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

Physics basis for similarity experiments

• n 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

(molecular assisted recombination)

C.Guillemaut, EDGDE2D-EIRENE, NF2014

Understanding of dissipative divertor

• 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. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 2

Heat conduction zone: transport

• T. Eich et al NF 2013
• R. Goldston JNM 2015

Heuristic Drift (HD) model leading theory reproduces lq 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

s-s0[mm]

qmax

q⊥(MWm-2)

max int

) ) ( ( q ds q s q

BG



  l

𝜇𝑟~ 1 𝐶𝑞 𝜇𝑟~2 𝑏 𝑆 𝜍𝑞

Upstream Downstream

𝜇𝑗𝑜𝑢 = 𝜇𝑟 + 1.64 𝑇

• T. Eich PRL 2011
• M. Makowski Phys. Plasmas 2012

lint and S only accessible in low-density plasmas; for high density plasmas  modelling

• A. Scarabosio JNM 2015

𝑇~𝑔(𝑈

𝑓,𝑞𝑚𝑏𝑢𝑓)

𝑟||

𝑛𝑗𝑒 ≈

𝑄

𝑡𝑓𝑞

2𝜌𝑆𝐶𝑞,𝑛𝑗𝑒

𝐶𝑢 𝜇𝑟

𝑟||

𝑞𝑚𝑏𝑢𝑓 ≈

𝑄𝑒𝑗𝑤 2𝜌𝑆𝐶𝑞,𝑞𝑚𝑏𝑢𝑓

𝐶𝑢

𝜇𝑗𝑜𝑢

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 4

Power dissipation by radiation: JET vs Asdex-U

A Kallenbach NF 2015 N2 seeding

𝑛𝑏𝑦. 𝑄

𝑡𝑓𝑞

𝑆 ≈ 10

• JET: frad=70-75% at maximum Psep/R ~ 6; highest frad with N2 seeding only

 evolves to complete detachment at both targets with strong X-point radiation

• ASDEX-Upgrade reaches frad>80% (but higher cW, W-wall)
• Pronounced detachment achieved in case of strong X-point radiation; no radiating belt formed

Is it possible to match frad at similar Psep/R in both devices with similar level of detachment? If not, why?

JET AUG

• M. Wischmeier et al. IAEA 2014

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)

Be N Ne

Unseeded (attached) Partially detached Pronounced detached

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

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. | 1st 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: ri*, ni*, b, plasma shape: q, a/R, d, Mrot
• Edge plasma transport: ri*, ni*, b, flux tube length (i.e. Lc), lD, and T
• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 7

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”)

Lackner‘s approach 1994 (2/2)

Assuming geometrical similarity (i.e. same connection length Lc, and SOL width lq)  the similarity parameters: T temperature n density n* = Lc/lei ~ nLc/T2 parallel collisionality can all be matched if PSOL/R = const, but issues:

• q|| is not conserved along the SOL in most cases:

at mid-plane: q|| ~ P/(Rlq) = P/R ∙ 2a/R ∙ rp = P/R ∙ 2a/R ∙ Ti

1/2/Bp can be made identical (HD),

but along the SOL q|| is usually unknown due to dissipation effects

• In Lackner’s scaled experiment: b ~ Lc 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 ri ~ (BTLc)-1 (req. fixed current Ip at given q, difficult when scaling)

 Divertor r* = ri/ Dd 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, l0/Dd can be matched simultaneously if the divertor field line pitch angle ad = tan-1(Bp/BT) can be relaxed by flux-expansion fx  Variation of divertor depth: dx = adLd = am/fx

• Caveat: Although neutral motion perpendicular to B correctly modelled (~l0/Dd), in

projected parallel direction: l0,pol/dx not preserved (however, less relevant in VT configurations)

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 9

Main result: Scaling for required power: P ~ R1.5, i.e. significant lower power needed for smaller devices (based on Bohm or gyro-Bohm assumptions for anomalous transport)

Example sketch of the relaxed ad similarity

Hutchinson & Vlases 1996

Reference experiment e.g. AUG R=1.5m, dx=0.75m Scaled experiment e.g. JET, R=3.0m, dx=1.5m

With the relaxed ad similarity, perfect match of T, n*, ndDd, r* and b is possible when lq=1/2 by choosing dx=1/2, Dd=1, Ld=1 and Psep/R = 1/2

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 10

Underlined quantities: ratios between reference and scaled experiment

Comparison: Lackner‘s & Hutchinson‘s approach

Quantity Relaxed ad scaling Psep/R scaling T 1 1 n* 1 1 l0/Dd 1 1 r/Dd 1 2 b 1 2 Ld 1 1/2 ad 1/2 1 Psep/R 1/2 1 l0/dx 2 1 q|| 1 2

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 11

Assuming lq = 1/2 and B=1 Hutchinson & Vlases 1996 dx=1/2 fx=2 fx=1

Adding constraints to the relaxed ad similarity

• In reality the similarity parameters are not directly accessible
• In existing tokamaks there are limitations on accessible control parameters

BTLc, nmLm, fx, Ld/Lm, Paux

• 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. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 12

Example: JET similar to AUG (Vlases 1995)

Vlases EPS 1995  Good match of all quantities possible at reasonable level of power CONTROL SIMILARITY REQUIRED

AUG JET dx= 0.60 JET dx= 0.45 JET dx= 0.35 BLm 1 1.82 1.82 1.82 fx 1 0.77 0.75 0.75 Psep/(R ∙ 4pBp/Bt) 1 1.59 1.43 1.30 nmLm 1 1.54 1.56 1.58 Td 1 1.20 1.03 0.90 n*d 1 1.03 1.15 1.26 ntDd 1 0.91 1.00 1.08 r*d 1 1.03 0.96 0.90 Tt 1 1.17 1.08 1.00 n*t 1 1.10 1.02 0.94 ntlint 1 0.93 0.96 0.98 r*t 1 1.01 0.98 0.95 b 1 1.03 1.01 0.96 ntdx 1 1.96 1.49 1.17 P(MW) 8.0 23.8 21.4 19.5 nm 1 0.82 0.83 0.84

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 13

Divertor entrance Target plate

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

• Tt,d,m, n*t,d,m, r*t,d,m, nt,d,mDt,d,m, b

by varying system size parameter BLm to derive cost functionals  of accessible control parameters 

• geometry, i.e. Ld/Lm
• flux expansion fx  divertor length dx
• Paux or Psep
• particle content, i.e. nmLm

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 frad or impurity concentrations ci as extra control parameter constraint
• Neutral pressure: could be included as control parameter, but p0 in JET divertor not available
• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 14

Improved 1D model: c.f. A. Kallenbach et al. subm. PPCF 2015:

• non-coronal model for impurities
• AUG specific flux-tube geometry
• lq & lint scaling (HD/Eich model)
• stepwise increase of heat flux bundle assuming

fixed ratio Ld / Lm, assume Dd=lint

• simplified 2-energy recycling model
• inclusion of momentum loss parameter
• other simplifications and assumptions

(e.g. taking into account flow estimates for p0)

Alternative approaches to similarity scalings

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 15

JET, VT, lint=5mm cN cNe cAr Psep/R = 6, p0= 5 Pa 2.9% 1.2% 0.6% Psep/R = 6, p0= 10 Pa

• Psep/R = 10, p0= 5 Pa

8.6% 3.4% 1.7%

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 Psep/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 Psep/R scaling by a 1D SOL

model constraint (c.f. A. Kallenbach) are interesting and should be exploited

• S. Wiesen et al. | 1st IAEA TM Divertor Concepts| Vienna | Sep 30 2015 | Page 16