Understanding Collisionality Effects on Transport Models for Divertor Detachment in JET

1. Relevance of collisionality on the transport model assumptions for divertor detachment multi-fluid modelling on JET O-11S.Wiesen, W.Fundamenski, M.Wischmeier, M.Groth, S.Brezinsek, V.Naulin and JET EFDA contributors 19th PSI San Diego, USA, 24-28 May 2010

2. Missing links: model  experiment • currently, 2D SOL multi-fluid modelling fails to predict a smooth transient froman attached divertor regime  partially detachment  full detachment • although: we are able to model steady-state scenarios for fixed mid-plane density • but we are not yet able to reveal for instance: - a smooth time dependent recycling flux roll over at the targets with the flux dropping to near zero values - asymmetric transition into detachment (experimental observation: inner target detaches before outer target) - inner/outer target flow asymmetry at point of transition and beyond - the roll over happens at lower densities • what is lacking in the model?

3. Collisionality dependence of radial flux • turbulent cross-field transport is ofdiffusive-advective nature and normallyintermittent transport cannot be parametrisedby an effective particle diffusivity and convectionvelocity [eg Naulin et al. NucMat 2007] • probe fluctuation measurements in TCV density scans show that the radial decay lengths scale with plasma collisionality n* ~ n/T2suggesting that the radial particle flux G^ is depending on n* [Garcia et al.PPCF 2007,..] • edge turbulence simulations support the fact that the radial particle flux increases with n* [Ribeiro et al.PPCF2008, Garcia et al.PPCF2006 earlier refs] • general picture: with increasing n* the filamentary structures in the SOL become electrically disconnected from target sheaths & the radial blobby transport becomes less damped by parallel flows  rel. enhancement of G^ • But still we can try to improve our understanding of detachment modellingand assess heuristically what would happen if we make eg. D = D(n*)(by averaging over turbulent time-scales)

4. EDGE2D transport model modification spx D^(n*) variation in SOL D^ref • parallel transport: classical, Spitzer-Harm like • perpendicular heat conductivity: spatially constant profile eg. ci = ce = 1 m2/s everywhere • perpendicular diffusivity: inside separatrix and in PFZ: D^ref fixedin SOL: n* dependencyn* ~ ne/Te2 is solely dependent on midplane separatrix plasma conditions (LC fixed) freedom of choice for n*ref (or D^ref), select n*ref to calibrate with experiment • assume no additional velocity dependent convection here, ie Vpinch = 0

5. Test-scenario: JET 50401 w/ vertical targets 6e22 1/s 4e22 1/s 0.1 e22 1/s 0 sec 4 sec 6 sec log Te 2D profiles (7MW) case with linear collisionality dependence e=1 without collisionality dependence e=0 Gas-fueling ramp

6. Transitional detachment characteristics Inner target Outer target oldmodelw/ fixedtransport,ie e = 0 Long phase of semi-detachment newmodelw/ linearn-dep.on D,ie e = 1 Earlier inner full detachment Widening of flux footprint peak flux roll-over

7. Powerscan: vertical targets, 3.5MW log Te log ne • n*ref is selected to match the 7MW ne-profile at the midplane in the beginning of the time-dependent run (now for 3.5MW: n*ref=23.1), the temperature is thus reduced due to lower power • the gas fueling ramp is the same as before • oscillations (~10Hz) in the final state, similar to those experimentally observed at JET L-modedischarges [cf. Loarte et al., PRL 1999] • oscillations not observed in case with no n*-dependence on transport

8. Modeling of asymmetric JET divertor geometry • JET 78647 density step scan into high-recycling • L-mode, Ip 2.5MA, Bt 2.7T, Ptotal ~ 3MW (PNBI 1.6 MW) • asymmetric divertor plasma geometry • density steps into high-recycling regime:nspx ~ 0.8e19, 1.5e19, 2.0e19 m-3 • EDGE2D-EIRENE model: • D+C, phys. sputt + fixed chem. erosion (Ychem =1%) • A&M: ionisation, recombination, dissociation and CX • no cross-field drifts included • parallel transport classical, no flux limiters • selection of reference radial transport model(ie D^ref profile) to fit lowest density from experiment • with increasing density: best-fit when comparing to experimental up/downstream profiles in case of e=0 divertor geometry plays a stronger role

9. JET 78647 simulation:smoothly decaying flux roll over revealed artificially • in EDGE2D-EIRENE the gas fuelinghas been ramped up to push the simulation into the detached regime(ie. beyond the high-recycling regime) • with increasing e roll over occurs atlower density and is smoothly decayingin time • now: Gplate 0 for e > 0possible reason for this:inclusion of intrinsic impurites • no asymmetry Ginner/Gouterpossible reasons:transport model still insufficient ?asymmetric divertor geometry ?(OSP on horizontal plate & XP near ISP) ne,spx Ginner Gouter Pzrad [s] gas fueling ramp

10. Inclusion of ballooning factor log Te Gplate • in this case: even ballooning factor does not reproduce the measured in-out asymmetryrather it leads to a delay of flux roll-over and increase of peak flux valueindependently from inclusion of ballooning factor: • open outer divertor: Te drop begins in far-SOL and is moving to the inside • inner target is much longer attached than outer target

11. Divertor geometry strongly influencing detached state anddensity limit • outer target: • detaches from far-SOL moving to inside: feature of open outer divertor ? cf. A.Loarte et al, NF 38(1998)inner target: • when outer target has low enough Te and pressure: build-up of additional flux spot(or shift) on top of inner bafflestabilises partially detached period • some influence of geometry also seen in experiments(flux footprints) • in the modelling: any other modification on transport modelis strongly masked by these geometric effects

12. Conclusions • the inclusion of a collisionality dependency on 2D edge transport models seems promising: asymmetric and smooth transitions into partial detachment: Te drop and pressure loss •  a smoothly decaying recycling flux roll over is achieved, which happens at lower density •  the recycling flux drops to zero when impurities are included in the model, too • but still, there is no in-out asymmetry for the plasma flows • vertical target scenarios are more sensitive to transport model modification • power-dependent global oscillations in plasma solutions near density limit similar toexperimental observations when transport is dependent on collisionality

13. Backup: JET 78647 low density case,outer-midplane profiles Te o HRTS + ECE ne o HRTS + LIDAR spx spx spx spx 1.0 D^OMP 0.7 0.5 0.5 0.5 0.5 0.5 0.5 Ggas 1e21 1e21 0.8e21 1e21

14. JET 78647 density steps, transition into high-recyclingouter midplane and outer strike-point profiles OMP ne ooo HRTS OT ne L.probes OT jsat L.probes OT qtarget IRTV OMP Te ooo HRTS OT Te L.probes nspx : 0.8e19, 1.5e19, 2.0e19 m-3e = 0.0 : Gpuff = 1e21, 3.5e21, 5.5e21 s-1e = 0.5 : Gpuff = 1e21, 4.1e21, (5.5e21) s-1, roll-over already at 1.9e19 m-3e = 1.0 : not shown roll-over already at 1.2e19 m-3  in this shaped div.plasma geometry: best fit with no collsionality dependence e = 0.0

15. Backup: target particle fluxes, 50401 • no clear roll-over of integrated flux when the innertarget completely detaches • but peak flux roll-over demonstrated, but very sharp • only when both targets completely detachthere is a drop for the integrated flux also(and peak flux drops sharply too) • for the case with no n* dependence on Dit is harder to see what goes on at highdensity (unstable solutions) • there is no clear inner/outer asymmetry of flux roll-over at the time of transitions intodetachment  ie this remaining problem is notsolved by the current SOL transport model asymmetric flow generation?parallel momentum sources/sink? IT CD integratedparticle fluxes peakparticle fluxes

16. backup slides