1. Slide 1 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Modelling on Wall Surfaces and Tokamak Plasma Consequences of ITER Transient Events 1 Forschungszentrum Karlsruhe (FZK), Germany 2 Troitsk Institute for Innovation and Fusion Research (TRINITI), Russia Contents Surface melting of W divertor armour and Be main chamber wall Brittle destruction of Carbon Fibre Composites (CFC) and cracking of W Contamination of the SOL and core plasma after ELMs Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft FUSION-PL FZK – EURATOM FUSION ASSOCIATION I. Landman 1, B. Bazylev 1, S. Pestchanyi 1 with contributions from A. Zhitluckhin 2, V. Podkovyrov 2 N. Klimov 2 and V. Safronov 2

2. Slide 2 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Introductory comments: Available tokamaks cannot provide required transient loads Q up to 15 MJ/m 2 Therefore we develop own codes to apply to ITER predictions -- behavior of candidate materials for fusion (Be, C, W) -- tolerable sizes of off-normal events (ELMs and disruptions) For validation, tokamak simulators – pulsed plasma guns are engaged ( up to 0.5 ms) The objectives of our EFDA tasks running in 2006: TW3-TPP/ MATDAM (finished Jun), TW5-TPP/ ITERTRAN, TW5-TPP/ BEDAM Modelling support for plasma gun experiments with ITER divertor materials of EU trademark (TRINITI facilities QSPA-T and MK-200UG) Modelling of damage to ITER divertor and main chamber after transients Modelling of tokamak plasma contamination following ITER ELMs The codes MEMOS, PHEMOBRID, PEGASUS, FOREV and TOKES are engaged

3. Slide 3 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe MEMOS calculates melt motion at heated metallic surfaces (Be, W) accounting for melting, resolidification and evaporation. Melt motion is due to 1) p, 2) surface tension, 3) J B force It was validated against electron beam- and plasma gun experiments (e-beams: JUDITH, plasma guns: QSPA-Kh50 (Kharkov), QSPA-T, MK-200UG) The code MEMOS: earlier validations Q melt works well MEMOS validations by plasma guns MEMOS validations by e-beam at 5 MJ/m 2 on the depth of resolidification crater

4. Slide 4 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Simulation of W-brushe with MEMOS Validation by QSPA-T The 2D profile of W-brushes is implemented Main conclusion: the depth of W melting and resolidification profile are rather similar to that of bulk W target. However, melt velocity in W-brushes is less by a factor 0.3 - 0.5 Validation by QSPA-T is carried out Relevance of QSPA to ITER: Q ~ 0.5 – 1.5 MJ/m 2 and = 0.5 ms as in ITER QSPA: plasma velocity V is 10 5 m/s, in ITER ~ 10 6 Pressure at the target: p ~ nE i Density n follows from Q = E i nV p 1/ E i E i is ion kinetic energy, in QSPA 100 eV only Thus in ITER the pressure should be much lower. (Particular figures significantly depend on the size of transient event) ITER transients Kind of damage Disruption (10 MJ/m 2, 3 ms) ELM (3 MJ/m 2 0.5 ms) W vaporization loss 1 m0.1 m W melt roughness 5-10 m1 m Single ELMs and disruptions Therefore, the QSPA experiments should result in much more pronounced melt motion Therefore the MEMOS was engaged for ITER predictions

5. Slide 5 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe MEMOS (in 2006): simulation of Be melting under radiation impact Bulk temperature at 0.5 ms. Radiation load duration 0.5 ms Full resolidification after 1.1 ms Radiation heat load distribution over Be target surface Melt depth vs. heat load duration (T 0 = 300 K) Evaporation depth vs. heat load duration Melting and evaporation thresholds vs. heat load duration Resolidification profile on Be target surface under plasma action Validation by radiation load experiments is required

6. Slide 6 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe PHEMOBRID validation against the QSPA PHEMOBRID calculates evaporation and BD of CFC based on BD threshold 10 kJ/g (as GOL-3 results) The recent QSPA experiments (ELM relevant loads with 0.5 ms): Mass losses appear at the impact energy density W 0 > 1.4 MJ/m2 The rate of CFC erosion exceeds 1 μm/shot (evaporation at T 0 = 500 C) Numerical simulations: The heat flux at the surface was calculated as W(t) = W 0 exp(-h(t)/h 0 ), h(t) calculated thickness of evaporated material, h 0 = 1.5 μm (vapour shield). Plasma impact was assumed under 30 deg CFC target layout Evaporation rate of CFC NB31 vs. absorbed energy

7. Slide 7 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe PEGASUS simulation for CFC with inclined fibres versus MK-200UG tests It calculates BD of CFC and cracking on W surface The last idea was to incline the PAN fibres under 45 deg to the pitch fibres In PEGASUS simulations, BD erosion rate under ELM-like loads has decreased by ~5 times Experiments at MK-200UG to proof this qualitative prediction are performed The experiments have not confirmed the modelling results: CFC erosion rate does not depend on orientation of CFC sample PEGASUS: standard (a) and inclined (b) CFC fibres a)b) It seems that the CFC surface was so damaged that the CFC properties became isotropic, and at the large temperature the pitch- and PAN fibres acquire equal thermoconductivities. PEGASUS: BD damage to improved CFC structure (The PEGASUS is an abbreviation of Particle Ensemble for Grain Aggregate Simulation )

8. Slide 8 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe PEGASUS modelling of cracks on W target surface A model of W surface cracking is developed by S. Pestchanyi to explain experimental crack patterns with crack depth scales of 500 and 50 µm A thermostress that appears in the thin resolidified layer after fast cooling causes the cracks through the bulk Typical W parameters: Youngs modulus E 3 10 2 GPa The Poisson ratio 0.3 (shear modulus/E) Tensile strength T < 1 GPa Thermal expansion coeff. 10 -5 K -1 Melt layer thickness h ~ 10 m Typical thermostress c ~ T melt E ~ 10 GPa At c >> T cracking should occur W cross-section with the cracks: QSPA results versus PEGASUS simulation. Q = 0.9 MJ/m 2, = 0.5 ms

9. Slide 9 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe PEGASUS simulation of cracks on W target PEGASUS simulation of cracks on W surface W surface (QSPA, 100 shots of 0.9 MJ/m 2, 0.5 ms. Primary cracks depth ~500 µm Secondary meshes sizes and depth ~10 2 µm Typical thermostress F applied to the cracks on W surface (h melt << L) A formula for crack depth (F relates with E T ) Cracking scenario: W surface is fast heated, higher than T melt. Thus pre-surface bulk gets stressed, but in melt c = 0 even just after resolidification The surface temperature decreases and after c exceeded T, large cracks appear, which decreases c. Further cooling increases thermostress, and again c exceeded T cracks of small size

10. Slide 10 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Main features of FOREV: Magnetic toroidal geometry of ITER and JET SOL multi-fluid plasma description (D +, T +, He +2, C + to C +6 ) Radiation transport in toroidal geometry for C ELM scenario as calculated by FOREV: 1.Due to a short large increase of cross-diffusion coefficient D diff in the pedestal and the SOL, the pedestal plasma fills the SOL. 2.SOL DT-He plasma hits in both divertor surfaces. 3.At the targets, heat flux and plasma pressure cause evaporation, with account of heat transport into carbon material 4.Eroded material propagates back into the SOL. Comments on the simulations: Experimental DT plasma flux was reproduced approximating D diff by suitable dependencies from existing tokamaks. The calculations had been performed at W ELM = 3.5 to 12 MJ. ITER layout in FOREV RMHD code FOREV: applications for ELM simulations targets maximum heat fluxes and behaviour of D diff during an ELM

11. Slide 11 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe FOREV modelling for heat flux and plasma pressure at ITER divertor surfaces In this example ELM size is Q = 0.8 MJ/m 2, = 0.5 ms Distributions of impacting DT heat flux and pressure over inner divertor surface. Those load profiles at different times are used by MEMOS, PHEMOBRID and PEGASUS. along separatrix, 1.1 ms SOL contamination as calculated by FOREV The vaporization threshold is obtained at W ELM = 4.0 MJ (Q = 0.4 MJ/m 2 ). During 0.5 ms a significant carbon plasma density in SOL can occur, up to 10 21 m -1. Carbon ions occupy SOL for a few ms, with their temperature dropping down to 1-2 eV (due to radiative cooling) Further ELM consequences are simulated with the code TOKES using the FOREV data on carbon influx into the pedestal

12. Slide 12 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Newly available features: wall and neutrals Heat transport in the wall, surface evaporation Underground triangle meshes Propagation of neutrals (atoms, photons and neutrons) in the vessel volume as random (Monte-Carlo) beams Ionization of atoms by plasma (immediately to Posts Z) The magnetic surfaces are chains of segments through the triangle meshes, which provides optimal plasma- neutral coupling Vessel surface of arbitrary poloidal cross-section The algorthm of TOKES allows magnetic islands The TOKES is still under development (ITER preliminary layout) Features of TOKES on plasma The Grad-Shafranov equation Pfirsch-Schlüter transport Multi-fluid plasma, (from D to C, and W ions) D- and T-beams heat and feed, radiation cools (by Post) D+T He + n fusion reaction Coil currents feedback upon plasma shape ITER layout in TOKES a b w

13. Slide 13 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Contamination of ITER core by carbon after ELMs using the FOREV data Whole ITER discharge of 400 s was simulated Carbon ions of FOREV were injected into plasma edge Power losses have been calculated: radiation losses and fusion power decrease Q from 0.8 to 1.4 MJ/m 2. Magnetic field was fixed. Main result: Tolerable ELM size 1 MJ/m 2 for ELM frequency ~1 Hz Carbon impurity propagation into the core after ELM Benchmark scenario:

14. Slide 14 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Conclusions and further objectives MEMOS Validations for W under plasma impact and Be under e-beams are done Validation for Be under radiation load experiments is required (experimental activity on Be using plasma guns is assumed in Kurchatovs and TRINITI) PEGASUS and PHEMOBRID In the modelling the CFC erosion develops mainly due to cracking of PAN fibres At the validation of PHEMOBRID the account for vapor shield became necessary PEGASUS should be validated extrapolating pitch fibre thermoconductivity down to PAN fibres at ~ 4 10 3 K PEGASUS modelling on W cracking seems successful. Further development is needed (cracking below the melting threshold: implementation of plasticity). FOREV and TOKES The tolerable 1 MJ/m 2 obtained is at the minimum of expected ITER ELM sizes. In FOREV, Be and W plasma species should be implemented In TOKES, at first the radiation transport and the ionization modelling should be improved (now Posts data are used)

15. Slide 15 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe

16. Slide 16 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe

17. Slide 17 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Additional informations Main results from MK-200UG and QSPA-T at large Q CFC NB31 and NS31 were exposed to 200 shots 15 MJ/m 2 Both CFC behaved similarly (regime with vapour shield) Maximum erosion rate is proportional to pulse duration PAN fibres max. erosion rate is of 20 m/ms Pitch fibres max. erosion rate is of 3 m/ms (evaporation) Graphite particles of sizes of 1 to 10 2 m are collected Start of vaporization: Q min =0.3 MJ/m 2 for 0.05 ms (MK-200UG) (Q min : at 0.5 ms would be Q min = 1 MJ/m 2 ) MatrixTow Direction to axis || to axisradialaxial 10 -2 k [W/m/K] 2 - 50.4 - 0.80.510 - 20 10 6 [1/K] 1~30~101 10 -2 E [GPa]3 – 70.3-0.80.1-0.24-8 CFC properties (T < 2 10 3 K) W melt damage after single ELM: Melting threshold 1.0 MJ/m 2 ( = 0.3 ms) Vaporization threshold: 2.5 MJ/m 2 Melt velocity less than 0.5 m/s Maximum crater depths ~ 0.5 m Vaporization thickness ~ 0.1 m

18. Slide 18 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Additional informations (continued) Damage to the dome gaps and the divertor cassette gaps the melting of copper at the W-Cu adjoins is significant protective tungsten aprons of the gaps may be necessary PEGASUS features: 3 10 6 cells of 1 m represent 3D material structure Thermal- and mechanical bonds between the grains Anisotropic (for CFC) heat transport through grain boundaries Stress due to anisotropy and ( c ) temperature gradients Cracking of the bonds above elasticity threshold ( T )

19. Slide 19 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe Transient energy fluxes expected at the ITER divertor target ITER EventRepetitionDurationTarget loadImpact energy Disruptionseldom1.. 10 ms10..30 MJ/m 2 up to 10 keV Type I ELMs1-10 Hz0.3..0.6 ms0.5..4 MJ/m 2 1..3 keV Normal tokamakoperation500 s10 MJ/ m 2 /s1..3 keV Main parameters of plasma guns Facility MK-200UGQSPA Pulse duration [ ms ]0.050.2-0.5 Target load [ MJ/m 2 ]0.3 - 150.6 - 30 Load spot size [ cm ]6 – 74-5 Magnetic field [ T ]20.5 Impact energy [ keV ]1.5 (ions)0.2 (ions) Plasma gun QSPA Plasma gun MK200UG schematically

20. Slide 20 12-15 Nov 2006, EFDA PWI meeting, LjubljanaI.S. Landman, FZ-Karlsruhe FZK codes for consequences of ITER off-normal events Material surface modelling MEMOS-1.5D (fluid dynamics) Melt motion at heated metallic surface (W and Be targets) PEGASUS-3D (thermomechanics) Brittle destruction of graphite and CFC Cracking on W surface PHEMOBRID-3D (BD threshold model) Brittle destruction of graphite and CFC Plasma modelling FOREV-2D (radiation MHD) Pulse transient loads at targets Plasma shield (disruptions, Type I ELMs) SOL contamination (C, W, Be) TOKES-2D (equilibrium MHD) Confined plasma equilibrium Core contamination (by C so far) Core plasma wall coupling effects