1. Ringberg Theory Meeting
Impact of momentum correction on bootstrap current and ECCD in W7-X Yu. Turkin, C.D. Beidler, H. Maaßberg, N.B.Marushchenko
Max-Planck-Institut fűr Plasmaphysik ,17491 Greifswald, Germany
2008, November 17

2. Outline
Improved kinetic model (with momentum conservation and generalized formulation for trapped particle fraction ft ) is implemented in ray tracing and transport codes
Results of predictive modeling of ECR heating of plasma in W7-X with focus on levels of bootstrap and driven currents are presented:
Bootstrap current: DKES approach and Taguchi techniques (realization by C. Beider)
Current drive models: high velocity limit (Lin-Liu, Taguchi-Fish) none- and relativistic Spitzer function, fraction of trap. particle: collisionless limit and generalized formulation.
Bootstrap current for different magnetic configuration; density scan BC/ECCD for X2, O2
Motivation of this work is a necessity to know/control the toroidal currents in W7-X

3. Geometry of the ECRH system
ECRH system: 10beams x 1MW , 30min

4. Geometry of the ECRH system
ECRH system: 10beams x 1MW , 30min

5. Geometry of the ECRH beams
6 beams are shown, beam in red is the spare beam
the other six beams are located in the next module;
The beams propagate at angles optimized with respect to the absorption efficiency for O2 or X3-mode operations C1
reflecting stainless-steel liners
V. Erckmann, P. Brand et al. Electron cyclotron heating for W7-X: physics and technology. Fusion Science and Technology, 52, 291(2007).

6. Transport Equations Ray tracing code TRAVIS calculates heating source
Electric field
Diffusion equation for current
Boundary conditions:

7. Diffusion model Anomalous heat diffusivity at the edge only.
D22 neoclassical heat diffusivity
To avoid any confusion I would call this empirical diffusivity, because we don’t have any well established anomalous model.

8. Thermal transport matrix
Neoclassical transport matrix D is the energy convolution of monoenergetic coefficients produced by DKES runs.
Typical file of monoenergetic coefficients created by H.Maassberg
contains ~3000 records D(r, Er/v, /v)
Thermal D = Interpolation + Integrating with Maxwell distribution function, New! - this Database is used by C. Beidler for realization of Taguchi techniques
Our working set for W7-X:
Standard Configuration: <b>=0%, 2%, 4%; Low Mirror; High Mirror

9. Diffusion model with momentum correction
Taguchi techniques
realization by C. Beider,
Compare with ‚old‘ model
To avoid any confusion I would call this empirical diffusivity, because we don’t have any well established anomalous model.

10. Simulation procedure run till steady-state
In simulation density is kept fixed.
Density is rather flat: (W7-AS -> most shots have flat profiles)
Temperatures, Fluxes, radial Electric field are calculated self-consistently
Power deposition is updated periodically calling the ray tracing code TRAVIS with the new ne, Te
semi-self-consistent coupling of codes
run till steady-state

11. Dependencies on configuration
Standard Configuration: <b>=0%; 2%; 4%
Low Mirror
High Mirror
On-axis heating -> electron root
Off-axis heating -> ion root only

12. Dependencies on configurationSC
SC 4%
Standard Configuration; Low Mirror; High Mirror HM LM
Full line and symbol ---
‘Momentum corrected’ bootstrap current
B/B00=1+b01cos(5) +b11cos(-5)… LM
SC 4% HM

13. Dependencies on configurationSC
SC 4%
Standard Configuration; Low Mirror; High Mirror HM LM
On-axis heating with electron root
Off-axis heating with ion root only

14. ECCD: Dependencies on configuration
Max. available ECCD at X2-mode
ECCD in case of on-axis heating
ECCD in case of off-axis heating
<b>=2%;

15. configuration scan : interim summary
We have done configuration scan for n=1020m-3 and X2-mode ECRH:
Momentum correction for IBC : IBC
Bootstrap current increases with mirror term decrease, but….
Enough ECCD to compensate bootstrap current
Let’s move to high density: X2  O2 (2·1020m-3)
density scan for <b>=2%

16. Density scan for 5MW ECRH
With O2-mode we don’t have freedom of launching angles as for case of X2.
That why we choose only 5MW (5 beams)
Only beams produced counter current are used

17. BC : Density scan for 5MW ECRHX2 O2
Standard Configuration, <b>=2%
Full line and symbol ---
‘Momentum corrected’ bootstrap current

18. ECCD: Density scan for 5MW ECRHX2
No significant difference between and
high velocity limit (Lin-Liu, Taguchi-Fish)
relativistic Spitzer function, ft in col.-less limit
non-relativistic Spitzer function, ft in col.-less limit
non-relativistic Spitzer function, ft is general (new!) ft
n/v

19. BC and ECCD : density scan for 5MW ECRHX2
Our latest theoretical model for plasma currents:
bootstrap current with momentum correction
ECCD is calculated using relativistic Spitzer function with momentum conservation, ft in col.-less limit

20. Magnetic configuration control
Before summary: why precise calculations of currents ?
Magnetic configuration control
W7-X magnetic configuration concept:
Super conductive coils, no Ohmic transformer, low shear machine, flat iota, minimized bootstrap current
Toroidal current changes rotational transform and magnetic configuration : low order rational values of iota can appear (islands inside) moves X-point -> potential danger for island divertor
Fig. By A. Werner

21. Iota modification due to currents
Before summary: why precise calculation of currents
Ibc=+72kA
Ieccd=-72kA
So called current hole owing strong on-axis current drive
Rotational transform calculation:
-- current free part of the rotational transform
see susceptance matrix S definition in P.I. Strand and W.A. Houlberg.. Physics of Plasmas. 8, 2782(2001).

22. More problems: time scales
no transformer
 skin-time ~ 1..2sec ~ a2 ,
L/R ~ sec ~ Rmajor 
diagnostics : measurements of current (profile) ?
…. However, control of current is other topic….

23. Summary & outlook
Strategy is to have/create/apply the best tools available (H. Maassberg)
Improved kinetic model (with momentum conservation and general ft ) is implemented in ray tracing and transport codes
Perpendicular transport is not affected
BC is noticeably affected  it is decreased we have benchmarked two modules written by H.M. and by C.B.
For ECCD relativism is more important (at least for 2nd mode heating) ? relativistic Spitzer function for general ft is needed.
Awaiting tasks: current evolution, design the current free scenarios:
10-30sec discharges, up to 30min discharges,
avoid flat edge-iota,
rationals, current hole
NBCD
Testing, benchmarking, extend DB of mag. configurations, …….

24. The END

25. Can we trust in our modeling? W-7x tau_E

26. Neoclassical predictions for LHD (Japan)
Scan: n = (0.4 – 1) x 1020m-3
P = (1 – 4) MW
B = 3T
Configuration:
lhd_boz10.r360q100b004a8020

27. Why do we use edge an ~ 1/n ?
This choice consistent with W7-AS experience: some analysis of experiment gives D~ P0.85 / n
LHD, W7-AS : no profile stiffness*: central part is not affected by the edge transport
we choose 1/n ; edge 1-3m2/s
For our calculations:
5 time increase of edge an leads only to 20% degradation of tE
Transport is local in our modelling and does not necessarily influence the core transport. The profile stiffness was never seen in W7-AS
However something must be added at the edge, because with only neoclassic losses the transport is stopped. In lack of knowledge we choose
*IAEA Fusion Energy Conference *W7-AS: One step of the Wendelstein stellarator line, F. Wagner et al, PHYS. OF PLASMAS, ,

28. 4MW ECRH, density ne(0)=0.6
Dependencies of tE, Te(0),Ti(0), <b> on edge value of anomalous heat diffusivity 5 10
Te(0), keV
Ti(0) c
edge
, m2/s 5 10 1
1.5 2
2.5
<b>, % c
edge
, m2/s 5 10
0.3
0.4
0.5 t E c
edge
, m2/s
, s

29. Collection of Plasma Profiles

30. Geometry of the ECRH system
ECRH system: 10beams x 1MW , 30min