Scaling of divertor plasma effectiveness for reducing target-plate heat flux T.D. Rognlien, I. Joseph, G.D. Porter, M.E. Rensink, M.V. Umansky, LLNL S.I. Krasheninnikov & A.Yu. Pigarov, UCSD; M. Groth, Aalto U Presented at the US-EU TTF Meeting Salem, MA April 28 May 1, 2015 Prepared by LLNL under Contract DE-AC52-07NA27344. This material is based upon work supported by the U.S. DOE, Office of Science, Fusion Energy Sciences. LLNL-POST-669938
Outline UEDGE-related BPMIC workshop goals: 1. Impact of upper divertor geometry and cross-field drifts (I. Joseph) 2. Impact of lower divertor geometry on heat-flux with power and density (T. Rognlien) 3. Impact of poloidal flux expansion and B tor (M. Umansky) Thanks to Steve Allen and LLNL expt. team for support/discussions Other UEDGE studies ongoing by Groth, Pigarov, Porter + SOLPS work TTF-April 2015 2
Method here emphasizes scaling and trends Use UEDGE with existing DIII-D geometry, MHD equilibria, and typical power/densities Simulate impact on divertor heat flux (and sputtering) by vary geometry (plates), power, and separatrix density For efficiency and separating effects, most runs have fixed fraction impurities and no drifts TTF-April 2015 3
1. How does the physics of the upper and lower divertor differ? Different target plate angles & pumping 40 O upper shelf vs 0 O lower shelf 2 upper cryopumps vs 1 lower pump upper has smaller private flux region Upper Inner Cryopump Ar (1. Joseph) Upper Outer Cryopump D 2 Different drift directions opposite radial drift directions: Vr = ± Ep x Bt due to opposite poloidal gradient directions similar poloidal drift directions: Vp = Er x Bt due to similar radial gradient directions but opposite flows toward/away from X-pt (a) (b) (c) (d) Shelf Extention TTF-April 2015 4 B B B B Lower Outer Ar Cryopump T. Petrie, et al. J. Nucl. Mater. 390-1, 242 2009
UEDGE predicts detachment can be induced/ enhanced by steeply inclined target plates (1. Joseph) 0 o 20 o 40 o T e contours Model of DIII-D #134074 USN; L-mode transp. P inj = 1.3 MW Peak heat flux is reduced as target plate angle increases; high T e, low n e outside strike-pt No impurities q tot (MW/m 2 ) 0.5 sptrx 0 o 20 o 40 o T e (ev) sptrx 10 0 40 20 0 TTF-April 2015 5 sptrx Radial index
t Drifts have an important effect on detachment threshold for DIII-D #134074 no drift te-in LSN drift (1. Joseph) T e,in T e,in T e,out te-in T (ev) te-in ti-in T i,in te-out T (ev) te-out ti-in T i,in T e,out ti-out T i,out ti-out T i,out Attachment/detachment transitions appear as jumps in temperature at the peak heat flux position as input power is raised at a fixed upstream density n e =2x10 19 m -3 at ψ=0.95 P ISP (MW) P OSP (MW) Drifts play an important role in determining the threshold power TTF-April 2015 6 P inj (MW) P inj (MW) no dri' 4 6.5 LSN dri' 2.5 3.5
UEDGE predicts ExB drifts are dominant in the divertor and play an important role in pumping ~ 1% x sound speed V p = E r x B t (1. Joseph) V p V p Experimental observation that pumping efficiency improves when B x Grad B à toward X-point can be explained by E x B drifts! G.D. Porter, T.W. Petrie, T.D. Rognlien, and M.E. Rensink, Phys. Plasmas 17, 112501 (2010) TTF-April 2015 7
2. Lower divertor already possesses tilted-plate / flat-plate features to aid geometric understanding (2. Rognlien) Possible pumping locations Tilted plate Flat plate TTF-April 2015 8
Profiles of T e,i and n i,g show substantial differences for the two geometries, but similar peak values Tilted plate 10 (2. Rognlien) Flat plate T e H-mode-like transport: D=0.15, χ=0.4 (m 2 /s) Temperature (ev) 10 Sep. T i Outer divertor Temperature (ev) T e T i P core = 5 MW 2% carbon n sep ~ 4x10 19 m -3 Density (10 20 m -3 ) 4 2 n i n g Density (10 20 m -3 ) 4 2 n i n g TTF-April 2015 9 0 0.2 Radial dist. from sep (m) 0 Radial dist. from sep (m) 0.2
Peak heat fluxes show similar scaling with n sep for the 2 geometries (outer divertor) Tilted plate Flat plate (2. Rognlien) Peak heat flux (MW/m 2 ) 8 4 ½ pumping rate n sep (10 19 m -3 ) n sep (10 19 m -3 ) TTF-April 2015 10
Peak heat fluxes versus total number of SOL particles partly removes pumping difference (2. Rognlien) Tilted plate Flat plate Peak heat flux (MW/m 2 ) 8 4 ½ pumping rate ½ pumping rate N SOL (10 20 particles) N SOL (10 20 particles) TTF-April 2015 11 Plotting instead versus total SOL ion + gas density partially resolves pumping variation (Krasheninnikov et al., JNM, 1999)
Increasing the separatrix density mainly reduces the central-peak region of the heat-flux profile (2. Rognlien) Heat flux (MW/m 2 ) 6 8 3 4 Sep. Tilted plate n sep = 4.45x10 19 m -3 Outer divertor n sep = 5.60x10 19 m -3 Sep. Flat plate n sep = 5.09x10 19 m -3 n sep = 6.29x10 19 m -3 0 0 0 0.2 0.2 Distance along target plate (m) Distance along target plate (m) TTF-April 2015 12
Presently moving divertor nose horizontally to assess change in peak heat flux (2. Rognlien) Tilted plate TTF-April 2015 13
3. Varying flux expansion at outer plate by moving target plate toward the x-point (3. Umansky) Δz is distance btwn plate & X-point consider 3 cases: Δz = 21 cm, mp flux expansion = 3.0 Δz = 31 cm, mp flux expansion = 2.5 Δz = 41 cm, mp flux expansion = 2.0 TTF-April 2015 14
Outer divertor parameters vary strongly with core-edge density eventually leading to detachment (3. Umansky) L-mode-like transport = 1 m 2 /s 0 0.5 1.0 N core (10 20 m -3 ) Peak T e (ev). Peak heat-flux (MW/m 2 ) 0 0.5 1.0 N core (10 20 m -3 ) TTF-April 2015 15 0 0.5 1.0 N core (10 20 m -3 )
For attached plasmas (n core =2.5x10 19 ), flux expansion sometimes reduces temperature at strike point (3. Umansky) TTF-April 2015 16
In the detached regime, peak heat-flux shows reduction with flux expansion (3. Umansky) Peak heat-flux (MW/m 2 ) 10 0 0.5 1.0 N core (10 20 m -3 ) Peak T e (ev). 20 0 0.5 1.0 N core (10 20 m -3 ) TTF-April 2015 17 0 0.5 1.0 N core (10 20 m -3 )
Changes to B tor has modest effect on outer divertor normalized heat-flux profiles (3. Umansky) Standard B tor 2xB tor Fixed D, χ D, χ between these values may yield both midplane & divertor unchanged D ~ 1/B tor, χ ~ 1/B tor 2 Heat flux (normalized) Heat flux (normalized) TTF-April 2015 18 Radial index across divertor plate
Conclusions Upper divertor simulations (without impurities): tilting plate aids detachment onset ExB flows are important for detachment onset, and in unbalanced in/out particle flow/pumping Lower divertor simulations (with impurities): Despite T, n profile differences, peak heat flux is weakly affected by plate geometry (strong impurity role?) Variation in pumping controls relation between n sep and total SOL particle content N SOL, which in turn controls peak heat flux Flux expansion simulations (with impurities): Peak heat flux in detached region roughly scales with flux exp. B tor variation modestly affects heat-flux profiles; need midplane profile match TTF-April 2015 19