Timedependent modelling of ELMing Hmode at TCV with

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 EPS 2007 material 20/6/2007 Barbora Gulejová 1 of 2

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

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 divertor targets and main walls erosion HFS first wall power deposition Dα LFS ELMing H-mode=baseline ITER scenario Energy stored in ELMs: TCV 500 J JET 200 k. J ITER 8 -14 MJ => unacceptable => W~600 J Small ELMs on TCV – same phenomena ! => Used to study SOL transport EPS 2007 material 20/6/2007 Barbora Gulejová 3 of 2

Type III Elming H-mode at TCV Ip = 430 k. A, ne = 6 x 1019 m-3 , felm = 230 Hz # 26730 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 telm ~ 100 μs tpre ~ 2 ms tpost ~ 1 ms Pre-ELM phase = steady state ELM = particles and heat are thrown into SOL ( elevated cross-field transport coefficients) Post-ELM phase EPS 2007 material 20/6/2007 Barbora Gulejová 4 of 2

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

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 AELM at LFS From the cross-field radial transport can be estimated the combination of transport parameters corresponding to the given expelled energy WELM, t. ELM and AELM Dα Many different approaches possible => changes in D┴, ┴ only or in v┴ too … W~600 J time AELM= 1. 5 m 2 * W = 600 J D┴ Diff. [e. V. m-2. s-1] D┴ ┴ EPS 2007 material 20/6/2007 Conv. [e. V. m-2. s-1] Barbora Gulejová 6 of 2

Tools to simulate ELM in SOLPS 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 main SOL ELM radial profile for chosen poloidal region Inner div. leg No TB main SOL ELM x. M preelm core pedestal outer div. leg wall EPS 2007 material 20/6/2007 Barbora Gulejová 7 of 2

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 * Jsat at the targets * Heat flux at outer target (IR soon) * Upstream ne, Te (TS) -> just orientation EPS 2007 material 20/6/2007 Barbora Gulejová 8 of 2

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

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

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

Simulation of ELM - results D, Chi (ELM) : Same shape as pre. ELM => TB, just multiplied D x 100, Chi x 8 D, Chi (ELM): smaller TB + Gaussian function poloidally inner 16 Target profiles – Heat fluxes outer inner 20 Like Jsat, Te, and ne, heat flux is higher for the case with smaller TB IR data available soon outer (J. Marki) Time-dep. heat flux estimated from LP measurements at outer target 9 R. Pitts, Nuc. Fusion 2003 EPS 2007 material 20/6/2007 Barbora Gulejová 12 of 2

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

ELM-Time-dependent solution at targets ELM inner outer TB during ELM midplane separatrix Jsat [A. m-2] ne [m-3] Te [e. V] Ti [e. V] time [s] EPS 2007 material 20/6/2007 time [s] 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 Barbora Gulejová 14 of 2

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

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

Timedependence of target Te, Ti ELM ‘end’ inner SOLPS ELM ‘end’ outer peak Te [e. V] peak 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 Ti [e. V] => reasonable shift of Te, Ti peaks R. Pittts, IAEA, 2006 EPS 2007 material 20/6/2007 Barbora Gulejová 17 of 2

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

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