1. *Work performed under the auspices of the U.S. DOE by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-432819 Modeling Boundary Plasma/Neutral Characteristics for ARIES* T.D. Rognlien, G.D. Porter, & M.E. Rensink LLNL ARIES-Pathways Project Meeting Bethesda, MD Oct. 25-26, 2010

2. 2 ARIES October 2010 – 2 Outline 1.Outline of important edge plasma input available for ARIES (1 slide) 2.Our tools and examples of past work (12 slides) 3.Return to discuss the “plans” slide (at any time)

3. 3 ARIES October 2010 – 3 Discussion of plans for edge modeling of ARIES 4 point-designs (similar to ITER concerns) 1.Baseline analysis using documented “best assumptions” –ideally use same divertor geometry and impurity seeding –however, each point design may have different optimal choices, e.g., pedestal density, temperature, and power flux may dictate different geometry and impurity levels 2.Sensitivity studies –turbulent radial transport is largest unknown, but better empirical scaling and turbulence modeling developing (e.g., D, V conv, and  –wall conditions, i.e., sputtering and recycling, especially if mixed material walls/divertor 3.Transient heat and particle fluxes –(small) ELMs are present baseline; impact material fatigue and heat removal & impurity control 4.Ash removal and DT fueling –adequate He pumping is key to divertor geometry choice (#1) –separate D & T recycling/transport; how does T get back in core

4. 4 ARIES October 2010 – 4 Background Mark Tillack & I have been discussing strategies to utilize existing modeling codes In addition to some involvement from me, Gary Porter & Marv Rensink are retired edge physicists interested in part-time involvement Presentation sketches some history/capability and possible contributions to ARIES goals 100 MW/m 150 MW/m 50 MW/m 200 MW/m Near-term facilities ITER NHTX (Princeton) FDF (GA) CTF (Princeton) ARIES-ST 0 Exhaust Power (MW) Major radius (m) Heat flux is a growing issue Interactive questions/discussion encouraged

5. 5 ARIES October 2010 – 5 UEDGE is a 2D plasma/neutral fluid transport code covering closed & open field-line regions Features of UEDGE Physics: –Multispecies plasma; var. n i,e, u ||i,e, T i,e,  –Flux-limited kinetic corrections –Fit radial plasma transport coefficients or coupling to BOUT turbulent fluxes –Reduced Navier-Stokes or Monte Carlo for wall-recycled/sputtered neutrals –Multi-step ionization and recombination Numerics: –Finite Vol.; Newton-Krylov implicit solver –Non-orthogonal mesh for fitting divertor –Steady-state or time dependent –Parallel version with 2D decomposition –PYTHON or BASIS scripting control DIII-D UEDGE mesh

6. 6 ARIES October 2010 – 6 UEDGE is built in a modular fashion UEDGE source code; 98% FORTRAN, 2% C; revision control - CVS/SVN Turbulent fluxes - 3D Fluid BOUT Precond.; NK-solvers Transport equations; multi-species Common utilities & variables Atomic physics tables; ioniz., recomb., rad. or Monte Carlo Neutrals: fluid or Monte Carlo Flux-surface mesh generator BASIS or PYTHON provides scripting control MHD equilibrium Core/wall bdry. conds. External to UEDGE

7. 7 ARIES October 2010 – 7 Some history of UEDGE development & use Marv & I continue to develop UEDGE capabilities & applications −Divertor geometry, cross-field drifts, convective blobs −Double null, fluid or DEGAS-2 neutrals −PFC modeling including APEX, ALPS, ITER −DIII-D, C-Mod, NSTX, & ITER modeling Gary has developed diagnostics/applic. −H-alpha, impurity radiation −Extensive DIII-D, C-Mod, ASDEX-U, JET modeling Also, all 3 of us performed detailed comparative study of FIRE, IGNITOR, & ITER for Snow Mass 2002

8. 8 ARIES October 2010 – 8 ARIES-specific history In 2001, Marv & I performed some simulations for ARIES AT & RS for the APEX project −both solid and liquid wall options were considered −the solid wall option work published as part of Fusion Eng. Design review of edge modeling in 2002 About 2005, T.K. Mau from ARIES visited us a couple of times to learn UEDGE −we started him with our 2002 ARIES-AT example −I believe T.K.’s extensions were part of the published 2006 (Jardin et al.) ARIES paper, but we didn’t participate directly in that extended work 3-weeks ago, A. Mahdavi queried me about our ARIES models & results, & I now understand from Mark that there is some question about the impurity radiation – but Ali & I didn’t discuss any discrepancy; we are interested if there is an issue here

9. 9 ARIES October 2010 – 9 In 2001, we used ARIES AT and FIRE to illustrate options to reduce for divertor heat-flux Rognlien, Rensink, Fusion Eng. Design, 60 (2002) 497. Mantle radiation loss 77% assumed for comparison tilted-plate case - next 47 MW/m 2 ARIES-AT double null, orthogonal plates

10. 10 ARIES October 2010 – 10 Now tilt the divertor plate to reduce the heat-flux – no explicit impurities considered here Rognlien, Rensink, Fusion Eng. Design, 60 (2002) 497. Large mantle radiation loss 77% assumed here

11. 11 ARIES October 2010 – 11 Impact of seeding with neon illustrated by FIRE example – full multi-charge-state simulation; transport each Ne ion Rognlien, Rensink, Fusion Eng. Design, 60 (2002) 497. FIRE heat-flux to outer divertor with neon FIRE geometry/mesh with tilted plates

12. 12 ARIES October 2010 – 12 Radiation power to main-chamber wall computed by mapping local power at each cell as isotropic radiator Rognlien, Rensink, Fusion Eng. Design, 60 (2002) 497. Radiated power computed by method similar to RADLOAD diagnostic in ARIES ‘06 FIRE geometry/mesh with tilted plates (Here neon level slightly increased gives a slowly-evolving detached plasma)

13. 13 ARIES October 2010 – 13 UEDGE simulations for ARIES-AT reported in FED ‘06 used orthogonal plates and a simpler impurity model S. Jardin et al., Fusion Eng. Design, 80 (2005) 25. ARIES-AT double null, orthogonal plates Relation between ‘02 and ‘06 ARIES-AT simulation –’02 consider tilted plates to reduce power, ‘06 did not –‘02 left impurity effect to the FIRE example, ‘06 includes impurities –‘02 FIRE example used non- coronal, multspecies model for Ne, ‘06 used fixed concentration coronal model for Ar –we did the ‘02 modeling, Mau did the ‘06 modeling Any mix can be done in the future

14. 14 ARIES October 2010 – 14 Neutrals can be important; we usually use fluid model for efficiency; can use Monte Carlo, which is similar Radial neutral fueling-flux across separatrix in DIII-D Gap region is beyond normal UEDGE mesh Neutral flux High-energy CX- neutrals can sputter the first wall

15. 15 ARIES October 2010 – 15 Classical ExB and grad_B drifts are important for argon transport into the core plasma of DIII-D (Porter)

16. 16 ARIES October 2010 – 16 Connection to OFES FY10 Joint Research Target on scaling of heat-flux width Primary experimental scaling of heat width narrowing with plasma current, I p ; => heat flux increases –Both DIII-D and NSTX observe strong I p scaling in H-mode –C-Mod may see strong peak heat- flux scaling in EDA-mode (see LaBombard, APS-DPP) – Kinetic ion modeling may help explain the I p scaling a transport model giving 1/I p width can be used in UEDGE DIII-D - Lasnier et al. NSTX - Maingi et al.

17. 17 ARIES October 2010 – 17 Discussion of plans for edge modeling of ARIES 4 point-designs (similar to ITER concerns) 1.Baseline analysis using documented “best assumptions” –ideally use same divertor geometry and impurity seeding –however, each point design may have different optimal choices, e.g., pedestal density, temperature, and power flux may dictate different geometry and impurity levels 2.Sensitivity studies –turbulent radial transport is largest unknown, but better empirical scaling and turbulence modeling developing (e.g., D, V conv, and  –wall conditions, i.e., sputtering and recycling, especially if mixed material walls/divertor 3.Transient heat and particle fluxes –(small) ELMs are present baseline; impact material fatigue and heat removal & impurity control 4.Ash removal and DT fueling –adequate He pumping is key to divertor geometry choice (#1) –separate D & T recycling/transport; how does T get back in core

18. 18 ARIES October 2010 – 18 Summary A width range of edge model experience/tools available Previous ARIES modeling has made various assumptions, but we understand the basic consequences We should continue discussion of priorities for ARIES edge modeling

19. 19 ARIES October 2010 – 19 Backup slides

20. 20 ARIES October 2010 – 20 Some of what you should know above edge/PMI modeling - an outline Impressive features of fluid transport modeling (UEDGE, …) –complex magnetic geometry –multispecies impurity transport/radiation –neutral transport/sources –wall sputtering/recycling/re-deposition –partial fitting of experimental data Limitations and emerging improvements –physics-based turbulent radial transport (D, V,  blobs; ELMs) –kinetic plasma effects – parallel perpendicular to B-field –integrated/self-consistent edge/wall and edge/core coupling –toroidal (3D) asymmetries, peaking factors

21. 21 ARIES October 2010 – 21 Edge transport modeling has primarily used fluid equations obtained by moments of kinetic eqn. Continuity and momentum equations are solved for plasma & neutrals ∂n k  ∂t + div(n k V k ) = S pk ∂(n k m k V ||k )  ∂t + div(n k m k V ||k V k ) = -grad || P k + qn k E || - F ||k - R ||k + S mk Similar energy equations solved for T e and T i Radial velocities are convective-diffusive (fit) + classical drifts V r = V conv - D(dn k /dr)/n k + ExB/B 2 + V grad B Turbulence fit or from simulation; parallel transport classical Parallel electron thermal conduc. timescale (≤ 10 -7-8 s); implicit solver Electrostatic potential from  J = 0 Turbulence Classical