperature in TF coils2∑σ rk ,mises

Nb3Sn

Maximum field in TF coils

(11)

p=

€

18

SC strand(15)

The design stress Sm is determined by two-third yield stress(=2/3Sy). Incidentally, the structural material of ITER is JJ1,
and the designed€ Sm is 667 MPa. At present, Sm of about
750 MPa is achieved [10].

	 Tab. 3 Comparison between ITER TFC and SCONE code

11.8T
164MA
41GJ
134

SCONE
code
11T
166MA
43GJ
136

15s

20s

0.765

0.80

ITER

Fig. 5

Maximum field in TF coils
Total magneto motive force
Magnetic energy in TF coils
Number of turns
Equivalent discharge time
const.
Operation current density(Jop/Jc)

Distribution of the von Mises stresses of the
conductor area.

4. Application to ITER-like TF coils

To validate the calculation result obtained from the
SCONE code, the result was compared with the design307

H. Utoh et al., SCONE Code: Superconducting TF Coils Design Code for Tokamak Fusion Reactor

12

SCONE

(Bmax=11T@RTF)

10

From TOROIND
Extrapolation

BT (T)

8
6
ITER

4

(B=5.3T@Rp=6.2m)

20Fig. 6

2

4

6

8

10

12

R (m)

Material composition ratio of conductor on Nb3Sn

Fig. 7

Magnetic field distribution on ITER fromTOROIND and the SCONE extrapolation2µ 0I t H πsin(θ ) 2dθ
(16)
∫0 R + R
4π
21+ cos(θ )R2 − R1
where, H is the height of TF coils and τ is calculated by Et,
Lt
2Et
τ=
=
V
N ⋅Vterm ⋅ I 0
N ⋅ term
(17)
I0
Et =

€

conductors are widely distributed over the coil crosssection and thus Bmax tends to be lower than the actual coil.
It should be noted that such an underestimation of Bmax
tends to impose strenuous requirements for plasma
parameters and thus leads to a safety side design from thepoint of view of reactor system design. Apart from thissmall disagreement, it should be stressed that this approachis useful in the baseline design study of fusion reactors
where one is interested in dependences of Bmax on different
parameters such as coil size, shape, conductor current,
operation temperature, etc., rather than an exact Bmax for a
specific TF coil design. By using the SCONE code, thecalculation time becomes longer than existing TF coil
design module, but the difference is a few seconds by apersonal computer. Integration of the SCONE code into
the existing system code can be useful in the demo
conceptual design.

2
1
Lt I 02
Figure 6 shows the composition ratio of conductormaterial in the conductor area A, such as SC material,stabilizing copper and structure material. As shown in thisfigure, the structure material dominates in the SC coil.
There is the difference of 1T on “maximum field in
TF coils” between ITER TF coils and the SCONE result.
To evaluate the magnetic field distribution, the magnetic
field distribution on ITER was calculated by a TOROIND
code. The TOROIND is a magnetic field calculation code
based on coil shape and current. Bmax obtained by the
SCONE code is extrapolated using B ∝1 R . Figure 7
shows the magnetic field distribution on ITER fromTOROIND and an extrapolation of Bmax of the SCONE
result. As shown in this figure,both magnetic field€
distributions are good agreement. On ITER design, themagnetic field at Rp=6.2m is 5.3T. The magnetic field
distribution on SCONE code at axis (Rp=6.2m) is equal to
ITER design value. A difference in calculation models is
responsible for the difference between the ITER design
values and the SCONE result. Bmax of ITER is calculatedwith a detailed model taking account of actual coilstructure. On the other hand, the SCONE code calculates
Bmax using imaginary conductors over the entire coil crosssection. The imaginary conductors are assumed to be a
uniform mixture with superconductor, stabilizing copperand structural material and so on. This means that the	 

 Et =€

5. Summary

The SCONE code has been developed to survey
reactor concept widely. The SCONE code consistently
solves heat balance, electromagnetic stress and maximum
magnetic field generated by the TF coils. It was
confirmed that the calculated result from SCONE code
was reasonable in comparison with existing coil design.
These result suggests that by using SCONE code, therough evaluation of Bmax generated TFC system isavailable. The SCONE code seems invaluable in design
study of the TF coil for tokamak fusion reactor.

Acknowledgment

The authors would like to dedicate this paper to late308

H. Utoh et al., SCONE Code: Superconducting TF Coils Design Code for Tokamak Fusion Reactor

Satoshi Nishio who developed main parts of the SCONE
and passed away in last May. They also acknowledge Dr.
Y. Ogawa (University of Tokyo), K. Okano and R.
Hiwatari (Central Research Institute of Electric Power
Industry) for stimulating discussions.
[1]
[2]
[3]
[4]
[5]

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[6]
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[7]
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(2004).
[8]
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(2003).
[9]
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309