Max-Planck- 531st Heraeus Seminar, April 2013 Institut für Plasmaphysik Physics of stellarator divertors Thomas Sunn Pedersen, for the W7-X team Director of Stellarator Edge and Divertor Physics with special contributions from H. Hölbe, J. Boscary, T. Eich, Y. Feng, M. Hirsch, R. König T. Sunn Pedersen 531st Heraeus Seminar 1 Outline • Intro: 2D (tokamak) divertors and 3D (stellarator) divertors • LHD helical divertor versus Wendelstein-line island divertor • Scrape-off layer widths in tokamaks and stellarators • Experience from W7-AS divertor operation • Status report on the W7-X divertor(s) • Scraper element prototype • Summary 531st Heraeus Seminar 2 Limiter vs 2D divertor vs 3D divertor: schematic Limiter plasma Single null Double null Island divertor divertor divertor 531st Heraeus Seminar 3 The tokamak divertor vs a stellarator island divertor 2D vs 3D - experiments W7-AS 531st Heraeus Seminar 4 Stellarator island divertor principle From J. Kißlinger, W7-X divertor design review 531st Heraeus Seminar 5 The W7-X edge topology • “Standard configuration”: Edge iota=1=5/5=m/n • Island chain consists of five independent island bundles • “High iota”: edge iota=5/4. • Island chain is one long bundle • “Low iota”: edge iota=5/6 • Island chain is one long bundle • In all three cases the magnetic shear is low and the island are large and can be diverted From J. Kisslinger, W7-X divertor design review 531st Heraeus Seminar 6 The W7-X divertor 3D layout Ten identical, discrete divertor units, each aligned to the local magnetic field (4-7 degree inclination angle in W7-X) Simple field line diffusion model (Kisslinger) gives maximal loads of 2 10 MW/m From J. Kisslinger, W7-X divertor design review 531st Heraeus Seminar 7 LHD edge topology and helical divertor divertor plate ergodic layer LCFS divertor leg • Large shear makes it difficult to make large islands • But it allows overlap of islands with different low-order resonances è stochastic layer is formed easily • Due to the existence of this stochastic layer, the quantity L|| varies strongly from field line to field line • Field lines are diverged “naturally” by helical coils via an “edge surface layer” to a helically continuous divertor relatively far away from the plasma N. Ohyabu et al. Nuclear Fusion 34 p. 387 (1994) 531st Heraeus Seminar 8 Background: tokamak edge and divertor physics • Large amount of data available from machines with a spread in size, shape, and B-field strength • Potentially problematic projections to ITER and a tokamak reactor: • Wetted area (next slides) • ELM heat loads on divertors (not mentioned further in this talk) • Impurity accumulation in ELM-free H-mode • Identification of various attractive regimes that might solve these problems: • Detachment, radiating mantle (solve wetted area problem) • EDA H-mode, Improved L-mode, RMP’s for ELM suppression (solve ELM problem without creating impurity accumulation ) • Uncertainty in how well these attractive regimes are ITER relevant 531st Heraeus Seminar 9 Background: tokamak edge and divertor physics • Large amount of data available from machines with a spread in size, shape, and B-field strength • Potentially problematic projections to ITER and a tokamak reactor: • Wetted area (next slides) • ELM heat loads on divertors (not mentioned further in this talk) • Impurity accumulation in ELM-free H-mode • Identification of various attractive regimes that might solve these problems: • Detachment, radiating mantle (solve wetted area problem) • EDA H-mode, Improved L-mode, RMP’s for ELM suppression (solve ELM problem without creating impurity accumulation ) • Uncertainty in how well these attractive regimes are ITER relevant 531st Heraeus Seminar 10 Empirical extrapolations of λq to ITER (T. Eich et al. PRL 107 2011) −1.19 −0.8±0.1 1.05±0.2 0.1±0.1 0±0.1 λq (mm) = (0.63± 0.08)× Bpol,MP λq (mm) = (0.7± 0.2)⋅ Btor ⋅ q95 ⋅ PSOL ⋅ Rgeo MAST NSTX C-Mod .) .) AUG exp exp DIII-D JET C-Mod [mm] ( [mm] q [mm] ( [mm] q λ AUG λ DIII-D JET λ [mm] (regr.) Bpol,MP [T] q • Extrapolations to ITER (Bpol=1.18 T) give rather robustly λq,ITER ≤ 1mm • Not a “carbon PFC” effect – seen in all-metal machines as well Why does Bp determine λq in a tokamak? • Heuristic model (R. Goldston, Nuclear Fusion 52 013009 (2012)) • Magnetic drifts cause cross field transport • Plasma flows along the B-field at v=cs/2 towards the divertor • My quick and dirty version of Goldston’s model: v v 2T / eBR " ∇B+Rc = D = $ 2T 2L m Tm L L v || i 4 i || 4 || T # ⇒ λq = ∇B+Rcτ || = = = ρi τ || = 2L|| / $ eBR T eB R R m i %$ • Note the linear proportionality between L|| and λq • But where does Bp come in then? Why does Bp determine λq in a tokamak? " L|| λq = 4ρi $ R $ miT a Bt miT 4a # ⇒ λq = 4 = Bt eB RB eB R L ≈ a $ p p || B $ p % Why does Bp determine λq in a tokamak? " L|| λq = 4ρi $ R $ miT a Bt miT 4a # ⇒ λq = 4 = Bt eB RB eB R L ≈ a $ p p || B $ p % • Main scaling is with Bp, as seen in the data. • T at the separatrix does not differ substantially between the tokamaks or at different heating powers in the study (“Tsep is clamped to 50 eV due to power balance”) • Even though ITER may have Tsep≈200 eV, that just brings λq up from 1 to 2 mm relative to Tsep≈50 eV Status: stellarator edge and divertor physics • Divertor data only available from a few high-performance machines, first and foremost: • W7-AS (until 2002) • LHD (currently active area of research) • Some optimism regarding wetted area • Theoretical predictions about impurity accumulation are troubling: • Ambipolarity constraint leads to inward pointing E-field (ion root) • Electric field causes inward transport of high-Z impurities • Need for avoiding edge impurity sources • Identification of various attractive regimes that might solve these problems: • W7-AS detachment • W7-AS High Density H-mode (HDH-mode) • Uncertainty in how HDH will project to W7-X (and to a stellarator reactor) 531st Heraeus Seminar 15 Status: stellarator edge and divertor physics • Divertor data only available from a few high-performance machines, first and foremost: • W7-AS (until 2002) • LHD (currently active area of research) • Some optimism regarding wetted area • Theoretical predictions about impurity accumulation are troubling: • Ambipolarity constraint leads to inward pointing E-field (ion root) • Electric field causes inward transport of high-Z impurities • Need for avoiding edge impurity sources • Identification of various attractive regimes that might solve these problems: • W7-AS detachment • W7-AS High Density H-mode (HDH-mode) • Uncertainty in how HDH will project to W7-X (and to a stellarator reactor) 531st Heraeus Seminar 16 The W7-X divertor 3D layout Ten identical, discrete divertor units, each aligned to the local magnetic field (4-7 degree inclination angle in W7-X) Simple field line diffusion model (Kisslinger) gives maximal loads of 2 10 MW/m From J. Kisslinger, W7-X divertor design review 531st Heraeus Seminar 17 Long connection length may save us • An important difference to the tokamak divertor is that a very long connection length is possible • The long connection length comes from the fact that the local rotational transform inside the island is very low • Illustrated here for CNT with visualized field lines using an electron beam, originally near 100 eV, in neutral gas 531st Heraeus Seminar 18 λq is not determined by Bp in a stellarator • For the picture in CNT (at least 3*7=21 transits) we get L||=21*2πR=120R (R=0.3 m in CNT) L λ = v τ = 4ρ || > 480ρ q ∇B+Rc || i R i • And we have seemingly broken the correlation between Bp and λq • In W7-X, we would achieve L λ = v τ = 4ρ || ≥100ρ ~ 4 cm q ∇B+Rc || i R i Status: stellarator edge and divertor physics • Divertor data only available from a few high-performance machines, first and foremost: • W7-AS (until 2000) • LHD (currently active area of research) • Some optimism regarding wetted area • Theoretical predictions about impurity accumulation are troubling: • Ambipolarity constraint leads to inward pointing E-field (ion root) • Electric field causes inward transport of high-Z impurities • Need for avoiding edge impurity sources • Identification of various attractive regimes that might solve these problems: • W7-AS detachment (also observed in LHD) • W7-AS High Density H-mode (HDH-mode) • Uncertainty in how HDH will project to W7-X (and to a stellarator reactor) 531st Heraeus Seminar 20 Can detachment be achieved in a stellarator? In W7-X? • Detachment is favorable for tokamaks and divertors alike, since it reduces the divertor heat loads by a large factor (~10) • In W7-AS the plasma detached from the divertor, ie. glowing ‘clouds’ of recombining cold plasma appeared above the divertor plates • Occurs at higher densities: No Greenwald density limit in stellarators – access to high density and detachment should be possible in W7-X and a stellarator reactor 531st Heraeus Seminar 21 Favorable operating mode in W7-AS: HDH High-Density H-mode observed near the end of the W7-AS program • Plasma density high and stable. • Good energy confinement. • Impurity density low and steady due to: • Reduced impurity confinement • Reduced impurity influx • Basic physics of HDH not fully understood; • Will it be reached in W7-X? • Is it a low-temperature phenomenon? • (resistive-ballooning modes?) • Is it similar to the C-Mod EDA mode? 531st Heraeus Seminar 22 Outline • Intro: 2D (tokamak) divertors and 3D (stellarator) divertors • LHD helical divertor versus Wendelstein-line island divertor • Scrape-off layer widths in tokamaks and stellarators • Experience