dimensioning magnetic systems for tokamaks · pdf filedimensioning magnetic systems for...

Matefu Spring School « Château de Cadarache » Jean-Luc DUCHATEAU 1

AssociationEuratom-CEA

DIMENSIONING MAGNETIC SYSTEMS FOR TOKAMAKSFrom ITER to DEMO

J.-L. Duchateau

Association EURATOM-CEA, CEA/DSM/IRFM



An illustration FromY. Iwasa (MIT)



An illustration FromY. Iwasa (MIT)

ITER CS model coilAt Naka

Magnet Engineers perpective



Dimensioning a magnet system for tokamak is a complex operation which is not yetcompletely codified

The exercise performed for ITER with the present solution is a good illustration.The aim is to build the cheapest machine capable of performing plasma discharges of500 s duration with inductive generation of current and an amplification factor of 10.

Simplifying the problem, it is possible to describe it as the identification of the drivingtriplet (R major radius, a minor radius, Bt plasma magnetic field) satisfying the initialrequest within a range of aspect ratio and elongation brought by the experience onprevious machines. This is an iterative process.

The same type of exercise is now starting for DEMO a fusion reactor delivering anelectrical power of 1000 MW whose construction could start 20 years from now.

Dimensioning magnet systems for Tokamaks



ITER Artist’s view

Initiation of ITER construction at CEACadarache

In parallel with reflexion on DEMO



The dimensioning of the superconducting tokamaks and of fusion reactors rely on the technological developments made during the preparation phase of ITER (1990-2002) starting with the conductor development and the manufacture of two model coils:

- A model coil of the toroidal field system

- A model coil of the central solenoid

1. Technological developments during ITER preparation (1990-2002)



The ITER TF model coilManufactured and tested in Europe (2001-2002)

A major step for fusion technology required by fusion reactors

A system of structural plates in which the conductors are embedded



CSMC51 mm x 51 mmm 40 kA 13 T

TFMCΦ 40,7mm, 80 kA, 9.7 T

The Nb3Sn conductors for fusion magnetsA crucial component



2. The role of Plasma magnetic field in fusion reactor performanceExpression of the Lawson criterion

Deriving simply n τ τ τ τE = f(Q,T) Lawson criterion

Pα + Pext = Wth/τE =Pnet Pext = Pfus/Q Plasma thermal equilibriumQ amplification factor

Wth ~ nTR3 Pnet ~nTR3/τE

Pfus ~ n2 T2R3 10 keV < T< 18 keV (Law in T2 for the reaction rate D-T, valid for ITER not for DEMO)

nTττττE =3 1021/(1+5/Q) (1)

Valid for Te=Ti and flat profile for density and temperature



The role of Plasma magnetic field in fusion reactor performanceThe use of scaling laws to express nTττττE as a function of Bt and R

τE ~H Ip0.93 Bt

0.15n0.41R1.39a0.58/Pnet0.69 energy time constant

Ip~Bta2/R expression of the plasma current

ngr ~ Ip/R2 ~ Bt/R Greenwald limit for density

(nTττττE)0.62~ B2.98R1.98 /Pfus0.38 (2)

(nTττττE)0.62 =B1.46R0.84ββββN -0.76 (3)

βt = βNIp/aBt

βt ~ nT/(Bt2/2µ0 )



The coupled role of plasma magnetic field and major radius on plasma performances

62.0

38.0

82.02

68.2

298.298.1

)/51(0410.9

Q

P

nH

qCCBR fus

N

impgeomt +≅ − ψ

From Johner

(1) +(2)

Thus for a given project characterized by Pfus and Q it is possible to find a family of couples (R,B) fitting to the project.

-It has to be however checked that βN is not exceeded

-It has to be checked that the magnetic system is not « virtual » which means that it can take place in the given radial built of the project

-That the flux available with a central solenoid is sufficient to drive inductively the plasma up to the nominal current

-It is not sure that the « optimum » project is at the highest field; large machines associated with large R can represent the best solution.



The coupled role of plasma magnetic field and major radius on plasma performances. The factor of merit ζζζζ

98.298.1

tBR=ξITER case

R=6.2 m Bt =5.3 T is a couple fitting the project :

P=400 MW Q=10

It can be checked that βN=1.6 is OK

The space available for the CS is sufficient to inductively drive the plasma up to 15 MA and maintain it for 500 s

Other solutions could have been possible with lower field Bt and higher R opening the possibility to keep NbTi in the TF system



At given machineInfluence of magnetic field on plasma performances

62.0

38.0

82.02

68.2

298.298.1

)/51(0410.9

Q

P

nH

qCCBR fus

N

impgeomt +≅ − ψ

At given fusion power

1+5/Q ≈ B-4.81 from (4)

At given βN

1+5/Q~ B-2.35 from (3) + (1)

βt = βNIp/aBt

βt ~ nT/(Bt2/2µ0 )

(4)



Influence of a decrease of B in ITER on Q

At given machineInfluence of magnetic field on plasma performances

0

2

4

6

8

10

12

10 10,5 11 11,5 12Maximum TF Field (T)

Am

plifi

catio

n fa

ctor

Q



Similar laws can be found for a reactor, the reaction rate for D-T has to be taken in T and not in T2.

This slightly affect the factor of merit ζ

The parameter βN plays a leading role for the expected plasma performances of a reactor.

At βN constant the fusion power follows the factor of merit.

Pfus ~ B3R2 (DEMO)

The coupled role of plasma magnetic field and major radius The case of the reactor



Btmax

re

ri

r’ i

re-ri’ → TF radial extension

3. The radial extension of the TF systemThe important role of the magnetic field through Jcond



3. The radial extension of the TF systemThe important role of the magnetic field through Jcond

Performance factor : ζ= R2Bt3

→ At given ζ re2 – ri

’2 ~R0.33/Jcond(Btmax)

1) TF radial extension is marginally affected by major radius R

2) TF radial extension is driven by Jcond the overall current in the TF including structures.



Central solenoid

TF magnet inner leg

Major Plasma radius

Plasma Distance Plasma-magnet (∆int)

4. From toroidal magnetic field Bt to magnet dimensioning field Btmax

A focus on the DEMO inner radial build (in the equatorial plane) starting from the major plasma radius and showing the main DEMO components



Inner radial Build

From toroidal magnetic field Bt to magnet dimensioning field Btmax

Plasma minor radius

Plasma center

TF radial extension

CS radial extension

Tokamak central axis

∆int

Major Tokamak radius R

r=0. r=ri B=0. r=re B=Btmax r=R-a r=0. B=Bt



RR

ak

tint

tmax

∆1

BB

−−=

tiTFecond RBrrJ ππµ 2)( 220 =−−

The crucial role of ∆int in the amplifying factor from Bt

to Btmax

The role of Jcond

In the TF radial extension

Which value of Jcond ?

Inner radial BuildFrom toroidal magnetic field Bt to magnet dimensioning field Btmax



Bt

Btmax

Inner radial Build

From toroidal magnetic field Bt to magnet dimensioning field Btmax



The crucial role of ∆int

distance from plasma edge to magnet conductor

Plasma chamber

First wall and shielding modules

Vacuum vessel

∆int = eso + esh + evac + ebp

inner leg of TF coil(Btmax)

eso scrape off layeresh first wall + blankets+vacuum vesselevac coil vacuumebp TF backplate

∆int plays a major role in the amplification of magnetic field from Bt

to BaveITER vacuum vessel



Btmax

re

ri

r’ i

aFrom Bt (plasma centre) to Btmax there is an amplification factor

re-ri’ → TF radial extension

The crucial role of ∆int




2.382.08α

14.611.8Btmax (T)

1.91.225∆int(m)

5.86 T5.3 TBt (T)

0.120.1Ebp (m)

0.15/1.65/0.10.15/0.88/0.1eso/esh/evac (m)

14.11.02Btave (T)

DEMOITER

11.1 14.1Bteffective (T)

∆int at given fusion power is not affected by the magnetic field value level

The crucial role of ∆∆∆∆int




The effective field

Due to the large size of the fusion conductors, a large magnetic field gradient (>1 T)exists in the superconducting cable

→ twisted strands oscillate between Bminand Bmax due to the self field

→ Conductor can be dimensioned at intermediate magnetic field value Beffective

which can be calculated

Φ

e

Bmin Bmax

n

effectivenoncu

c

n

A noncu

c

TBJ

JEdA

TBJ

J

A

EE )

),,((

sin/),,( εθε=

= ∫



ITERElectricity generating reactor: DEMO

High field zone in fusion reactor magnet system constitutes a very important technological stake



5. The TF radial builtthe dominating role of structures on the current density

In ITER the low value of Jcond (12 A/mm2) is driven by the structures and not by the superconducting material

1152ITER

(superconducting TF) (11.8 T) steady state

1720JET upgrade

(copper TF) (8T) pulsed operation (10s)

1939TORE SUPRA

(superconducting TF)

(9T) steady state

Average current density

in the TF inner leg

Jcond(A/mm2)

TF cable current density

including cooling

Jcable (A/mm2)

Tokamak

(TF maximum magnetic

Field on conductor)



Radial built of the TF systemA simplified approach to take into account the structures

(case of the vault)

-the TF system is a mechanical vault (as in ITER)

-the conductor is a circular cables inserted in a square structural jacket

-the TF vault is submitted to centring and hoop stress, the most loaded conductor is situated at ri

-in a first approach, the Lorentz stresses can be calculated analytically and the amount of structural material in the casing and in the conductor jacket can be calculated → Jcond

-→ stresses are proportional to Btmax2, stresses increase when ri

decreases.



Radial built of the ITER TF systemA simplified approach to take into account the structures

r’ i

ri

re

Vault

Hoop force

Centringforce r’i

re

ri



Radial built of the TF systemA simplified approach to take into account the structures

max20

2max

2

)(3

)2(2σ

µσ ≤

++

= frrr

rrBr

iei

ietecentering

e

isoef

2

22 ++Φ=

The centring force is dominating

σmax (MPa)=700 MPa– σhoop

Btmax

re

ri

r’ i

'2 0

12max

f

krBhoop δµ

σ =1

2

21

r

rLogk =

Similar expression exists to dimension the vault which has to resist the centering forceBut the vault is also partially taken all along the side of the casing

)'()/(2 22

2

ii

icenteringrr

rf −= σσ



FR

Fz

Fphi

Radial built of the TF system OF JT-60SAA simplified approach to take into account the structures

Fz =9.4 MN T= 4.7 MN

Fr=5.8 MN/m (L= 4.8 m)

Fphi=2Fr/(Sin 10 °) =16.7 MN/m

The centring force is supported by a vault effect in the TF nose (Fphi)



Radial built of the TF system OF JT-60SAA simplified approach to take into account the structures

s Insulation Stress Sphi

-400

-300

-200

-100

0

100

0 100 200 300 400

s(m)

Sig

(Mp

a)

Sphi

WPVE VI

Fphi VE →→→→ (71%)

Fphi WP→→→→ (8%)

Fphi VI →→→→ (21%)

Ansys results

VI

WP

VE

Maxi= 378MPa< 600MPa (limit)



It can be demonstrated that until Jnoncu<150 A/mm2, Jnoncu only marginally affectsthe overall current density in the TF radial extension Jcond.

As for Nb3Sn, Jnoncu measured in fusion conductors is far from the values measured on VAMAS mandrels due to differential thermal contraction (Nb3Sn/steel) and Lorentz forces.

Nb3Sn industrial strands have Jnoncu in the range of 150 A/mm2 for the magnetic field considered for DEMO. Progresses are expected.

6. Radial built of the TF systemSuperconducting material: the role of Jnoncu



Capability of several industrial superconducting strands at different design temperatures

Radial built of the TF systemSuperconducting material :the role of Jnoncu



7. Radial built of the TF systemThe role of the copper in the cable for protection

Prototype of TF ITER cable manufactured by NexansOverall cable current density around 50 A/mm2

copper strands (protection)

superconducting strands

HeliumVoid (30 %)



33 %

42 %

20 %

5 %

100 %

428

540

250 (Jnoncu=272 A/mm2)

70

1288

52.3 A/mm2

Helium

Total copper (τ’=11 s)

Non copper

Wrappings

Total

Jcable (I=57.3 kA)

Relative occupation

Section

(mm2)

Type of strand

Radial built of the ITER TF systemThe role of the copper in the cable for protection



Radial built of the ITER TF systemThe role of the copper in the cable for protection

(the hot spot criterion)

As soon as a quench is initiated in a coil, heat dissipation exists with associated temperature increase. This temperature increase is a function of the current decay and of the current density and copper content. A maximum voltage to the ground is fixed by the project.

max)()()(

)(max

0

2

0

TUdTTTC

dttJT

T

== ∫∫∞

ργ

τ> Wmag /(Iop Nc Vmaxg )

Tmax<250 K

Application to ITERIop=68 kAWmag=40 GJNc=9Vmaxg=3.5 kVτ=11 s (2s delay)



Other notions

Vlooptplateau = ΨΨΨΨCS +ΨΨΨΨvert -ΨΨΨΨind -ΨΨΨΨres -ΨΨΨΨbreak

)()6,03.4(00215,0 5.1295EXTBSp

effloop III

TaRZ

aRV −−−= κ

Flux consumption for plasma current increase

ΨΨΨΨind=LplasmaIplasma

ΨΨΨΨres =0,45 µµµµ0RIplasma

8. The role of the central solenoid to increase the current plasma in inductive mode and to maintain it for a duration tplateau

Flux consumption during plateau : ΨΨΨΨres= Vlooptplateau

The flux is provided by the central solenoid and by the verticalflux created by the plasma current



9. The ripple of magnetic field at the plasma external edge

R1 R2

Ripple=(R1/R2)N

Ripple<0.5 %

+ ferritic inserts

Ripple=∆∆∆∆B/B

Bmin)(Bmax21

BminBmaxRipple+

−=



The DEMO fusion reactor should provide 1000 MW electrical in dc,its construction could start 20 years hence

One major question for DEMO regards the magnet system of DEMOwhich will probably represent 30 % of the investment cost.

Should it be an extrapolation of ITER or is a technological revolutionneeded which will be difficult in 20 years ?

10. An illustration of problems associated with the dimensioning of large magnetic systems for fusion :

the dimensioning of DEMO



ITERElectricity generating reactor: DEMO

From ITER to DEMO, is the DEMO magnet system a simple extrapolation of ITER magnet system ?



7.5

2.46

19.4

5.86

15.

14.4

2401

1000

6.2

2.

15.

5.3

11.

11.8

500

0.

Major Plasma radius R(m)

Minor plasma Radius (m)

Plasma current Ip (MA)

Toroidal Magnetic Field Bt(T)

Overall current density in TF inner leg Jcond (A/mm2)

Maximum field on TF conductor Btmax (T)

Fusion Power Pfus (MW)

Electrical Power Pen (MW)

DEMOITERFusion machine

A preliminary design of DEMO

Tentative set of parameters currently under investigation for DEMO

Probably too high value



7.5

2.46

19.4

11315

15

1.902

5.86

15.

14.4

2401

1000

DEMO

8.5

2.79

20.6

11955

15

1.902

5.49

10.3

12.6

2400

1000

DEMOL

6.2

2.

15.

5772

10

1.225

5.3

11.

11.8

500

0.

Major Plasma radius R(m)

Minor plasma Radius (m)

Plasma current Ip (MA)

R2B3t

Q

∆int(m)

Toroidal Magnetic Field Bt(T)

Overall current density in TF inner leg Jcond (A/mm2)

Maximum field on TF conductor Btmax (T)

Fusion Power Pfus (MW)

Electrical Power Pen (MW)

ITERFusion machine

A new version of DEMOL relaxing the TF current density inner leg



The advantage of the new version DEMOL

The TF current density is more realistic (in the range of 10 A/mm2) corresponding to 40 A/mm2 in the cable and not to 100 A/mm2 as in DEMOL.

The increase of the major radius relax the mechanical constraints associated with the centring force.

For the same project the magnetic field is now smaller which makes the project simpler.

There is more space for the central solenoid which gives a higher CS flux and thereby a longer plateau time.

The increase in cost investment is moderate in the range of 15 %

For both versions Nb3Sn current density should be sufficiently high



Influence of the TF temperature for a reactor like DEMOThe emergence of Bi2212 round wire with high Jc(Nexans)

Nexans round wire10 % filling factor

Recent results from CEA Saclay

Jc(B)Brin Rond 10K

0

500

1000

1500

2000

2500

0 5 10 15B(T)

Jc (A

/mm

²)

Brin 01 - 22/04/2007Brin 02 - 22/05/2007Brin 02 - 29/05/2007Brin 01 - 31/05/200710 K



Influence of the TF temperature for a reactor like DEMOThe emergence of Bi2212 round wire with high Jc(Hitachi))

ROSAT wire - Round wire HTc Hitachi, Bi2212Jc=2500 A/mm2 T=4.2 K B=0.T

Katsumi Ohata et al. Development of a New Bi-2212



Applied Magnetic Field (T)

0 5 10 15 20 25

J E (

A/m

m2 )

200

400

600

800

1000

1200

1400

n-va

lue

10

15

20

25

30

35

40

45

JE(A/mm2)

n-value

At 4.2K, 25 T:Ic = 224 A

JE = 448 A/mm2

n-value = 16

E

OST 0.8 mm wire28 % filling factor

Influence of the TF temperature for a reactor like DEMOThe emergence of Bi2212 round wire with high Jc (OST)

A. Vostner Presentation at the EFDA expert meeting (tasks HTSPER, HTSMAG) Barcelona 8-9 May 2007



Influence of the TF temperature for a reactor like DEMOCalculation of the refrigerator electrical power Pc1

0

2

4

6

8

10

12

0 20 40 60 80Cold temperature (K)

Ref

riger

ator

ele

ctric

al p

ower

(M

W)

Further cold temperature improvement has no impact

Pc1= P5K(T1 –T2 )/(T2 f)

T2 cold temperature

T1 room temperature

f∼0.25

Decreasing the coil temperature affects only the cryogenic electrical power related to the winding pack Pc1 and not the cryogenic part associated with the thermal shields Pc2



Influence of the TF temperature for a reactor like DEMOThe benefit of HTS material in question

12.2 MW18.4 MWTotal Power for cryogenics

6.2 MW0.Benefit

10.6 MW10.6 MWCryogenic power

Thermal shield (80 K)

5.86T5. 86TToroidal magnetic Field Bt

2.46 m2.46 mMinor radius

7.5 m7.5 mMajor radius R

1.6 MW7.8 MWCryogenic power (magnet)

DEMO

(20 K)

DEMO

(5 K)Heating power in DEMO 303 MW

He pumping power in DEMO : 194 W

Impact of benefit low in comparison with recirculatingpower level in DEMO

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