F. Warmer1, P. Knight2, C.D. Beidler1, A. Dinklage1, Y. Feng1, J. Geiger1, F. Schauer1, Y. Turkin1, D. Ward2, R. Wolf1, P. Xanthopoulos1

1Max-Planck-Institut für Plasmaphysik, EURATOM Association, Teilinstitut Greifswald, D-17491 Greifswald, Germany

2Culham Centre for Fusion Energy, EURATOM Association, Abingdon, Oxfordshire, OX14 3DB, United Kingdom

[1] D. WARD, Fusion Sci. Technol. 56 (2009) 581.

[2] K. LACKNER, Fusion Sci. Technol. 54 (2008) 989.

[3] J. GEIGER, personal communication (2013)

[4] Y. TURKIN, et al., Fusion Sci. Technol. 50 (2006) 387.

[5] P. XANTHOPOULOS, et al., Phys. Rev. Letters 99 (2007).

[6] F. SCHAUER, et al., Fusion Eng. Des. 88 (2013) 1619

Stellarator modules for PROCESS have been developed and implemented

Future potential for blanket, shield, tritium systems, heating systems,

fuelling and profiles

expertise must be accumulated to further advance the models (concerns

also Tokamak)

Outlook :

Stellarator-Specific Developments for the

Systems Code PROCESS

2nd IAEA DEMO workshop, 17 – 20 December 2013, Vienna, Austria

1. Motivation

In order to study and design plant layouts for next-

step fusion devices, Fig. 1, systems codes for overall

performance assessments and reactor economy

studies are employed. The code package

PROCESS [1] is a tool widely used for Tokamak

systems studies. In this study, however, the

application of PROCESS to Stellarators is

addressed.

3-D GENE

1-D Transport Code

0-D PROCESS

cTLw ,,

renE f,

The existing coil design of Helias 5-B [6]

builds the basis of this model which is

scaled according to the geometry

employing the following scaling factors: This model relates the power crossing the separatrix with

an effective wetted area allowing estimation of the

expected heat load with the following assumptions [10, 11]:

1) Large frad at X-point

2) Diffusive cross-field transport

Generally, systems code employ empirical confinement time scalings to describe and

estimate the plasma transport in fusion devices. But the resulting power balance is very

sensitive to the chosen scaling, Fig. 2. Therefore a predictive ansatz is followed to derive a

confinement time scaling based on most recent advancements of plasma modelling from 1-D

simulations [4] which employ a combination of neoclassical and ITG turbulence transport [5].

a

s

x

radSOLdiv f

c

mRF

fPq

lim

4

1

• Current / magn. Energy / max. field on coil / winding pack dimensions

• Divertor size / heat load

• Power balance /

reactor performance

● Application of PROCESS for Stellarator system studies

● Comparative studies Tokamak / Stellarator

● Stellarator COE-scaling, minimal size, …

4. Plasma Transport 3. Plasma Geometry

5. Modular Coils

6. Island Divertor

effm

m

n

nn

nm

m

m

n

nn

nm

rAV

Nnvmuszvusz

NnvmusRvusR

,,

)sin()(),,(

)cos()(),,(

max max

max

max max

max

0

,

0

,

The plasma geometry is described by

the Fourier coefficients of the LCFS

obtained from VMEC [3].

• Important for neutron / heat fluxes

2. PROCESS Review

Module Tokamak Stellarator

Plasma Geometry Elliptic-axisymmetric Fully 3-D

Coils (incl. currents,

stresses, etc.)

Identical planar D-shaped coils Different non-planar modular coils

Plasma Transport Empirical confinement time scaling

(basically anomal. tr.)

Prevalence of neoclassic effects

(ions, iompurities), Er 3D anomalous

transport, …

Divertor Single/double null divertor Island divertor

vs.

New developments required:

Very general model, applicable for ALL

configurations, arbitrarily scaleable

lim

xD Fn

mRL

lim

2

n

mR2

Plasma core

helical (n/m resonance)

radial

n

mR2

X-point of n/m resonance

DT nLL 2

xFn

mR2

Fx=channel broadening

Divertor plate

Island

B

RR

Rf

5

0

Ratio of major radii

Bcoil

coils

D

Df

5,

Ratio of coil width

RBB ffII 5

[MA-turns] total coil current

4/3

5

5

B

mag

BstrucW

WMM

[t] total mass of support structure

(empirical scaling [7])

Assumptions:

- Coils (turns) are approximated by circular filaments

- Inductance / field can be calculated in good approximation

using elliptic integrals

- (code by F. Schauer)

max

4/1

max

339.10 )2

B

Bfq

Equation (2) from [9]:

(Nb3Sn ITER scaling)

Equation (1) from field calculations

by iterating fq :

)( )1 maxmax qfBB

Example:

BWP

WPq

A

Af

5,

Field calculations [8]:

HSR4/18

parameters

Geometry:

|| q

2/1

s

TXq

c

L

TXL

9. References

Device Coil Model W7-X

Coil Length [m] 8.6 8.5

Field on Axis [T] 3.0 3.0

Field on Coil [T] 6.6 6.7

Magnetic Energy [MJ] 680 620

Mass of Sup.Struc. [t] 206 ~300

Winding Pack [m*m] 0.17 x 0.18 0.18 x 0.19

Ampere Turns [MA] 1.74 1.74

Total weight of Coils [t] 68 40

Material NbTi scaling NbTi

Heat flux:

qT

RadSOL

eff

Divdiv

L

PP

A

Pq

Ratio of WP-area

Consistent coil cross-section:

But:

- Coil cross-section is

free parameter

- Small correction

factors for Coil shape

In order to incorporate a

Stellarator module in the

systems code PROCESS,

Stellarator-specific models

must be considered which

can reflect the differences

due to the confinement

concept.

Fig. 1: Dimensionless parameter representation for

measuring the reactor relevance of Stellarator

experiments [2]

Fig. 2

?

Coil model: Divertor model:

[7] F.C. MOON, J. Appl. Phys. 53 (1982).

[8] S. BABIC, et al., Transactions on Magnetcis 46 (2010) 3591.

[9] Y. ILYIN, et al., Supercond. Sci. Technol. 20 (2007) 186.

[10] Y. FENG, et al., Nucl. Fusion 45 (2005) 1684.

[11] Y. FENG, et al., Nucl. Fusion 47 (2007) 1265.

8. Conclusions

7. Test Case: Wendelstein 7-X

The validity of the coil and divertor model is assessed by comparison with values from W7-X.

Exploration of parameter space and design points

Output parameters: Island Divertor model 1) / 2) W7-X EMC3

Island size [cm] 19 13.2 14

Delta [cm] 12.5 12.5 12.5

Divertor plate length [m] 1.9 1.4 1~1.5

Power decay width [cm] 6.1 8.2 7.4

Effective wetted area [m²] 1.1 1.1 1~2

Heat load “peak” [MW/m²] 8.3 8.4 6.5

Heat load “avg.” [MW/m²] 4.2 4.2 4.4

5.50 R

MWPSOL 10

2lim

05.0radf

eVT 15

sm²5.1

001.0, nm

rb

0005.0, nm

rb

1) 2)

Although the coil model is downscaled a

factor four from Helias 5-B, good

qualitative and quantitative agreement is

found. The only exception is the mass of

support structure which was not

optimised for W7-X.

Good qualitative agreement is found

between the island divertor model and

EMC3-Eirene.