Modelling for ITER of W, Be and Li Melting, W Cracking and Massive Gas Injection FZ-Karlsruhe I. Landman Major contributions from B. Bazylev and S. Pestchanyi KIT-FZ-Karlsruhe, Germany All our modelling concerns transients (ELMs, disruptions) Outline Relevant EFDA WP09-PWI Tasks W melting 05-02/FZK/BS Melt damages to Li 06-01/FZK/BS Runaway damage to Be 08-01/FZK/BS W cracking MGI: Radiation impact on Be wall 09-02/FZK/BS 1 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Disruptions (duration t ~ 3 ms) Modelling of melting of W-macrobrushe with the code MEMOS Main processes: Melting (Navier-Stocks shallow fluid model) Bulk thermoconductivity Evaporation, vapour shield (melt motion due to gradient of vapour pressure) Melt splashing Resolidification Melt pool depth ~ 200 µm. Peak power load ~ 2.5 GW/m2 Vapour shield pressure ~ 5 bar There are many parameters over which we calculate melt damage with MEMOS: W/Be, Q, t, J, , p||, Qlateral, … Classification of ITER transient loads (divertor armour) Disruptions (duration t ~ 3 ms) Type Max impact energy, Qmax Max current, Jmax MJ/m2 MA/m2 Maximal 30 Typical 10 5 Mitigated 1.5 (First wall) ELMs (t ~ 0.5 ms) Uncontrolled 15 ‘Halve-controlled’ 2 Controlled 1 Example of disruption damage to W macrobrush armour In 2009 MEMOS aimed at Bulk target SSP motion ( = 5 cm) Cross-current Tangential pressure Lateral loads 2 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Main results after 100 disruptions: by W. Fundamenski The heat loads at the outer divertor calculated with the MHD code FOREV Reference pulse shape Erosion profile after 20 disruptions As an example: Main results after 100 disruptions: With moving (=5 cm) separatrix, the melt erosion (crater depth) is about 1.5 mm If assuming fixed separatrix, the crater depth exceeds 5 mm Q (MJ/m2) J kA/cm2 P|| (mbar) Vmelt (m/s) Melt (µm) Mount (µm) Crater Comments 28 1.5 0.5 60 16 5 FOREV’s load, shield 0.37 8 2.6 --’’-- 10.5 0.2 33 0.016 0.04 --’’--, vaporiz. only 3 0.45 35 1.3-1.6 0.7 1.57 7 0.17 12 3.5 Trian, no shield, 30 0.3 44 23 5.5 Rectangle, --’’-, 30 0.36 32 2.3 0.87 Ref. pulse shape 50 6.2 0.52 0.15 4 0.07 26(Lat) 0.12(Lat) Triangle 0.55(Lat) Rectangle 0.08 28(Lat) 1.5(Lat) Those results need some appropriate systematization 3 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

W splashing: QDPA-T experiments and extrapolation upon ITER Dm Vm Plasma gun QSPA-T, p=2.4 bar Q = 0.5-2 MJ/m2, t = 0.5 ms, B=0 Distribution of droplets (Q = 1.6 MJ/m2, p = 2.3 bar). Dmax= 100 µm, Vmax = 25 m/s Traces of droplets, Qthr=1.2 MJ/m2 Experimental investigations on the splashing of W melt layer were carried out at the plasma gun QSPA-T (Troitsk, Russia) Upper Limit Log Normal distribution function f(x)  exp(-(ln(C(xmax/x-1)))2) matches the droplet emission measurements (x = D or V, =0.9, CD=0.4, CV=0.25) Assuming the Kelvin-Helmholtz (KH) instability as the mechanism of droplet emission, the model parameters fKH and gKH were fitted to the experiments Projecting the KH-model upon ITER a conclusion is drawn that the melt splashing would not occur (B. Bazylev et. al, PFMC-12, Juelich) Inclined plasma impact (a standalone 2D gas-dymamics code, B=0) In the KH-model the droplet velocity U and the droplet size D are given by In QSPA-T: plasma velocity V||p ~ 102 km/s plasma density p ~ 20 mg/m3 ITER parameters: V||p~300 km/s, p~0.1 mg/m3 I.e. Vm1 m/s, Dm  0.5 mm. Dm>0.1 m means: below splash-threshold. Thus the splashing in ITER is not probable Fitting the KH-model to the experiment: fKH = 0.4 and gKH = 0.6 (W = 2 J/m2) 4 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Modelling with MEMOS of Li melting damage Wall processes are assumed like that of W. Li 40 m coating on W traget so far. Target initial temperature 500 K (molten) and 300 K Impact energy Q = 0.1 MJ/m2 and pulse duration 0.5 ms Influence of JB force and tangential pressure are assessed Main conclusions: Even small ELMs completely remove Li away from W subtrat. At both 300 K and 500 K the vapour shield does not develop. Crater depth vs. cross-current on Li layer (B = T, 1 ms) Influence of tangential pressure on Li surface solid and molten Li behave similarly (1 mbar, Tmelt = 450 K) Crater depth vs. tangential pressure (At crater depth above 40 µm, W outcrops) 5 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Modelling with ENDEP and MEMOS of melting damage caused by runaways (B. Bazylev et al., ICFRM-14, Sapporo, Japan) Main features of the code ENDEP : Diverse mechanisms of slowing down of relativistic electrons in target bulk Applied magnetic field Secondary avalanche processes ITER specification (M. Sugihara): E = 15 MeV, Q up to 25 MJ/m2, t = up to 0.1 s Transversal energy of electrons E/E up to 0.2 incidence angle  = 1.5 deg sandwich target (1 cm Be top, 1 cm Cu bulk) MEMOS Ref. scenario: Q = 20 MJ/m2, Tw0 = 500 K, t = 0.1 s Main results: Evaporation 70 m (hvap) melt pool 0.5-0.7 mm (hmelt) (w/o vaporization 2 mm) Weak dependence of hvap and hmelt on E/E Distribution of energy deposition Absorbed energy fraction vs. E/E Melt layer gets thicker with Q and thinner with t 6 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

W cracking: QSPA-Kh50 experiments and PEGASUS simulation S. Pestchanyi et al. To be presented at ICFNT-9, Dalian, China In QSPA experiments W surface melts (Q = 0.75 MJ/m2) or not (0.45 MJ/m2) Experimental results: Crack width grows up with shot number At large shot numbers the width saturates. Maximum crack width: 0.75 MJ/m2: 60 m 0.45 --“-- 7 m With surface melting Q = 0.75 MJ/m2 Without melting Q = 0.45 MJ/m2 Mesh of cracks after W irradiation after many shots. Crack pattern does not change. Crack average width vs. shot number Earlier PEGASUS simulated armour cracking above melting threshold Now the code simulates below melting threshold To achieve it, plasticity thermosetress was implemented in the thermomechanic model of the code Theoretical background: the Kelvin-Voigt model:  ~ 10 Mpa,  ~ E ~ 1 GPa,  ~ 50 s MPa 7 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Mechanism of cracks appearence: During the heating compressive thermostress appears in ~ 50 m sub-surface layer. At the high temperature the deformations become plastic which relaxes stress The following decrease of temperature fixes local material deformations beause it increases the viscosity . This results in the cracks (because large tensile stress appears) PEGASUS simulation: the net of cracks developed at the W sample below melting point. At   50 s MPa, the average crack mesh size is of 0.5 mm and crack width 7 m (in agreement with the measured value). 8 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Simulation of Massive Gas Injection with the code TOKES I. Landman et al. To be presented at ICFNT-9, Dalian, China TOKES is MHD tokamak plasma and wall code 2D code (toroidal symmetry) Multi-fluid plasma (from D to W) Radiation losses Plasma is dumped into SOL and comes to wall Wall sputtering and vaporization Neutral fluxes in whole vessel Preamble: After discussions in ITER our work in 2009 is focused on MGI. To better simulate MGI, the code is significantly generalized: previous 1D plasma model  2D 2D plasma model is necessary because the radiation flush comes from rather cooled and located region of plasma edge Aim of current simulations: Estimation of maximum radiation impact on ITER wall during MGI, i.e. maximum Be wall temperature Initial Be wall temperature 500 K Main features of current MGI simulation: Gas injector (G = Ar, Ne) is horizontal in mid-plane Quasistationary radiation model (which is simplified compared to previous 1D plasma non-stationry model) Standard ITER initial plasma profile (Ne(x) and Te(x)) T>0: Nm and Tm are functions of x and y (m = e, D, Ar) The Euler’s equations for the longitudinal expansion of the fluids as well as 2D diffusion- and thermal conduction equations are numerically solved. Inflow G(t) is assumed given: inj 9 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman Cadarache 23.04.09

Previous models used in TOKES Validation of TOKES radiation model Spatial profiles of Ne-ion density at different time moments and initial ne cooling time versus max 0D model allows detailed ionization and radiation losses 10 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Example of ITER MGI simulation (G=Ar): Ar-ion density at different time moments Te at the moment of reaching the separatrix value of q = 2. The mapping onto the (x,y)-plane with the varying numbers of radial plasma cells is shown. Density distribution of neutral Ne-atoms 2 ms To achieve most fast and adeqate simulation, sophisticated rectangular mesh for 2D plasma and very fine triangle mesh to guide slowly moving G-atoms are developed Min triangle size ~ 0.5 cm 11 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Comparison of TOKES simulation with DIII-D argon experiment 2007 E.M. Hollmann et al., Nucl. Fus. 48 (2008) 115007 No validation yet, scaling ITER  DIII-D only: R  R/4, Bt 0.4Bt and Ip  Ip/10. Thus q(x) is self-similar. The injector location remains like ITER’s. However, the gas inflow G(t) fits that of DIII-D. Centre Te and averaged ne retrieved from DIII-D and predicted for ITER Prad and Ar masses MG0 and MG for DIII-D and ITER Cooling in TOKES is 2 times faster than that in DIII-D The discrepancy is attributed to the quasistationary radiative model of temporarily used 2D plasma different locations of injector Current model does not contain the ionization time ~ 1 ms However, for ITER with expected TQ time >> 1 ms it can be adequate Therefore the preliminary simulation of MGI in ITER seems reasonable DIII-D size: a=0.5 m Bt = 2.1 T Ip=1.5 MA q95=3.5 Te0=2.5 keV ne0=5×1019 12 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Summary for ITER modelling The results for ITER : Maximum temperature of Be wall surface during MGI Wall temperature near X = 10.8 m for ITER Wall radiation flux Qrad for ITER Summary for ITER modelling 2 ms 8 ms Neutral neon in vessel: max = 7x1025 at/s inj = 5 ms 13 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Objectives High-Z- and liquid metals (PWI-05-02: 0.6 PPY PS and 0.6 PPY BS; PWI-05-03: 0.3 PPY BS) Further model W erosion for transient heat loads at varying surface shaping Benchmark MEMOS (and PEGASUS) against plasma gun and tokamak data Continue simulations for liquid Li to assess stability against transients Transient loads and mitigation (PWI-07-02 1.5 PPY BS) Simulate with ENDEP runaway heat loads and with MEMOS the following melt erosion. Jobs for TOKES: Further model impact of eroded atoms on plasma operation after ELMs Transient loads on divertor and first wall plates Further develop 2D radiative MHD multi-fluid plasma model MGI simulations varying gases, gas inflow and valve positions. Validate the codes against JET, AUG, TEXTOR, JUDITH and plasma gun data. 14 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman

Conclusions W melting and splashing: For ITER weak transients (no vapour shield) absence of W melt splashing. Assesments for Li: Even small ELMs (0.1 MJ/m2) can completely remove Li away from W subtrat. Runaways: the vaporization of Be significantly decreases melt depth (2 mm  0.7 mm) (which decreases removal of Be by JB force) W cracking: Plasma gun experiments allowed validation of PEGASUS plastisity model. Massive Gas Injection: The radiation flush can result in ITER wall temperature above Be melting point. Melting can be avoided decreasing inflow of injected gas (keeping the cooling time within 7 ms) 15 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009 I.S. Landman