平成24	  年度 ダイバータおよびＰＷＩ合同研究会	  2012年7月23−24日	  筑波大学	

タングステンPWI	  モデリング進展	  原型炉タングステン壁損耗シミュレーション	
星野一生1,	  藤間光徳2,	  清水勝宏1,	  朝倉伸幸1,	  	  飛田健次1,	  畑山明聖2,	  滝塚知典3	  	1	  原子力機構 2	  慶應義塾大学 3	  大阪大学	

2	 /	  16	Background	
Tungsten (W) is the most preferable
candidate for the plasma facing material
in the DEMO fusion reactor.
From the viewpoint of erosion by
the seeded impurity species,
thick W armor is desirable.

5mm	  	( 5mm/year=0.16x10-9 m/s )Mono-­‐block	  W	  divertor	  for	  SlimCS	
(S.Suzuki,FED2006)	

On the other hand, it is necessary to make the W armor as thin as
possible, from the following points of view:(i) sufficient heat removal for allowed operation temperature,(ii) avoidance of decrease in tritium breeding ratioby the neutron capture,(iii) large decay heat in unit volume

Erosion	  of	  the	  W	  armor	  of	  SlimCS*	  in	  DEMO	  is	  	  numerically	  analyzed	  by	  SONIC	  and	  IMPGYRO-­‐EDDY	SlimCS (K. Tobita., NF 47(2007)892., K. Tobita., NF 49(2009)075029.)
Conceptual DEMO design for Pfus ≤3 GW (with reduced-size CS (R = 5.5m and A=2.6) 	

Simulation study for power handling in DEMO divertor 	3	 /	  16	

N.Asakura,	  JPFR	  Series	  2010	  	SONIC simulation for SlimCS demonstrates
the detached divertor plasma by the V-shaped
corner and large Ar impurity seeding.

Case-1:Case-2:Case-3:
Bottom slot V-corner
V-corner(nAr/ni=2%)	  (nAr/ni=2%)	  (nAr/ni=5%)	 

However, still qpk,div > 10MW/m2 (Pfus=3GW)	
For further reduction of the divertor heat load,
investigation of effects of seeded impurity
transport, kind of impurity, divertor geometry,advanced divertor and so on, are in progress.	
ex.	  Divertor	  geometry	  eﬀect	  (simple	  impurity	  model)	
(a)

Std	

/0

neutralradiation
recombination/.

ion heat

6

electron heat4
20.

+.,.3.

.,.3 .,/. .,/3 .,0. .,03 .,1.

Bgqr_lacdpmkqrpgicnmglr&k'/2

neutral

(b)

/0

(a)

Longleg	 radiation-3.5

recombination/.

ion heat

6

electron heat

4

Std	

K.Hoshino,	  PET12,	  (CPP2012)	
Prad (MW/m3)
100
50
10
5.0-4.0Z (m)/2/4
Bgtcprmpfc_rjm_b&KU-k0'

Bgtcprmpfc_rjm_b&KU-k0'/42(b)Longleg	Prad (MW/m3)
10050
105.0-4.5-5.00.

+.,.3.

.,.3 .,/. .,/3 .,0. .,03 .,1.

Bgqr_lacdpmkqrpgicnmglr&k'-5.5
5.0

5.5
6.0
R (m)

6.5

5.0

5.5
6.0
R (m)

6.5

Suite of integrated divertor codes SONIC*	D	  ionparXcle	  source	  momentum	  energy	  loss	

Steady-­‐State	  soluXon	  is	  obtained	  within	  10	  Hours	  on	  BA-­‐IFERC-­‐CSC	  energy	  loss		  	  	  	  (512PE)	  	SONICD	  neutralinteracEon

generaXon	  charge	  exchange	

4	 /	  16	

impurity

input	  parameters	
Core boundary at r/a=0.95: Fi = 6×1022 s-1
D2 Gas Puﬀ: 6×1022 s-1 from mid-plane 4×1022 s-1 from outer div.
SPump = 200 m3/s,
D=0.3 m2/s χ=1.0 m2/s （spatially constant）
Ar gas puﬀ to the outer divertor to achive Prad/Pin=92%	
*H. Kawashima, Plasma Fusion Res. 1(2006)031, K. Shimizu, Nucl. Fusion 49(2009)065028.

/	  16	

IMPGYRO code	
Monte-Carlo Transport Code for High-Z impurity	l Coupled to Erosion / Redeposition CodeDirect comparison with experiments(Background	  plasma	  proﬁle	  is	  given	  by	  	  SOLPS	  or	  SONIC)	  Total
Z=0
Z=1
Z=2
Z=3
Z=40.10.05(EDDY: K.Ohya, Physica. Script. T124 (2006) 70)l 3D Realistic Geometry(K.Hoshino, PSI08)

P(!)

l Full Gyro-Motion without
Guiding-Center Approximation

Incident Angle Distribution
0.15

00

10 20 30 40 50 60 70 80 90
Incident angle ! [degree]

Analysis of JT-60U W-Redep.
(K.Hoshino, JSPF08)l Implicit MC model for
multi-step Ionization/recombination processesfor high-Z impurityl Binary Collision Model for Coulomb Collision
with background plasma
Evaluation of Particle/Momentum/Energy
Source and Loss by High-Z impurities
for the background plasma 	
A. Fukano, JNM363-365(2007)211-215 M. Toma, JNM390-391, 207 (2009).	

Elec. radiation loss due to W
(M.Toma, JSPF08)6	 /	  16	Assumptions / Note	-Analysis is performed for DEMO conceptual design SlimCS
3 cases: 3GW, 2GW, longleg
Background plasma profile is fixed during W transport simulation.
Initial W is generated only from the outer divertor by Ar sputtering.
Self-sputtering/reflection is taken into account, but until 3 times.
The power control in the divertor has not been overcome yet,i.e., qpk,div>10MW/m2 in the Pfus=3GW case	

Numerical	  grid	  for	  SlimCS	

For	  3GW	  and	  2GW	  case	For	  Long-­‐leg	  case	3GW case (reference): divertor plasma profile 	
Pin=500MW	  	  	  Prad=460MW	  	  nmid=2.94x1019	  m-­‐3	  	FAr	  =	  1.09x1021	  s-­‐1	  qpk,	  od	  =	  20MW/m2	
outer	  divertor	

Ar	7	 /	  16	

2D	  proﬁles	  near	  the	  outer	  divertor	  target	

3GW case: 2D profiles of W density	log(nw)	

1st	  generaXon	
Fcore=0	8	 /	  16	log(nw)	

2nd	  generaXon	
Fcore=	  1.6x1018	  s-­‐1	  log(nw)	

1st generation is relatively localized,
while others are widely distributed.
Emitted energy of 1st generation
is lower than others.
3rd	  generaXon	
Fcore=	  2.8x1019	  s-­‐1	  The W influx to the core become highin higher generation.

3GW case: dep./ero. speed at outer divertor	

9	 /	  16	In the 1st generation, most of W
particles deposit near theerosion layer.

outer	  divertor	  	1st	  generaXon	

In 2nd and 3rd generations,
deposition rate decreases,
because W particles with highemitted energy are transported
upstream and some of them
deposit on the dome.

2nd	  generaXon	

3rd	  generaXon	

2GW case: divertor plasma profile	
Pin=320MW	  	  Prad=294.4MW	  	  nmid=2.76x1019	  m-­‐3	  	FAr	  =	  0.70x1021	  s-­‐1	  qpk,	  od	  =	  	  6.6MW/m2	

outer	  divertor	

Ar	10	 /	  16	2D	  proﬁles	  near	  the	  outer	  divertor	  target	

2GW case: 2D profiles of W density	log(nw)	

1st	  generaXon	
Fcore=	  5.2x1016	  s-­‐1	  11	 /	  16	log(nw)	

2nd	  generaXon	
Fcore=	  2.1x1017	  s-­‐1	  log(nw)	

Tendency is similar to the 3GW case.

3rd	  generaXon	
Fcore=	  2.9x1018	  s-­‐1	  2GW case: dep./ero. speed at outer divertor 	

12	 /	  16	The erosion/deposition speed
decreases by 2 orders ofmagnitude compared with the3GW case.
outer	  divertor	  	1st	  generaXon	

2nd	  generaXon	

3rd	  generaXon	

Long-leg case (Pfus=3GW): divertor plasma profile	
Pin=	  500MW	  	  Prad=	  460MW	  	  nmid=	  3.75x1019	  m-­‐3	  	FAr	  =	  0.49x1021	  s-­‐1	  qpk,	  od	  =	  	  15	  MW/m2	

outer	  divertor	

Ar	13	 /	  16	2D	  proﬁles	  near	  the	  outer	  divertor	  target	long-leg case: 2D profiles of W density 	log(nw)	

1st	  generaXon	
Fcore=	  3.6x1019	  s-­‐1	  14	 /	  16	log(nw)	

2nd	  generaXon	
Fcore=	  1.1x1020	  s-­‐1	  log(nw)	

Background plasma flow and the resultant
shielding effect is weak due to the highrecycling. Therefore the sputtered W iseasily transported upstream.

3rd	  generaXon	
Fcore=	  2.0x1020	  s-­‐1	  Although the amount of sputtered W issmall, the influx to the core is larger thanother case due to the small shielding
effect.	

15	 /	  16	Long-leg case: dep./ero. speed at outer divertor	
weded	  area	

outer	  divertor	  	1st	  generaXon	

Erosion/deposition speed ismuch smaller than other cases.
Because of weak shielding
effect, erosion/deposition of W
can be observed on the baffle.

2nd	  generaXon	

3rd	  generaXon	16	 /	  16	

Summary	Erosion and deposition of W armor in SlimCS has been analyzed
by using SONIC and IMPGYRO-EDDY.
3GW case:

Large erosion by the self-sputtering. ( strong background flowà large incident energy of W à large self-sputtering)

2GW case:qpk,od is less than 7MW/m2, but erosion is still too large as sameas the 3GW case.

long-leg case: Erosion is significantly small, but influx to the core isvery large because of weak shielding effect.
In the present condition, the erosion speed cannot be acceptable. The divertor
plasma design for W armor lifetime is necessary as well as the huge power
handling. ex) flow control by puff and pump, low Te and Ti by full detachment.
W density in the divertor is considerably high. The significant radiation cooling andthe resultant temperature decreases are expected. Therefore, the self-consistentanalysis by coupled of plasma transport with W impurity generation/transport arenecessary. (cf. SOLPS-IMPGYRO, )In the self-consistent analysis, the erosion of W armor is possibly decreased by
the W impurity radiation and the resultant decrease in Te and Ti.