Physics basis for similarity experiments on power exhaust between - PowerPoint PPT Presentation

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

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 30 2015 | Page 2

Heat conduction zone: transport R. Goldston JNM 2015 Heuristic Drift (HD) model 𝜇 𝑟 ~ 1 leading theory reproduces l q scaling 𝐶 𝑞 (low-density H-mode) 𝜇 𝑟 ~2 𝑏 𝑆 𝜍 𝑞 Concept: grad-B and curv. drifts drive plasma across 𝑄 surfaces, producing 𝑛𝑗𝑒 ≈ 𝑡𝑓𝑞 𝑟 || 2𝜌𝑆 𝐶 𝑞,𝑛𝑗𝑒 Pfirsch-Schluter return-flows 𝐶 𝑢 𝜇 𝑟 competing with near-sonic T. Eich et al NF 2013 parallel divertor flows Upstream Downstream l int and S only accessible in low-density plasmas; 𝑄 𝑒𝑗𝑤 for high density plasmas  modelling 𝑞𝑚𝑏𝑢𝑓 ≈ 𝑟 || 2𝜌𝑆 𝐶 𝑞,𝑞𝑚𝑏𝑢𝑓 𝜇 𝑗𝑜𝑢 𝑇~𝑔(𝑈 𝑓,𝑞𝑚𝑏𝑢𝑓 ) q ⊥ (MWm -2) 𝐶 𝑢 q max T. Eich PRL 2011 M. Makowski Phys. Plasmas 2012   𝜇 𝑗𝑜𝑢 = 𝜇 𝑟 + 1.64 𝑇 ( q ( s ) q ) ds l  BG int q max s-s 0 [mm] A. Scarabosio JNM 2015

Power dissipation by radiation: JET vs Asdex-U M. Wischmeier et al. IAEA 2014 A Kallenbach NF 2015 AUG JET 𝑛𝑏𝑦. 𝑄 𝑡𝑓𝑞 ≈ 10 𝑆 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 30 2015 | Page 4

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 2D edge codes do Be N reproduce the sequence Ne 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

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 30 2015 | Page 6

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 30 2015 | Page 7

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/(R l 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!)

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 30 2015 | Page 9

Example sketch of the relaxed a d similarity Hutchinson & Vlases 1996 Reference experiment Scaled experiment e.g. JET, R=3.0m, d x =1.5m e.g. AUG R=1.5m, d x =0.75m 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 30 2015 | Page 10

Comparison: Lackner‘s & Hutchinson‘s approach Hutchinson & Vlases 1996 Assuming l q = 1/2 and B=1 Relaxed a d Quantity P sep /R scaling scaling T 1 1 n * 1 1 l 0 / D d 1 1 r / D d 1 2 b 1 2 d x =1/2 L d 1 1/2 a d 1/2 1 P sep /R 1/2 1 l 0 /d x 2 1 f x =2 f x =1 q || 1 2 S. Wiesen et al. | 1 st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 11

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 two- point transport model  tedious algebraic optimisation procedure to derive similarity parameter scalings S. Wiesen et al. | 1 st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 12