1. J.N. Brooks, A. Hassanein, T. Sizyuk, J.P. Allain
Modeling of plasma/lithium-surface interactions in NSTX: status and key issues
J.N. Brooks, A. Hassanein, T. Sizyuk, J.P. Allain
Purdue University
2nd International Symposium on Lithium Applications for Fusion Devices, PPPL, April , 2011

2. Why analyze NSTX plasma/lithium interactions?
Lithium has been used extensively in NSTX*--will likely continue. Modeling can help explain device performance.
Flowing liquid lithium is a promising candidate for future devices (Fusion Nuclear Science Facility, DEMO, etc.). Code validation & model improvement is possible, using NSTX data.
Concerns for NSTX analysis: Much more difficult to model than future devices
--- Transient conditions: ~1 second pulse
--- Small device–edge/boundary effects dominate
--- Lithium is not a flowing liquid (i.e., is static liquid or solid)
--- Other materials present (C, Mo, etc.)
--- Non-standard boundary conditions
*H.W. Kugel, “NSTX Plasma Response to Lithium Coated Divertor”, PSI-19 (2010), J. Nuc. Mat. to be published.
*C.H. Skinner et al., “Deuterium Retention in NSTX with lithium Conditioning”, ibid,. to be published.

3. Lithium modeling issues
Lithium is the 2nd most complex surface material we have modeled (carbon is first due to chemical sputtering):
D trapping/pumping—highly dependent on surface content/structure
High vapor pressure
Temperature dependent sputtering & evaporation
Material-mixing issues: e.g. Li intercalation in carbon
Liquid vs. solid issues
Most (~2/3) sputtering is Li+ ions
Li+ ion redeposition in sheath and re-emission at surface

4. Past & Current Work-Lithium/NSTX Modeling
Liquid Lithium Divertor (LLD) plasma/surface interaction analysis
[J.N. Brooks, J.P. Allain, T.D. Rognlien, R. Maingi., J. Nuc. Mat (2005)1053]
[J.P. Allain, J.N. Brooks, Nuclear Fusion 51(2011)023002]
static liquid lithium response, low-D recycle plasma
Lithium Inner Divertor (HIBD)
static (pure) liquid Li or solid Li surface, high D-recycle plasma
Mixed material analysis:
 Li + C on Mo inner divertor, high-D-recycle plasma
surface evolution: composition and sputtering
 Li, C detailed analysis; e.g., sputtering of thin Li coatings on graphite

6. REDEP/WBC LLD Analysis
TRIM-SP computed total Li
sputter yields (ion+atom)

7. Interesting physics for sputtered lithium transport in the NSTX low-recycle plasma regime:
Large sputtered atom ionization mean free path, order of 10 cm
Large Li+1 gyroradius ( ~5 mm), due to low B field (0.5T)
Low collisionality of Li ions with plasma; due to high Te, low Ne
 Kinetic, sub-gyro orbit analysis required (i.e. WBC code)

8. WBC Simulation of LLD sputtered lithium transport: 50 trajectories shown;
UEDGE/NSTX GRID
Long mean free paths seen for ionization; subsequent long, complex, ion transport

9. NSTX Liquid Lithium Divertor Analysis-results
Results are encouraging:
--Moderate lithium sputtering; no runaway
--Acceptable Li contamination: ~7% SOL, ~1% Core
--Carbon (2%) flux to LLD appears acceptable
--LLD could apparently handle higher heat flux

10. NSTX is replacing Row 1 Horizontal Inboard Divertor (HIBD) carbon tiles with molybdenum —To reduce carbon sputtering & core plasma carbon content.
We are analyzing Mo, C, Li HIBD (“inner divertor”) sputtering erosion and plasma contamination, with high-recycle plasma.
REDEP/WBC NSTX Inner Divertor Analysis; with high-recycle plasma [with H. Kugel, R. Maingi, C. Skinner, et al.]

11. NSTX Inner Divertor High-Recycling Plasma Solution (J
NSTX Inner Divertor High-Recycling Plasma Solution (J. Canik SOLPS code)
R~1
Peak plasma values
at divertor
Ne ~ 1x1020 m-3
Te ~ 60 eV
strike point

12. Plasma Sheath
Sheath affects transport of sputtered and evaporated Li, and other materials
NSTX has non-standard tokamak boundary conditions—can affect sheath
NSTX sheath analyzed with BPHI-3D code (w/o full turbulence model)
Parameter
Outer divertor/
low-recycle plasma
Inner Divertor/
high-recycle plasma
Magnetic field
0.5 T
1.0 T
Field angle of incidence, from surface 5 3 Te Ne
~250 eV
5x1017 m-3
~50 eV
1x1020 m-3
Normalized sheath potential
e/kTe ~3
Sheath structure
Debye-only
Magnetic + Debye

13. WBC NSTX Lithium Divertor analysis: transport summary for two plasma cases (100,000 histories/simulation)
Parameter
Low-recycle
Plasmaa
High-recycle
Plasma
Location/surface-condition
Outer divertor/
“Liquid Lithium Divertor” (LLD) with high D pumping
Inboard divertor/
nominally C and/or Mo, but with assumed low-D-pumping Li coverageb
Plasma solution/D+ reflection coefficient
UEDGE
R=0.65 [Stotler et al.]
SOLPS
R~1 [Canik]
Peak electron temp. at divertor, eV
247 57
Peak electron density at divertor, m-3
5 x1017
3 x1020
Sheath structure
Debye-only
(~1 mm)
Magnetic + Debye
(~2 mm)
Ionization mean free pathc, mm 64
0.77
Sputtered Li currente (atoms)/D+ ion current to divertor, s-1
1.43 x1020/1.98 x1021
6.12 x1021/4.31 x1022
Fraction redeposited on divertor
.55
.99
Core plasma lithium contamination
potential
~1%
< 0.1%
a Values from [J.P. Allain, J.N. Brooks, Nuclear Fusion 51(2011)023002]
b 300 C surface assumed for D and Li on Li sputter yields
c normal-to-surface; for sputtered Li atoms ionized in divertor region.
d average for redeposited Li ions on respective divertor
e includes sputtered atoms, and sheath-reflected sputtered ions re-emitted as atoms from surface.
Major differences, but acceptable lithium erosion/redeposition in both cases

14. WBC analysis: comparison of three surface materials
NSTX inner divertor, high-recycle regime
a with 1% C+3 and 1% Li+2 plasma impingement
b normal-to-surface; for sputtered atoms ionized in divertor region.
c numerical bound
C and Li net sputter erosion is about 5-10 times higher than Mo erosion
No material highly contaminates core plasma

15. ITMC-DYN Computer Simulation Package ITMC-DYN Integrated Models
Dynamic evolution of mixed materials bombarded with multiple ion beams:
ITMC-DYN Computer Simulation Package
ITMC-DYN Integrated Models
A. Hassanein, “Surface effects on sputtered atoms and their angular and energy dependence”, Fusion Technology 8 (1985) 1735.
T. Sizyuk and A. Hassanein, "Dynamic analysis and evolution of mixed materials bombarded with multiple ions beams", J. Nucl. Materials, 40( 2010)60
T. Sizyuk and A. Hassanein “Dynamic analysis of mixed ion beams/materials effects on the performance of ITER-like devices“, to be published J. Nucl. Mat. (2010)

16. ITMC-DYN analysis: time dependent sputtering of NSTX Mo inner divertor (at strike point); with D, 1% C, 1% Li impingement
Substantial carbon and lithium sputtering occurs by end-of-shot

17. ITMC-DYM Analysis: Spatial distribution of the deposited C and Li impurities in Mo substrate; NSTX Mo inner divertor (at strike point)
C and Li surface contamination extend to ~10 nm
C and Li concentrations peak at ~ 5 nm depth and about equal the Mo concentration

18. Conclusions-NSTX Lithium plasma/surface interactions
Analysis of lithium erosion/transport in NSTX is important, but highly complex. (Results uncertain due to complexity of lithium/NSTX modeling, and general issues in plasma predictive modeling.) Key focus is on mixed-material modeling.
The static liquid lithium divertor (LLD) with high-power, D-trapping plasma shots, is predicted to work well—from the (sputtering & evaporation) erosion standpoint.
A lithium surface—solid or liquid, for low or high D recycle plasma—has high erosion but low core plasma contamination potential (~0.1-1%).
A Mo surface may be substantially changed, in 1 second, by C and Li impingement. Mo core plasma contamination by sputtering appears low (<0.01%), in any event. (Not clear if Mo substantially reduces NSTX core plasma carbon content).
Continuing work: Other plasma solutions (e.g., inner Mo with outer low-recycle LLD), self-consistent material-mixing/evolution, data-calibrated model refinements.
{Supercomputing needed for more complete plasma/material interaction analysis.}