Physics basis for similarity experiments on power exhaust between JET and ASDEX Upgrade with tungsten divertors

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1 Physics basis for similarity experiments on power exhaust between JET and ASDEX Upgrade with tungsten divertors S. Wiesen, T. Eich, M. Bernert, S. Brezinsek, C. Giroud, E. Joffrin, A. Kallenbach, C. Lowry, R. A. Pitts, F. Reimold, M. Wischmeier, JET Contributors, ASDEX Upgrade Team and the EUROfusion MST1 Team

2 Understanding of dissipative divertor (molecular assisted recombination) C.Guillemaut, EDGDE2D-EIRENE, NF2014 Impurity radiation: heat-flux and temperature reduction in SOL Neutral zone (cushion): plasma pressure & temperature reduction Volumetric recombination: particle loss to reduce plasma particle flux roll-over Strength of dissipation mechanism depends on machine size: neutral compression & rad. volume Suggested reading: cf. M. Wischmeier, JNM 2015 S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 2

3 Heat conduction zone: transport R. Goldston JNM 2015 T. Eich et al NF 2013 l int q (MWm -2) ( q( s) q q max BG q max ) ds λ q ~ 1 B p s-s 0 [mm] q mid Upstream Downstream q plate T. Eich PRL 2011 M. Makowski Phys. Plasmas 2012 λ int = λ q S P sep 2πR B p,mid λ B t q P div 2πR B p,plate λ B t int λ q ~2 a R ρ p Heuristic Drift (HD) model leading theory reproduces l q scaling (low-density H-mode) Concept: grad-b and curv. drifts drive plasma across surfaces, producing Pfirsch-Schluter return-flows competing with near-sonic parallel divertor flows l int and S only accessible in low-density plasmas; for high density plasmas modelling S~f(T e,plate ) A. Scarabosio JNM 2015

4 Power dissipation by radiation: JET vs Asdex-U M. Wischmeier et al. IAEA 2014 JET A Kallenbach NF 2015 AUG max. P sep R 10 N2 seeding JET: f rad =70-75% at maximum P sep /R ~ 6; highest f rad with N2 seeding only evolves to complete detachment at both targets with strong X-point radiation ASDEX-Upgrade reaches f rad >80% (but higher c W, W-wall) Pronounced detachment achieved in case of strong X-point radiation; no radiating belt formed Is it possible to match f rad at similar P sep /R in both devices with similar level of detachment? If not, why? S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 4

5 JET seeded H-mode: radiation pattern confirmed w/ 2D edge codes: JET-ILW w/ EDGE2D-EIRENE A.Jarvinen, 2014; C. Giroud IAEA 2014 N radiates mainly in divertor Ne radiates in SOL and close to pedestal Radiative power loss depends on non-coronal effects (transport) (cf. also A. Kallenbach PPCF 2013) Unseeded (attached) Partially detached Pronounced detached Be N Ne 2D edge codes do reproduce the sequence into detachment The codes work similarly well qualitative confidence e.g. towards ITER extrapolation, but: still no general scaling-law for radiative power dissipation existing

6 Rationale for a similarity experiment on power exhaust Impurity seeding essential for power dissipation in edge/sol for metallic devices (no carbon, high power H-mode discharges, partially detached conditions) Generalised scaling laws for describing the physics of edge plasma transport and power dissipation by interaction with neutrals (momentum loss) and radiation are not available we default to 2D(3D) edge codes to quantify power dissipation Present day tokamak devices differ in geometry and usually the parallel power flux density q does not match and thus are difficult to compare Transport is barely understood for high-density discharges, i.e. (partial) detachment (Goldston & Eich scalings derived for low-density discharges) Impact of divertor geometry on neutral compression A similarity experiment for radiative (seeded) H-mode discharges in JET and ASDEX Upgrade with W divertor in detached conditions with the relevant parameters matched would allow the closest comparison possible for the power dissipation mechanism. tackle the most prominent problems: a) transport & b) radiation loss pattern S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 6

7 Lackner s approach 1994 (1/2) In algebraic sense: a scaled experiment is possible if the number of dimension-less parameters in governing equations is less than the number of relevant free parameters. A similarity experiment is possible if we can match: Core plasma transport: r i *, n i *, b, plasma shape: q, a/r, d, M rot Edge plasma transport: r i *, n i *, b, flux tube length (i.e. L c ), l D, and T Lackner s result: Edge/divertor similarity achieved if absolute the temperature T can be made the same in separate devices (true for binary atomic collisions including radiation) However, an exact similarity of entire tokamak (core+edge+divertor) is NOT possible address similarity in isolated divertor only ( divertor simulator driven by the tokamak ) S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 7

8 Lackner s approach 1994 (2/2) Assuming geometrical similarity (i.e. same connection length L c, and SOL width l q ) the similarity parameters: T temperature n density n* = L c /l ei ~ nl c /T 2 parallel collisionality can all be matched if P SOL /R = const, but issues: q is not conserved along the SOL in most cases: at mid-plane: q ~ P/(Rl q ) = P/R 2a/R r p = P/R 2a/R T i 1/2 /B p can be made identical (HD), but along the SOL q is usually unknown due to dissipation effects In Lackner s scaled experiment: b ~ L c i.e. difficult to achieve Divertor: b low could be ignored, but then MHD effects like ELMs are ignored too and pressure driven interchange turbulence not matched In Lackner s scaled experiment r i ~ (B T L c ) -1 (req. fixed current I p at given q, difficult when scaling) Divertor r* = r i / D d can hardly be matched, particle drifts depend directly on r* SOL flows and transport (c.f. HD model) cannot be matched rigorously Lackner s approach is insufficient to match at the same time q (power dissipation!), does not preserve b (H-mode! transport!) and is incapable to match r* (transport! SOL-flows!)

9 Improvements by Hutchinson & Vlases 1996 In the isolated divertor all 5 divertor similarity parameters T, n*, r*, b, l 0 /D d can be matched simultaneously if the divertor field line pitch angle a d = tan -1 (B p /B T ) can be relaxed by flux-expansion f x Variation of divertor depth: d x = a d L d = a m /f x Main result: Scaling for required power: P ~ R 1.5, i.e. significant lower power needed for smaller devices (based on Bohm or gyro-bohm assumptions for anomalous transport) Caveat: Although neutral motion perpendicular to B correctly modelled (~l 0 /D d ), in projected parallel direction: l 0,pol /d x not preserved (however, less relevant in VT configurations) S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 9

10 Example sketch of the relaxed a d similarity Hutchinson & Vlases 1996 Reference experiment e.g. AUG R=1.5m, d x =0.75m Scaled experiment e.g. JET, R=3.0m, d x =1.5m With the relaxed a d similarity, perfect match of T, n*, n d D d, r* and b is possible when l q =1/2 by choosing d x =1/2, D d =1, L d =1 and P sep /R = 1/2 Underlined quantities: ratios between reference and scaled experiment S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 10

11 Comparison: Lackner s & Hutchinson s approach Assuming l q = 1/2 and B=1 Hutchinson & Vlases 1996 Quantity Relaxed a d scaling T 1 1 n* 1 1 l 0 /D d 1 1 r/d d 1 2 b 1 2 L d 1 1/2 a d 1/2 1 P sep /R 1/2 1 l 0 /d x 2 1 q 1 2 P sep /R scaling d x =1/2 f x =2 f x =1 S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 11

12 Adding constraints to the relaxed a d similarity In reality the similarity parameters are not directly accessible In existing tokamaks there are limitations on accessible control parameters B T L c, n m L m, f x, L d /L m, P aux Way out: constrain divertor similarity parameters of a given device relative to a reference (e.g. JET, AUG or ITER) by using extra assumptions Vlases 1995: use of a reduced SOL transport model, the two-point model, assuming Bohm or gyro-bohm prescription for anomalous transport The control parameters are then varied to minimise the mismatch between the simulated divertor and the reference in a least-square sense using the reduced twopoint transport model tedious algebraic optimisation procedure to derive similarity parameter scalings S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 12

13 SIMILARITY CONTROL Example: JET similar to AUG (Vlases 1995) AUG JET d x = 0.60 JET d x = 0.45 JET d x = 0.35 BL m f x Psep/(R 4pB p /B t ) n m L m T d n* d n t D d r* d T t n* t n t l int r* t b n t d x P(MW) n m Divertor entrance Target plate REQUIRED Good match of all quantities possible at reasonable level of power Vlases EPS 1995 S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 13

14 New Recipe for improved similarity parameter constraints Hutchinson & Vlases (1996) used a (0D) two-point model to constrain the divertor parameters To improve this and to include important aspects of neutral-plasma interaction (momentum losses, ionisation and radiation in 2D) use 2D edge codes like SOLPS or EDGE2D-EIRENE Optimize the similarity parameter set - T t,d,m, n* t,d,m, r* t,d,m, n t,d,m D t,d,m, b by varying system size parameter B L m to derive cost functionals of accessible control parameters - geometry, i.e. L d /L m - flux expansion f x divertor length d x - P aux or P sep - particle content, i.e. n m L m i.e. minimize the impact of size-scaling on [ ] on derived dependencies (i.e. power-law exponents) Free parameter anomalous transport: could be included in the variational ansatz to minimize [ ] to derive optimal anomalous transport coefficients in size scaling procedure Radiation: impose f rad or impurity concentrations c i as extra control parameter constraint Neutral pressure: could be included as control parameter, but p 0 in JET divertor not available S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 14

15 Alternative approaches to similarity scalings Improved 1D model: c.f. A. Kallenbach et al. subm. PPCF 2015: - non-coronal model for impurities - AUG specific flux-tube geometry - l q & l int scaling (HD/Eich model) - stepwise increase of heat flux bundle assuming fixed ratio L d / L m, assume D d =l int - simplified 2-energy recycling model - inclusion of momentum loss parameter - other simplifications and assumptions (e.g. taking into account flow estimates for p 0 ) JET, VT, l int =5mm c N c Ne c Ar P sep /R = 6, p 0 = 5 Pa 2.9% 1.2% 0.6% P sep /R = 6, p 0 = 10 Pa P sep /R = 10, p 0 = 5 Pa 8.6% 3.4% 1.7% S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 15

16 Conclusion A similarity study on power exhaust between JET and AUG seeded H-mode discharges in partially detached conditions seems to be feasible: Tackle most prominent issues: transport & radiation and their impact on dissipation The main difficulty is to fix important quantities like q all along the SOL flux tube The approach by Hutchinson & Vlases (based on Lackner s original P sep /R isolated divertor approach) was pioneering in the sense that it can preserve important SOL parameters q, b and r* by relaxing the divertor pitch angle through flux expansion However: to take properly into account the 2D nature of the problem, extended methods to find similarity parameter scalings are necessary proposal: switch from 2P-model constraints towards 2D edge codes to find improved set of scalings (Automated optimization techniques could be very useful here, c.f.o-5 M.Baelmans et al.) Alternative approaches which extend the simpler Lackner s P sep /R scaling by a 1D SOL model constraint (c.f. A. Kallenbach) are interesting and should be exploited S. Wiesen et al. 1 st IAEA TM Divertor Concepts Vienna Sep Page 16

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