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9 Design of ITER (International Tokamak Experimental Reactor)

9 Design of ITER (International Tokamak Experimental Reactor)

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15.9 Design of ITER (International Tokamak Experimental Reactor)



371



and the plasma current is

Ip (MA) =



5K 2 aBt

AqI



where K 2 = (1 + κ2s )/2 (Ip in MA, Bt in T and a in m).

The safety factor q95 is approximately given by (refer to (15.11))

q95 ≈ qI fδ fA

fδ =



1+



κ2s (1



+ 2δ − 1.2δ 3 )

1.17 − 0.65/A

fA =

.

2

1 + κs

(1 − 1/A2 )2

2



(15.39)



The volume average electron density n20 in unit of 1020 m−3 is

n20 = NG nG , nG ≡



Ip (MA)

πa2



(15.40)



where nG is Greenwald density(1020 m−3 ) and NG is Greenwald parameter. The beta

ratio of thermal plasma is expressed by

0.0403

( n20 Te keV + (fDT + fHe + fz ) n20 Ti keV )

Bt2

n20 Ti keV

= 0.0403(γT + fDT + fHe + fz )

.

(15.41)

Bt2



βth ≡



p



Bt2 /2μ0



=



Assuming that the spatial distributions of Te and Ti are the same, we have

γT ≡ nTe / nTi ≈ Te / Ti .

Scaling law of beta is

βth = fth βtotal , βtotal = 0.01βN



Ip (MA)

,

aBt



where βN is normalized beta. βtotal is the sum of βth (thermal plasma) and βfast (fast

(α) particle component) and fth = βth /βtotal . The notations fDT , fHe , and fI are the

ratios of fuel DT, He, and impurity densities to electron density respectively and the

unit of T is keV. X means volume average of X. Thermal energy of plasma Wth is

Wth (MJ) =



B2

3

βth t V = 0.5968βth Bt2 V

2 2μ0



(15.42)



where Wth is in unit of MJ and plasma volume V is in unit of m−3 . Plasma shape

with elongation ratio κs and triangularity δ is given by



372



15 Tokamak



R = R0 + a cos(θ + δ sin θ)

z = aκs sin θ

Plasma volume V is given by

V ≈ 2π 2 a2 Rκs fshape

where fshape is a correction factor due to triangularity

fshape = 1 −



δ

a



δ.

8 4R



In divertor configuration, V = 2π 2 a2 Rκs or S = πa2 κs are used to define the elongation ratio κs , S being the area of cross-section.

We utilize the thermal energy confinement scaling of IPB98y2 [38]

0.41 1.97 1.39 0.78 −0.69

a A κs Ph

τE = 0.0562 × 100.41 Hy2 I 0.93 Bt0.15 M 0.19 n20

2 1.34 0.41 0.05 1.49 2.49 −0.69

= 0.781Hy2 qI−1.34 M 0.19 κ0.78

NG A Bt a Ph

s (K )



(15.43)



where 0.0562 × 100.41 = 1.444, M(= 2.5) is average ion mass unit and Ph is the

heating power to compensate the loss power in MW by transport and is equal to

necessary absorbed heating power subtracted by radiation loss power Prad . The total

fusion output power Pfus is

Pfus =



Qfus 2

nDT σv

4



v



V



where Qfus = 17.58 MeV. σv v is a function of T . Since the fusion rate σv near

T = 10 keV is approximated by

σv



v



2

≈ 1.1 × 10−24 TkeV

(m3 /s)



the following Θ is introduced:

Θ( TkeV ) ≡

2

Then nDT

σv



v



2

nDT

σv



2

2

nDT

σv v

σv v

nDT

=

2

2

−24

−24

1.1 × 10

nDT TkeV

1.1 × 10

nDT TkeV



2



nDT T 2

.

2

nDT

T2



is expressed by

v



= 1.1 × 10−24 nDT TkeV 2 Θfprof ,



fprof =



2

T2

nDT

.

nDT T 2



15.9 Design of ITER (International Tokamak Experimental Reactor)



373



Θ is a function of average ion temperature TkeV in keV and is depend on the

spatial profiles of density and temperature. In the cases of spatial profiles of n(ρ) =

(1 + αn ) n (1 − ρ2 )αn , T (ρ) = (1 + αT ) T (1 − ρ2 )αT , (ρ2 = x 2 /a2 + y2 /(κs a)2 ),

the dependence of Θ on T is

Θ( Ti ) =



1 + 2αn + 2αT

1.1 × 10−24 (1 + αT )2 Ti



A fitting equation of T for σv

σv



v



=



v



1

2



(1 − ρ2 )2αn σv v 2ρdρ.



0



is already described in (1.5) of Chap. 1 as follows;



3.7 × 10−18 −2/3

−1/3

Ti

exp(−20Ti

) m3 /s,

h(Ti )



h(Ti ) =



5.45

Ti

+

.

37 3 + Ti (1 + (Ti /37.5)2.8 )



The dependences of Θ on average ion temperature T are shown in Fig. 15.23 in

the case of typical cases [51]. In the case of the flat density profile and parabolis

temperature profile (αn = 0, αT = 1), the profile parameter fprof is fprof = (αn +

αT + 1)2 /(2αn + 2αT + 1) = 4/3. In the case of flat density profile and peaked

temperature profile (αn = 0, αT = 2), the profile parameter is fprof = 9/5

Fusion output power Pfus is

2

fDT

fprof Θ( Ti )βth2 Bt4 V

(γT + fDT + fHe + fI )2

= 1.19fdil fprof Θ( Ti )βth2 Bt4 (2π 2 κs Aa3 )(MW)



Pfus = 4.77



= 2.35 × 10−3 fdil fprof Θ( Ti )κs fth2 βN2 Ip2 Bt2 Aa,



Fig. 15.23 Θ is function of

average temperature

T (keV) in cases with

profile parameters

(αT = 1.0, αn = 0.0),

(αT = 2.0, αn = 0.0),

(αT = 1.0, αn = 0.5) and

(αT = 2.0, αn = 0.3)



(15.44)



374



15 Tokamak



where Ip = (5K 2 /qI )(aBt /A). The dilution parameter of DT fuel due to He ions and

impurities fdil is

fdil ≡ 2

=



fDT

(γT + fDT + fHe + fz )



2

γT + 1



2



2



(1 − 2fHe − zfz )

1 − [fHe + (z − 1)fz ]/(γT + 1)



2



.



The output fusion power Pα due to α particle only is

Pα =



Pfus

.

5



since Pn : Pα = 4 : 1. When absorbed external hearing power is denoted by Pext and

the heating efficiency of α heating is fα , the total heating power is fα Pα + Pext . When

the fraction of radiation loss to total heating power is fR , the heating power Ph to

compensates transport loss power is

Ph = (1 − frad )(fα Pα + Pext ).

When Q value is defined by the ratio of total fusion power Pfus to external heating

power Pext

Pfus

Q=

,

Pext

Ph is

Ph = (1 − frad ) fα +



5

Pα .

Q



Therefore the burning condition is reduced to

5

Wth

Pα .

= (1 − frad ) fα +

τE

Q



(15.45)



From (15.42) and (15.45), we have

βth Bt2 τE =



1

2.503

.

(1 − frad )fdil (fprof Θ) (fα + 5/Q)



The term βth Bt2 τE is proportional to the fusion triple product n20 TkeV τE . From

(15.42) of Wth , (15.43) of τE , (15.44) of Pfus , the burning condition (15.45) is reduced

to, [52]



15.9 Design of ITER (International Tokamak Experimental Reactor)



Bt0.73 a0.42

A0.26



fα +



5

Q



0.31



= 2.99

×



375

0.31



1

(1 − frad )fdil (fprof Θ)



qI0.96 (fth βN )0.38

,

Hy2 M 0.19 NG0.41 K 1.92 κ0.09

s



(15.46)



that is,

1

qI0.96 (fth βN )0.38



6.83

+

=

Q

5

(1 − frad )fdil (fprof Θ) Hy2 M 0.19 NG0.41 (K 2 )0.96 κ0.09

s



A0.26

a0.42 B0.73



3.226



.



When Kaye–Goldston scaling (L mode) described in Sect. 15.6 is used instead of

IPB98y2 scaling, the burning condition becomes

Ip A1.25

a0.12



fα +



5

Q



0.5



=



146.9

HKG



1

(1 − frad )fdil (fprof Θ)



0.5



,



where HKG is the improved parameter of the energy confinement of Kaye–Goldston

scaling of L mode (HKG = 1). Necessary value of HKG for ITER is 2.57. It is interesting to note that the burning condition mainly depends AIp in this case.

When the parameters a, Bt , A are specified in the case of inductive operation

scenario of ITER, Q value and the other parameters can be evaluated. Specified

parameters are listed in Table 15.4a and the results of evaluated parameters in the

case of inductive operation scenario are shown in Table 15.4b. The results of this

simple analysis is relatively consistent with ITER design parameters of inductive

operation, which is given in the lefthand side column of Table 15.5 [53].

Ti in Table 15.5 is calculated by

Ti =



nTi

n



Ti n

nTi 1

nT

(2)

=

,

, fprof



(2)

nTi

n fprof

n T



(2)

where n and nT is given by (15.40) and (15.41) and fprof

≡ nT / n T ≈ (1 +

αn )(1 + αT )/(1 + αn + αT ).



There are constrains on plasma parameters by the engineering viewpoint of fusion

reactors.

When the distance of plasma separatrix and the conductor of toroidal field coil

is Δ and the maximum field of toroidal field coil is Bmax (see Fig. 15.24), there is a

constraint of

Δ 1

R−a−Δ

Bt

=1− 1+

=

Bmax

R

a A

By specification of Δ and Bmax , Bt is a function of a. Δ is the sum of thickness of

structural material of superconducting winding pack cM , of the blanket b and the

distance between the first wall and the separatrix of plasma dsep (Δ = cM + b +



376



15 Tokamak



Table 15.4 (a) Specified design parameters of inductive operation scenario. (b) Reduced parameters

of inductive operation scenario

(a)

a

Bt

A

qI

κs

NG

βN

fth

Hy2

fprof Θ frad



2.0



5.3



3.1



2.22



1.7



0.85



1.8



0.95



1.063



1.35



0.27



0.95



(b)

Q



R



Ip



τE



n20



Ti



Te



Wth



Pfus



Pext



Prad



βtotal



9.8



6.2



15.0



3.75



1.01



8.01



8.81



338



424



42



33.2



0.025



fDT = 0.82, fHe = 0.04, fBe = 0.02. γT = 1.1αn = 0.1, αT = 1.0 are assumed

qI = 2.22 is specified to be Ip = 15.0. fprof Θ = 1.35 and Hy2 = 1.063 are specified in order to be

Q ≈ 10 (refer (15.46))

Pn , Pα , Pext , Prad are in the unit of MW, Wth is in the unit of MJ and Ip is in the unit of MA

Table 15.5 Parameters of ITER outline design [53–55]

Inductive operation

Ip (MA)

Bt (T)

R/a (m)

A

κs 95 /δ95

ne (1020 m−3 )

NG

Ti / Te

Wthermal (MJ)

τEtr (s)

Hy2

Pfus (MW)

Pext (MW)

Prad (MW)

Zeff

βt (%)

βp

βN

q95

qI

li

Q

fR

fDT /fHe (%)

fBe /fAr (%)



15

5.3

6.2/2.0

3.1

1.7/0.33

1.01

0.85

8.0/8.8

325

3.7

1.0

410

41

48

1.65

2.5

0.67

1.77

3.0

2.22

0.86

10

0.39

82/4.1

2/0.12



Non-inductive

operation



Ip

Bt

R/a

A

κs 95 /δ95

ne (0)

NG /nG

Te (0)/Ti (0)



9 (MA)

(5.17) (T)

(6.35/1.84) (m)

(3.45)

(1.84/0.41)

0.6

∼0.62/0.85

37/34



Hy2



1.5∼1.7



PNB (MW)

PEC (MW)



34

20



βt,th (%)

βp,th

βN,th

q95



∼1.9

∼1.2

∼2

7



Q

Ibs

Icd



5

4.5 (MA)

4.5 (MA)



15.9 Design of ITER (International Tokamak Experimental Reactor)



377



Fig. 15.24 Geometry of

plasma, toroidal field coil

and central solenoid of

current transformer

in tokamak



dsep ). The thickness of blanket b consists of vacuum chamber, neutron shield, tritium

breeding Li blanket and first wall. The optimistic value of b is [56]

b ≈ 1.2 m

and

cM = R0 {1 − εB − [(1 − εB )2 − αM ]1/2 }

εB =



(a + b)

B02

, αM =

R0

μ0 σmax



2εB

1 + εB

1

+ ln

1 + εB

2

1 − εB



where σmax is the maximum allowable stress of structural material of the toroidal

coil.

There is maximum allowable neutron power flux qN passing through the first wall

(qN < 4 MW/m2 ) [56]. Then qN is the total neutron power Pn divided by the total

area S of the first wall, where Pn = (4/5)Pfus and S = (2π)2 R0 a[(1 + κ2s )/2]1/2 .

Then we have

1



R0 a (m2 ) =

4π 2



1+κ2s

2



0.8Pfus

2

> 5.04

1/2

qN

1 + κ2s



1/2



Pfus (GW).



In the case of κs = 1.7 and Pfus = 2.57 GW, there is constrains of R0 a > 9.8 m2 .

The ratio ξ of the flux swing ΔΦ of ohmic heating coil and the flux of plasma

ring Lp Ip is given by

ξ≡



2

)

ΔΦ

5Bmx ((ROH + dOH )2 + 0.5dOH

=

,

1/2

Lp Ip

(ln(8A/κs ) + li − 2)RIp



378



15 Tokamak



where ROH = R − (a + Δ + dTF + ds + dOH ), dTF and dOH being the thickness of

TF and OH coil conductors and ds being the separation of TF and OH coil conductors (refer Fig. 15.24). The average current densities jTF , jOH of TF and OH coil

conductors in MA/m2 = A/mm2 are

jTF =



1

2.5 Bmx

π dTF 1 − 0.5dTF /(R − a − Δ)

jOH =



2.5 Bmx

.

π dOH



Parameters of ITER outline design is listed in Table 15.5. q95 is the safety factor

in 95% flux surface. The maximum field of toroidal field coils is Bmax = 11.8 T. The

number of toroidal field coils is 18. Single null divertor configuration. One turn loop

voltage is Vloop = 89 mV. Inductive pulse flat-top under Q = 10 condition is several

hundred seconds.

In the case of non-inductive operation, the optimized parameters are different

from the optimized parameters in the case of inductive operation. The bootstrap

current is given by Ibs = cb (a/R)1/2 βp Ip from (5.29). Since βt = 0.01βN Ip /(aBt ),

Bp /Bt = μ0 Ip /(2πKaBt ) = 0.2(Ip /KaBt ), Bp /Bt = aK/RqI , βp is reduced to

βp = 0.25K 2 βN (aBt /Ip ) = 0.05AβN qI ,

the bootstrap current is given by

Ibs /Ip = Cbs A0.5 βN qI Cbs = 0.05cb .

When the driven current and the necessary power of the driver are denoted by Icd

and Pcd respectively, the current drive efficiency ηcd is defined by the equation

Icd =



ηcd

Icd

Pcd , ηcd ≡

n R.

nR

Pcd



(15.47)



All the current drive efficiencies of lower hybrid wave (11.47), electron cyclotron

wave (11.53) and neutral beam (11.63) are proportional to the electron temperature

Te . Therefore (15.47) is reduced to

Icd =



(ηcd / Te ) n Te

(ηcd / Te ) n ( Te + (fDT + fHe + fz ) Ti )

Pcd =

Pcd ,

2

n R

n 2 R(1 + (fDT + fHe + fz ) Ti / Te )







ηcd19 / Te keV





Icd (MA) ≈ 2.48 × 10−2 ⎝ (2)

fprof [1 + (fDT + fHe + fz )/γT ]



fth βN Ip (MA)Bt

Aa2 n 220



Pcd (MW),



15.9 Design of ITER (International Tokamak Experimental Reactor)



379



where ηcd19 is in unit of 1019 (A/Wm2 ) and Te keV is the volume averaged electron

temperature in keV unit and

βN Bt

Icd

= Ccd 2 2 Pcd (MW),

Ip

Aa n 20

Ccd = 2.48 × 10−2



(ηcd19 / Te keV )fth

(2)

[1 + (fDT + fHe + fz )/γT ]fprof



.



(15.48)



We must keep Ibs + Icd = Ip in the steady state operation, and the necessary driving

power Pcd is

Pcd =



2

2

Icd

aRn20

aRn20

=

Ccd βN Bt Ip

Ccd βN Bt



1−



Ibs

Ip



=



(1 − Cbs A0.5 βN qI )aRn2

.

Ccd βN Bt



Since the fusion output power Pfus is given by (15.44) as follows,

Pfus = Cfus βN2 Ip2 Bt2 Aa, Cfus = 2.35 × 10−3 fdil (fprof Θ)κs fth2 ,

Qcd ≡ Pfus /Pcd is [52, 55]

2

aR

(1 − Cbs A0.5 βN qI )n20

(1 − Cbs A0.5 βN qI )NG2

1

=

=

.

Qcd

Cfus (βN Bt )2 Ip (MA)2 AaCcd βN Bt

π 2 Ccd Cfus (βN Bt a)3



(15.49)



The increase of A1/2 βN qI is favorable to increase the bootstrap current and the increase

of (βN Bt a)3 /NG2 is favorable to increase of Qcd . However the increase of qI ∝ 1/Ip

(decrease of plasma current Ip ) and the decrease of ne degrade confinement time and

needs larger confinement enhance factor Hy2 .

Non-inductive steady state operation reference scenario 4, type II in [55] is examined. In non-inductive operation scenario, the bootstrap current and driven current

are 4.5 MA and 4.5 MA, respectively. The parameters of R, a, Bt , κs 95 /δ95 in noninductive operation are referred from [54]. NG , βt,th , βp,th , βN,th in non-inductive

operation are estimated values of Greenwald parameter and the thermal component

of β’s from [55] respectively. These data are used in Table 15.6a. Reduced parameters in the case of non-inductive operation scenario are listed in Table 15.6b. These

results are consistent to the parameters of non-inductive operation scenario in the

righthand side column of Table 15.5 [52].

The specified bootstrap current is Ibs = 4.5 MA. This specification requires Cbs =

0.0374, that is cb = 0.748. In the full non-inductive current drive experiment in JT60U (a/R = 0.24, βp = 2.7, reverse shear configuration), the estimated value of cb

is 0.6 (refer to Sect. 15.8).



380



15 Tokamak



Table 15.6 (a) Specified parameters in the case of non-inductive operation scenario. (b) Reduced

parameters in the case of non-inductive operation scenario

(a)

a

Bt

A

qI

κs

NG

βN

fth

Hy2

fprof Θ frad



1.84



5.17



3.45



3.35



1.84



(b)

Q



R



Ip



τE



n20



5.01



6.35



9.02



3.88



0.534



0.63



2.15



0.95



1.702



1.20



0.3



0.95



Ti



Te



Wth



Pfus



Pext



Prad



βtotal



12.0



13.0



241



228



45.5



26.6



0.020



fDT = 0.82, fHe = 0.04, fBe = 0.02 δ = 0.41. αn = 0.03, αT = 2.0, γT = 1.08

qI = 3.34 is specified to be Ip = 9.0MA. fprof Θ( Ti ) = 1.2 and Hy2 = 1.702 are specified to be

Q≈5

Pext = Pcd . T (0) = (1 + αT ) T ≈ 3 T . The value of the approximate equation q95 ≈ qI fδ fA is

4.69 and is different from the q95 ≈ 7 in Table 15.5



The specified driven current is Icd = 4.5 MA and the driving power is Pcd = Pext =

41.4MW . The necessary value of Ccd is Ccd = 0.329 × 10−2 and the necessary

current drive efficiency ηcd is given by (15.48) to be

ηcd19 = 0.133



(2)

[1 + (fDT + fHe + fz )/γT ]

fprof



fth



Te keV ≈ 0.259 Te keV .



The Q value and Qcd are quite different quantities with each other. Qcd does not

depend on Hy2 , while Q does not depend on Cbs and Ccd . However the sensitivities

of Q and Qcd on NG , qI , βN , . . . are different. It is necessary to keep Qcd = Q by

feedback control of sensitive parameters [52].

The conceptual design of tokamak reactors has been actively pursued according

to the development of tokamak experimental research. INTOR1 (International Tokamak Reactor) [57] and ITER (International Thermonuclear Experimental Reactor)

[53, 55] are representative of international activity in this field.

ITER aims achievement of extended burn in inductively driven plasmas with

Q ∼ 10 and aims at demonstrating steady state operation using non-inductive

drive with Q ∼ 5. Now ITER device is under the construction in Cadarache, France.

The experiment is scheduled to start in 2020. The cross section of outline design of

ITER and the bird-eye view of ITER are shown in Fig. 15.25 [53] and Fig. 15.26

[58] respectively.

1 The



working group of INTOR consisted of 4 parties namely Euratom, Japan, USA and USSR. A

note with the title of ‘Who’s job is it?’ was pinned on the wall of meeting room of INTOR in IAEA

building in Vienna. (This is a story about four peoples named everybody, somebody, anybody and

nobody. There was an important job to be done. Everybody was asked to do it. Everybody was sure

somebody would do it. Anybody could have done it, but nobody did it. Somebody got angry about

that, because it was everybody’s job. Everybody thought anybody could do it, but nobody realized

that everybody would’nt do it. It ends up that everybody blamed somebody when nobody did what

everybody could have done.)



15.9 Design of ITER (International Tokamak Experimental Reactor)



Fig. 15.25 The cross section of outline design of ITER



381



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