1. Steady state tokamak research
Lecture 3 at ASIPP, May 15, 2013
Steady state tokamak research
( Power and particle handling –
Is H-mode relevant for fusion reactor?)
M. Kikuchi
Supreme Researcher, JAEA
Chairman, Nuclear Fusion Board of Editors
Guest Professor, ILE Osaka University
Visiting Professor, Fudan University, SWIP
Guest Lecturer, the University of Tokyo
Acknowledgement:
A. Fujisawa for turbulence & measurement
L. Villard, A. Fasoli and TCV team
R. Goldston for SOL heat flow scaling
J. Rice, B. Lipschultz for C-Mod, I-mode
H. Sugama for NC polarization
Wulu Zhong/X. Duan for ITG/TEM work
Pat Diamond for discussion (WCI symposium)

2. Motivation of this talk
“Tokamak” is a most promising concept with its excellent energy confinement.
Tokamak with D-shaped, H-mode is optimized for core confinement.
3. Steady state operation needs more work (see my Reviews of Modern Physics (2012).

3. Motivation of this talk
Recent papers by Goldston (NF2012) and Eich(PRL2011) casted important question on reactor power handling in H-mode. Prediction for ITER heat flux 1/e length lq-SOL=5mm -> 1mm.
2. ITER may be able to manage power handling
for lower Pf~0.5GW and short pulse tduration~400s
by temporary measures such as RMP, pellet pace making, etc.
3. But DEMO/Commercial requires
Pf~3GW & tduration~10Months.
This may require
fundamental change in design philosophy
for tokamak reactor configuration.
“Optimize CORE” -> “Optimize power handling”.

4. Present Fusion power handling scenario
is very challenging
Surface / Volume ratio is small in Fusion but large in Fission
1000
Fission
100
w/o RRC
~1MW/m2 10
Fusion Divertor
(even with RRC)
Heat Flux (MW/m2)
Fossil
1.0
Fusion 1st wall
~0.3MW/m2
High thermal efficiency may be possible only at low heat flux!!
RRC=Remote Radiative Cooling
0.1
10-3s
1 year
Duration

5. Any energy system (Fusion) must have reliable heat exhaust scenario
Tokamak configuration is optimized for good confinement, but not for power handling.
[1] D-shape is good (MHD) for high pedestal pressure with H-mode (ETB), leading to large DW loss during ELM.
Temporary measure : RMP, Pellet pacing/SMBI
[2] D-shape leads to X-point toward small R region. This makes power handling more difficult.
Temporary measure : Snow flake, Super X

6. Do we see significant progress in these 20 years?
DEMO : Strong D and impurity puffs at divertor, shallow pellet at SOL
Ueda, Kikuchi NF1992
SOL transport : Sophisticated control is required to reduce q~7MW/m2 even with Bohm diffusion (L-mode)
Fe puff = 0.01Gp
Q=600MW
Gp=2.5x1023/s
tE=1.4s
tp=0.5s
Gas puff 7Gp
Imp. puff 0.01Gp
High Z : sheath acceleration (important even for He)
Stable semi-detach is challenging
In reactor : one failure is serious !!
Kajita, NF2009 (Top10) W nano structure

7. Divertor Plasma Control (Fluid simulation)
Should be kinetic at SOL !!
Imp. force balance
Particle balance
Ion force balance
Albedo=0.96
Ion energy balance
Electron energy balance
Ueda, Kikuchi, et al. NF1992
Bohm diffusion is assumed for SOL particle transport perpendicular to flux surface.

8. Where is question on power handling?
SOL heat flux e-folding length lq-SOL R
1mm
5mm
lq~rp
Previous estimate for ITER:5mm
Recent estimate for ITER:1mm
R. Goldston NF2012. H-mode SOL
Note: L-mode is governed by different physics , empirical scaling 1cm for ITER
Figure (Federici, NF2001)
Div heat flux e-folding length lq-div is larger by flux expansion ratio for attached plasma.

9. 2nd Goldston scaling(l~rp )
What is key physics of Goldston scaling?
(neo)classical particle transport in H-mode
Grad /curvature B drift into SOL
Parallel flow connect top and bottom
PSOL is Spitzer thermal conduction
Assumed as same order
<vd>
<vd>
l// l
0.5cs
2nd Goldston scaling(l~rp )
Fast parallel SOL flow reduces l to 1mm!!
ion
electron
A. Chankin NF2007:
Fast parallel flow ~ 0.5Cs comes not from fluid simulation, unresolved issue.

10. Experimental result seems in agreement with Goldston scaling
C-Mod (Bp~BpITER) SOL e-folding length~1mm
Key evidences :
H-mode particle flux from separatrix ~ neoclassical drift flux.
Particle flux GpELM free H-mode ~0.1 GpL-mode
is too low and,
Required flux multiplication factor G
becomes larger.
Tdiv ~ q//div / (GGp/ln)
Scale length difference ln>>lq
especially in H-mode
4. ELM to enhance Gp :
ELM must be minute.
Controllability of ELM Gp << L-mode
B. Lipschultz, FESAC meeting July, 2012
“ Goldston scaling needs more check.”

11. Why SOL flow is so fast as 0.5Cs ?
Takizuka, NF2009 showed PARASOL PIC simulation reproduces correct SOL flow pattern and fast SOL flow but not Er effect.
Trapped & Circulating ion excursion across the separatrix
comparably kick parallel ion flow to be 0.5Cs like a NC parallel viscous force!! Takizuka, CPP2010 (PET12)
- It is ion convective flux !! -

12. Can we increase GpH-mode?
Key questions :
Can we increase GpH-mode?
High recycling at main SOL is prohibitive!
2. Can we reduce SOL flow speed?
Drift across flux surface is key!
If not, shall we kill H-mode?
L-mode is best but not sufficient
I-mode as an alternative path?
4. High edge pedestal is good choice?
Shall we reduce edge beta limit for small ELM?

13. Modify H-mode to more high recycling?
Gas puffing at main chamber is prohibitive!!
[1] Wall saturation is natural consequence of steady state tokamak reactor.
[2] Ti at mid-plane SOL is order of eV, strong gas puff at mid-plane produces energetic neutrals to erode wall a few cm/year.
[3] DEGAS simulation in typical JT-60U condition showing non-negligible population of fast neutrals ( eV).
[4] Therefore control of neutral around main first wall is important.
Kikuchi, FED2006

14. Issues in present reactor design philosophy
(A) : Optimization of Core plasma
SSTR1990
(B) : Divertor design to match (A)
(C) : consistency of (A)& (B)
D-shape/H-mode is thought as optimum for CORE.
D-shape : Rdiv << Rp : bad for power handling !
H-mode : Large Pedge -> Large ELM energy loss !
3. H-mode : Low particle flux !
4. D shape : huge Amp Turn for “snow flake”.
5. D-shape : inboard blanket design not easy. Rp
Rdiv
Level of problem :
D-shaped > H-mode

15. I-mode (MIT) with peaked ne may be better, but --
I-mode : Grad B away from X-point and need high power L -> I (H) mode
High edge Te (low collisionality).
L-mode like tp but at lower edge ne. Note : Reactor needs high SOL ne.
[ NSTX Li discharge has high Te and low ne]
Trapped ion orbit
Takizuka CPP2010
Whyte NF2010
I-mode geometry has even faster SOL flow
-> leads to lower edge density?

16. ‘Core the first’ is not a good design philosophy
Think different !
First priority
：Configuration optimization
on power handling
(B)
(1) Core to
match (A)
(2) Divertor to
match (A)
Integration to
match (A)
We have rich knowledge

17. First Step : Divertor priority higher than core!
Stay foolish !
- S. Jobes -
A choice - negative D
Make edge pedestal b limit low!
Stay in L-mode edge or I-mode?
Find new transport reduction physics!
Ex.
Reactor core is more collisionless.
Optimization of TEM
- Trapped electron precession
Negative D reduce TEM growth.

18. Make power handling easier by an order of magnitude
R=7m, a=2.7m (A=2.6)
Standard D shape : Rx=4.3m
Inverted D shape : Rx=9.7m
Factor of 2.5 for Rdiv
Negative D makes DN possible
Factor of
(care on up-down asymmetry, controllability)
Snow flake at Rx : Factor of 2-3
Factors : 2.5 x 2 x 2 =10 !!!
4.3m
Note:
- DN in D-shape is difficult for piping to inboard blanket.
- Snowflake needs internal PF coil to reduce AT.
- Outboard is much easier to install internal PF.
Field becomes stiff by near-by PF coils
NbTi is possible at low field.
9.7m

19. MHD stability of negative triangular plasma
Negative delta has higher frequency ELM.
Strongly shaped negative delta has higher edge pressure limit at low J///<J> due to large shear.
Pochelon PFR2012
Courtesy : TCV team

20. Ip, Bt Structure of SOL flow in negative D High field side:
There is no trapped particles across Separatrix.
-> Absence of parallel acceleration mechanism
-> Absence of subsonic flow?
Ip, Bt
Low field side:
SOL is almost vertical
-> No NC drift across
separatrix.
-> No change in
pressure anisotropy
-> Do we see parallel
viscous force?
Larger local pitch
-> shorter connection L
Near X-point
-> lower local pitch
by snow flake

21. Ip, Bt Banana orbit loss in negative D Confined Banana :
Larger than banana width from separatrix, trapped ions will be confined.
Lost Banana:
Near the separatrix,
we have lost banana orbit.
-> This may induce Er<0 and resultant counter toroidal rotation >> standard D.
-> Effective RWM stabilization.
-> Nullify parallel flow acceleration in low field SOL.
Ip, Bt

22. 2nd Step : Consistent core plasma!
There are two paradigm to suppress turbulent transport
Flow shear/zonal flow suppression
De-resonance of trapped particle precession with TEM
Operationally, we have 3 core improved regimes
(See my RMP paper)
Weak positive shear
(High bp mode, optimized shear, improved H, etc)
2. Negative shear
(NS, RS, NCS, etc)
3. Current Hole
See Fujita NF review paper.

23. Negative d and Shafranov shift
Good for high bp scenario since Shafranov shift increases with bp
Precession drift
Negative d can reduce TEM growth rate
B.B. Kadomtsev, NF 1971
Shafranov shift can change precession drift
Connor, NF 1983
G. Rewoldt, PF 1982

24. Increasing experimental evidence of TEM/ITG transition
Wulu Zhong, 2nd APTWG
Tore Supra expl.
Dispersion relation for TEM/ITG modes in strong ballooning limit.
Weiland textbook, 2000
Also, J. Rice, FEC2012 bifurcation of intrinsic rotation TEM/ITG

25. Shaping effect of Residual Zonal Flow (RZF)
Xiao-Catto PoP2006, 2007
Belli, Hammett, Dorland, PoP2008
Key is to reduce NC polarization
Radial profile of d
- dd/dr is key to RZF -
NC polarization ~ (Banana width)2
Negative delta : strong outboard Bp
-> smaller banana width!!
Elongation increases RZF
Negative d may weakly reduces RZF.
Xiao PoP2007
GS2
GS2
(1)
(1)
Xiao PoP2007
Understanding of RZF in negative triangularity (k,-d, D) is necessary

26. Core improved confinements
WS regime
NS regime
CH regime
Reduce dp/dr
at qmin
Wall stab.
q(0) up
Kikuchi NF1990, PPCF1993
Ozeki IAEA1992
FujitaPRL2001,05
OzekiEPS2011
FujitaNF2011

27. TCV negative triangularity experiment
Camenen NF2007
Negative triangularity produces large Shafranov shift, which changes precession drift of trapped electron. This leads to a change in TEM stability.
Large tilting in negative delta
Similar effect like Er’ ?
More tilted
Less tilted
Non-locality will be reduced in Reactor

28. Summary
The power system should have reliable power handling but fusion power handling is challenging in divertor.
H-mode with D-shaping “Optimize Core choice” seems enhancing its challenge.
Tokamak physics is ready for new innovation. Good knowledge in core physics will make innovation possible.
Power handling-driven Tokamak optimization needs good core physics innovation.
We proposed “Negative D” as a candidate of this challenge.

29. We probably need order of magnitude change to solve this issue.
Prof. P.H. Rebut : Best Scientist in engineering and physics
He is in favor of Fusion-Fission Hybrid.
I asked him why?
P.H. Rebut : There is no solution for power handing in pure fusion, right now. Stay low fusion power. We have to boost fusion energy to have net energy. Fission is most effective to boost.
His word is important from engineering point of view on pure fusion.
We probably need order of magnitude change to solve this issue.