1. Barbora Gulejová 1 of 2 EPS 2007 material 20/6/2007 Time-dependent modelling of ELMing H-mode at TCV with SOLPS Barbora Gulejová, Richard Pitts, Xavier Bonnin, David Coster, Roland Behn, Jan Horáček, Janos Marki OUTLINE * SOLPS code package * ELM simulation – theory * Simulation of the ELM * Comparison of SOLPS with experiment

2. Barbora Gulejová 2 of 2 EPS 2007 material 20/6/2007 Scrape-Off Layer Plasma Simulation Suite of codes to simulate transport in edge plasma of tokamaks B2 B2 - solves 2D multi-species fluid equations on a grid given from magnetic equilibrium EIRENE EIRENE - kinetic transport code for neutrals based on Monte - Carlo algorithm SOLPS 5 SOLPS 5 – coupled EIRENE + B2.5 Main inputs: magnetic equilibrium P sol = P heat – P rad core upstream separatrix density n e Free parameters: cross-field transport coefficients (D ┴,  ┴, v ┴ ) B2 plasma background => recycling fluxes EIRENE Sources and sinks due to neutrals and molecules measured systematically adjusted Mesh 72 grid cells poloidally along separatrix 24 cells radially

3. Barbora Gulejová 3 of 2 EPS 2007 material 20/6/2007 Edge localised mode (ELM) H-mode  Edge MHD instabilities  Periodic bursts of particles and energy into the SOL - leaves edge pedestal region in the form of a helical filamentary structure localised in the outboard midplane region of the poloidal cross-section LFS HFS  divertor targets and main walls erosion  first wall power deposition ELMing H-mode=baseline ITER scenario Energy stored in ELMs: TCV  500 J JET  200kJ ITER  8-14 MJ => unacceptable => Small ELMs on TCV – same phenomena ! => Used to study SOL transport W~600J DαDα

4. Barbora Gulejová 4 of 2 EPS 2007 material 20/6/2007 Type III Elming H-mode at TCV # 26730 Pre-ELM phase = steady state ELM = particles and heat are thrown into SOL ( elevated cross-field transport coefficients) Post-ELM phase t pre ~ 2 ms t elm ~ 100 μs t post ~ 1 ms I p = 430 kA, n e = 6 x 10 19 m -3, f elm = 230 Hz ELMs - too rapid (frequency ~ 200 Hz) for comparison on an individual ELM basis => Many similar events are coherently averaged inside the interval with reasonably periodic elms

5. Barbora Gulejová 5 of 2 EPS 2007 material 20/6/2007 upstreamtargets J sat [A.m -2 ] LP, average SOLPS outerinner T e [eV] n e [m -3 ] Perp.heat flux [MW.m -2 ] LP, average SOLPS outer inner IR r-r sep v [m.s -1 ] D [m 2.s -1 ] Χ [m2.s-1] same solps result! V perp =0 Ansatz D ┴,Χ ┴ = radially constant in divertor legs D ┴ = 3 m 2.s -1 in div.legs 1m 2.s -1 in SOL Χ ┴ = 5 m 2.s -1 in div.legs 6 m 2.s -1 in SOL NO DRIFTS here But simulations with DRIFTs show early promise of expected effects * * Simulation of pre-ELM = steady state of H-mode presented at PSI 17, Hefei,China and published in JNM May 2006 Very good overall match Good basis for time-dependent ELM simulation Pre-ELM must be time-dependent too! + equal time-steps for kinetic and fluid parts of code ~ 10 -6 s * *

6. Barbora Gulejová 6 of 2 EPS 2007 material 20/6/2007 Simulation of ELM * Instantaneous increase of the cross-field transport parameters D ┴,  ┴, v ┴ ! 1.) for ELM time – from experiment coh.averaged ELM = t ELM = 10 -4 s 2.) at poloidal location -> expelled from area A ELM at LFS From the cross-field radial transport can be estimated the combination of transport parameters corresponding to the given expelled energy W ELM, t ELM and A ELM D┴D┴ Many different approaches possible => changes in D ┴,  ┴ only or in v ┴ too … time W~600J DαDα A ELM = 1.5m 2 W = 600 J Conv.[eV.m -2.s -1 ] Diff.[eV.m -2.s -1 ]  ┴ ┴ D ┴D ┴ *

7. Barbora Gulejová 7 of 2 EPS 2007 material 20/6/2007 Tools to simulate ELM in SOLPS outer div.leg main SOL Inner div.leg Several options in SOLPS transport inputfiles : * Multiplying of the transport coefficients in the specified poloidal region * In 3 different radial regions (core, pedestal, SOL) by different multipliers Added new options: * Poloidal variation of the multiplicator * Step function * Gaussian function * Choosing completely different shape of radial profile for chosen poloidal region pedestalwallcore No TB preelm ELMELM x M ELM

8. Barbora Gulejová 8 of 2 EPS 2007 material 20/6/2007 Simulation of ELM Experimental data to constrain the code: * Energy expelled by the ELM through separatrix (DML) ~ 600 J * Time of ELM-rise (D  coavelm) ~ 100 μs * J sat at the targets * Heat flux at outer target (IR soon) * Upstream n e,T e (TS) -> just orientation

9. Barbora Gulejová 9 of 2 EPS 2007 material 20/6/2007 Simulation of ELM - results Upstream profiles n e [m -3 ] T e [eV] r-r sep D,Chi (ELM): Same shape as preELM => TB, Just multiplied D x 100, Chi x 8 D,Chi (ELM): smaller TB + Gaussian function poloidally D, Chi increased only locally !

10. Barbora Gulejová 10 of 2 EPS 2007 material 20/6/2007 Comparison with TS – R.Behn TS measurements (R.Behn) => * Drop in pedestal width and height appears only for n e SOLPS * bigger pedestal collaps * higher n e and T e in SOL But the right tendency – pedestal collapse D┴D┴ nene R-R sep time Time evolution of D ┴ and n e t ELM =100 µs nene T e [eV] + different ELMing H-mode shots  ! TB no TB

11. Barbora Gulejová 11 of 2 EPS 2007 material 20/6/2007 Simulation of ELM - results Target profilesD,Chi (ELM): smaller TB + Gaussian function poloidally “removal” of TB => higher values at the targets LP coav data SOLPS inner outer targets inner outer D,Chi (ELM): Same shape as preELM => TB, Just multiplied D x 100, Chi x 8 27 16 22 30 35 40 J sat [A.m -2 ] preELM ELM preELM ELM preELM ELM J sat [A.m -2 ] T e [eV] n e [m -3 ] J sat [A.m -2 ] T e [eV] n e [m -3 ]

12. Barbora Gulejová 12 of 2 EPS 2007 material 20/6/2007 Simulation of ELM - results Target profiles – Heat fluxes D,Chi (ELM) :Same shape as preELM => TB, just multiplied D x 100, Chi x 8 D,Chi (ELM): smaller TB + Gaussian function poloidally outer inner Time-dep. heat flux estimated from LP measurements at outer target R.Pitts, Nuc.Fusion 2003 Like Jsat, Te, and ne, heat flux is higher for the case with smaller TB IR data available soon (J. Marki) 2016 9

13. Barbora Gulejová 13 of 2 EPS 2007 material 20/6/2007 ELM-Time evolution of jsat at targets Inner outer target DαDα J sat [A.m -2 ] SOLPS LP 5 LP 20 post-ELM ELM pre-ELM ELM post-ELM R.Pitts, Nuc.Fusion 2003

14. Barbora Gulejová 14 of 2 EPS 2007 material 20/6/2007 ELM-Time-dependent solution at targets ELM J sat [A.m -2 ] T e [eV] T i [eV] n e [m -3 ] targets inner outer time [s] midplane separatrix TB during ELM J sat [A.m -2 ] T e [eV] T i [eV] n e [m -3 ] Density is fixed at midplane separatrix => can’t change too much at the targets either => Jsat can increase mostly through Te,Ti => Necessary to increase D more then Chi in order to act on increase of ne time [s]

15. Barbora Gulejová 15 of 2 EPS 2007 material 20/6/2007 ELM-time-evolution of jsat at targets targets innerouter time [s] J sat [A.m -2 ] ELM rise time SOLPS LP 20 LP 5 Compared with LP close to strike point => Not exactly the same position

16. Barbora Gulejová 16 of 2 EPS 2007 material 20/6/2007 Timedependence of target Te,Ti Timedependence of simulated Te,Ti ( D.Tskhakaya ) for 120kJ ELM at JET (sheat heat coeff assumed 8) R.Pittts, IAEA,2006 outerinner T e [eV] T i [eV] SOLPS Te is rising quicker then Ti Propagation down to the target from upstream pedestal

17. Barbora Gulejová 17 of 2 EPS 2007 material 20/6/2007 Timedependence of target Te,Ti Ions are arriving to target later then electrons (~16 μs) In reality should be more, but : 1.) probably more collisional 2.) SOLPS – equipartition of energy between ions and electrons => reasonable shift of Te,Ti peaks outer inner T e [eV] T i [eV] SOLPS ELM ‘end’ peak R.Pittts, IAEA,2006

18. Barbora Gulejová 18 of 2 EPS 2007 material 20/6/2007 Thank you for attention

19. Barbora Gulejová 19 of 2 EPS 2007 material 20/6/2007 But not at strike point!! Probably more collisional