Constraining the divertor heat width in ITER D.G. Whyte 1, B. LaBombard 1, J.W. Hughes 1, B. Lipschultz 1, J. Terry 1, D. Brunner 1, P.C. Stangeby 2, D. Elder 2, A.W. Leonard 3, J. Watkins 4 1 MIT Plasma Science Fusion Center, Cambridge, MA, 02139, USA. 2 University of Toronto Institute for Aerospace Studies, Toronto, M3H 5T6, Canada. 3 General Atomics, San Diego, CA 92186-5608, USA. 4 Sandia National Laboratories, Albuquerque, NM 87185, USA. PSI meeting, Aachen Germany, May 2012 1
Introduction The issue of the scrape-off layer (SOL) radial power width λ r, remains a critical and unresolved issue for designing magnetic fusion boundary plasmas First-principles explanations explaining λ r remain elusive Empirical attempts at estimating λ r, in large-scale devices like ITER have historically shown large amounts of scatter and poor self-consistency Recent activities have sought to improve λ r measurement fidelity in many present experiments (e.g. [LaBombard, Eich]). Regression analysis of these data [Makowski, Eich] and a heuristic drift model [Goldston] have suggested λ r ~ 1-3 mm for ITER, a factor of 5-10 lower than previous estimate raising serious concerns for ITER divertor viability. 2
Motivation It is desirable to develop methods of constraining λ r in ITER (and future fusion devices) independent of the λ r measurements themselves. We develop here such a method, constraining λ r based on SOL and pedestal pressure Sheath heat transmission Global power balance. This strategy is motivated by several recent observations and improvements in understanding these constraints 3
Sheath heat transmission coefficient γ~8-10 per standard sheath theory Accurate energy / plasma accounting in C-Mod divertor [Brunner] Gives confidence in using local plasma parameters at divertor to calculate heat flux since C-Mod most prototypical of ITER Vertical target High-Z metal target Density ~ 10 21 m -3 High power density Grazing field of ~5 T. 4
H-mode pedestal stability modeling predictive of ITER pedestal Points here ITER p ped ~ 92 kpa or p 20 ~ 3000 p 20 2 n 20 T ev [Snyder] 5
Present experiments inform us to expected ratio of separatrix and pedestal pressure Must avoid persistent issue of unmeasured main ion temperature in vicinity of upstream separatrix. Example C-Mod upstream electron pressure profile Measure electron pressure at the divertor plate. Collisionality (high n, low T) assures T i ~T e Dynamic + static pressure must be conserved along separatrix for attached divertors (used here) p sep = 2 p div (Bohm criterion) T i ~ T e at top of pedestal from impurity ion T. Pressure of separatrix From divertor probes 6
Expect separatrix-to-pedestal pressure ratio ~5% for ITER From DIII-D and C-Mod divertor (separatrix) and upstream (pedestal)profiles JET point from upstream only [Beurskens] Best organizes to global power density ITER 7
Simple pressure + power balance model for ITER constrains λ r and T divertor Parallel exhaust area Divertor sheath heat flux Global divertor power exhaust. Q=10 P fusion = 500 MW P div = 50 MW 8
ITER divertor heat flux width must be λ r > 8 mm for divertor T < 100 ev T div =10 solution 9
Upstream separatrix temperature is also constrained by ITER operating near Greenwald density limit Multi-device database [Kallenbach] showed that in H-mode the separatrix density ~ 0.4-0.5 core density Suggests most likely upstream density n 20 ~ f Gr ~ < 0.4 10
Upstream temperature provides further constraints on power exhaust Spitzer-Harm // conduction Flux-limiter // convection 11
Combining pressure + global power exhaust further defines allowed regions of Tdiv and λ r 12
Scanning allowed range of separatrix density λ r < 10 mm requires T div > 100 ev which has never been measured 13
Conclusions If the ITER divertor temperature ~ 10 ev (as presently expected) a power widths ~ 3 mm and less would require a separatrix pressure ~ pedestal pressure This clearly violates physical reasoning and/or the concept of a pedestal. For the divertor power width to be ~3 mm would require a divertor temperature ~ 1000 ev. This also likely violates physical reasoning regarding the thermal stability of open field lines and also strongly violates observation that all divertors to date have T < 60 ev (see discussion) This suggests we should consider simple pressure ratio constraints given here in understanding ITER (and reactor) heat flux widths. 14
References [LaBombard] B. LaBombard et al. Phys. Plasma 18 056104 (2011) [Snyder] P. Snyder, et al. Nucl. Fusion 51 (2011) 103016 [Eich] T. Eich, et al. PRL 107 215001 (2011) [Makowski] M. Makowski, APS-DPP 2011 [Brunner] D. Brunner, B. LaBombard Rev. Sci. Instrum. 83 033501 (2012) [Goldston] R. Goldston Nucl. Fusion 52 (2012) 013009 [Beurskens] M. Beurskens Plasma Phys. Control. Fusion 51 (2009) 124051 15
Physics Discussion: Divertor plasmas cannot be really hot because they are thermally unstable: // conduction case (width decreased to smallest allowed) P SOL 1 GW/m2 1000 ev 999 ev P SOL 5 GW/m2 P rad P SOL P SOL 1000 ev 996 ev 995 ev 1 GW/m2 P rad 995 ev 5 GW/m2 P rad 996 ev ~200 ev. 990 ev < 50 ev 16
Physics Discussion: Divertor plasmas cannot be really hot because they are ionization unstable: // convection case (width decreased to smallest allowed) Γ SOL, P SOL 1 GW/m2, M=1, no source 1000 ev, n Gr Γ SOL, P SOL <1 GW/m2, M<1 1000 ev, n Gr S ion 1000 ev, n Gr 1000 ev, n Gr P SOL 1 GW/m2 P rad 1000 ev, n Gr. <1000 ev, >n Gr 17
Physics Discussion: why the separatrix participation in the (known) pedestal stability is consistent with heat width trends Trend /w power Trend /w Ip 18
Physics Discussion: why the separatrix participation in the (known) pedestal stability is consistent with heat width trends Pedestal primarily regulated by peeling- ballooning instability NOT transport r/a 0.95 1????? 19