SPECIFIC FEATURES OF MECHANISM FOR DUST PRODUCTION ...

SPECIFIC FEATURES OF MECHANISM FOR DUST PRODUCTION FROM TUNGSTEN ARMOR UNDER ACTION OF ELMs S. PESTCHANYI,a* V. MAKHLAJ,b and I. LANDMANa a

Karlsruhe Institute of Technology, IHM, 76344 Karlsruhe, Germany Institute of Plasma Physics of the NSC KIPT, Kharkov, 61108, Ukraine

b

Received October 29, 2013 Accepted for Publication April 3, 2014 http://dx.doi.org/10.13182/FST13-736

Analysis of comprehensive investigations of divertor armor erosion under action of edge-localized modes (ELMs) using the PEGASUS-3D code has been performed. Different erosion mechanisms for tungsten (W) and carbon fiber composite (CFC) armor materials have been revealed. This difference explains almost 3 orders of magnitude difference in the erosion rates of CFC and W. Investigation of the crack pattern evolution under repetitive ELM-like surface heat load has been done.

I. INTRODUCTION

Tungsten is foreseen as the reference divertor armor material for ITER and DEMO tokamaks. Simulations of the tungsten armor cracking due to the type I ELMs of various energy depositions have been successfully performed in Refs. 1 and 2 using the PEGASUS-3D code and the results are verified with experiments in plasma guns. The results of these investigations read that under action of ITER ELMs tungsten will definitely crack at the surface. The reason for tungsten cracking under severe heat loads is thermostress, generated due to temperature gradient perpendicular to the heated surface as well as due to re-solidification and cooling down of the surface melt. The grains of ITER armor elongated perpendicular to the armor surface, so the cracks propagate mostly along the grain boundaries and do not *E-mail: [email protected] 150

Special treatment for tungsten armor tiles has been proposed for reduction of dust production rate in ITER operation regime. KEYWORDS: plasma-facing materials, tungsten, brittle destruction Note: Some figures in this paper may be in color only in the electronic version.

deteriorate the thermoconductivity. The only possible danger from tungsten armor for ITER operation would be the dust produced during its cracking. Tungsten is extremely efficient radiator for plasma thermal energy, so even small W concentrations in the tokamak core plasma may drastically cool it down, thus reducing the thermonuclear gain of D-T reaction or run the confinement into the disruption. Analysis of experimental data on the tungsten cracking and dust production allows us to conclude that the mechanism of dust production from tungsten is qualitatively different from the dust production process from CFC and graphites. Simulations of the dust production from tungsten armor under action of ELMlike surface heating have been performed using the PEGASUS-3D code. The simulation results have proved that the dust produced mainly from the intergranular subgrains as it has been anticipated from analysis of available experimental data.

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FEATURES OF DUST PRODUCTION FROM TUNGSTEN ARMOR DUE TO ELMs

II. DIVERTOR ARMOR CRACKING AND THE DUST PRODUCTION MECHANISMS II.A. Common Features of the Erosion Mechanisms for CFC and W

The divertor armor has been designed for the divertor protection against plasma heat flux from SOL. Originally CFC has been chosen as the armor material for ITER tokamak. CFC can withstand the stationary heat flux of 5– 10 MW/m2, characteristic for ITER. But, in the ELMy H mode, being the ITER reference scenario, ELMs produce additional armor heating on top of the stationary flux. ELMs increase the heat flux to the armor by 2–3 orders of the magnitude over the stationary value, but the time duration of this flux is very small t j 0.5 ms. These short severe heatings of the divertor armor with repetition rate of 1–10 Hz cause main armor erosion. Simulations and experiments in plasma guns have revealed intolerable CFC erosion by ELMs (Refs. 3 and 4). Besides, the eroded carbon co-deposited with tritium onto the vessel walls. This co-deposited tritium intolerably contaminates the ITER vacuum vessel. This is why tungsten has been chosen to substitute CFC as the divertor armor material. Tritium accumulation on tungsten is negligibly small comparing with carbon and the W erosion rate under action of ELMs is at least three orders of the magnitude smaller in comparison with the CFC erosion rate. Smaller erosion rate of tungsten is explained by different erosion mechanism comparing with that of CFC. The erosion mechanisms have been revealed in simulations and in plasma guns experiments, producing plasma impact similar to that of ELMs in ITER. Erosion of both materials, CFC and W, under ITER conditions is mainly due to cracking (brittle destruction) under action of the thermostress, which arises close to the armor surface when fast severe heat flux hits the surface. Huge difference in erosion rates of CFC and W is explained by difference in the cracking mechanisms. Under action of ELM-like heat flux the armor surface heated up to temperatures, comparable with the melting temperature in case of tungsten and with the sublimation temperature in case of CFC. Heated ispffiffiffiffiffi only the surface layer with characteristic depth of l~ kt * 200 mm for both materials having comparable thermal diffusivity k*1cm2/s. Such fast heating generates the temperature gradient of +T*105 K/cm. This +T value depends of the heating time t and of the deposited energy only. The thermostress arising due to steep temperature gradient during ELM is much larger than the tensile strengths for both materials and the yield strength for W, so both materials are eroded because of brittle destruction of the surface. However, because CFC is very anisotropic and brittle material, the cracks arise everywhere at the interfaces between fibers and matrix during compression with the thermostress. In contrast, W is isotropic and plastic material, so compressive thermostress relaxed due to plastic deformations. FUSION SCIENCE AND TECHNOLOGY

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Cracking of W proceeds due to action of tensile stress during cooling down of the armor surface. CFC is a material with extremely anisotropic microstructure. Structural component of CFC – the fibers – have characteristic diameter of *10 mm; coefficient of thermal expansion (CTE) for the fibers along the fiber axis and in perpendicular direction are *10 times different. CTE values of the CFC matrix are in between these two values. PAN fibers in CFC are packed in parallel bunches of *500mm diameter separated by *2mm distance. For CFC the thermostress is concentrated at the interfaces between the fibers and the matrix due to huge anisotropy of the fibers. The thermostress concentration at the interfaces between the fibers and the matrix cause its cracking during surface heating. The erosion of CFC occurs due to cracks arising at the interfaces between the fibers and the matrix. As a result of this cracking the erosion proceeds mainly along the PAN fiber bunches under action of ELMs. After formation of characteristic surface profile, with valleys along the PAN fibers, erosion proceeds with equal rate along the whole surface. The regions with pitch fibers are ‘undermined’ from valley side, so the erosion proceeds at the whole heated surface as it has been simulated using PEGASUS-3D code, see Fig. 1 and the results are verified with experiments.3,4 II.B. W Erosion Mechanism due to Surface Re-Solidification

In contrast with CFC, tungsten erosion mechanisms are very different. Under action of powerful ELM-like heat loads with E w 2 MJ/m2 and t 5 0.5 ms tungsten surface melts and the melt layer splashed out, but such severe ELMs are fully intolerable in thermonuclear reactor and should be mitigated. Less powerful ELMs cause erosion by brittle destruction. ELMs of E j 1 MJ/m2 are tolerable, despite of the marginal surface melting because they does not cause splashing, so the melt re-solidifies after each ELM. The most topical erosion mechanism for tungsten is cracking and dust production with ELMs of the energy deposition, which enough to melt thin layer of few micrometers or to heat it up to several thousand degrees Kelvin, without melting the surface. Most severe erosion has been found in regimes with melting and re-solidification of the tungsten surface. The dust is produced due to split of particles from the crack sides. The crack pattern consists of a network of irregular cells with the sides following the cracked tungsten grains boundaries. The crack sides are closed and opened during repetitive heating and cooling of the tungsten surface. These movements cause split of ‘beards’ and ‘teeth’ at the crack edge. The cracking mechanism for this case has been investigated in Ref. 1. Main cause for thermostress generation in this case is the difference in densities of solid and molten tungsten: melt density is *9% smaller than the density of solid.

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Fig. 1. CFC fiber structure on the top of heated armor tile consists of vertical PAN fiber bunches of 0.5 mm diameter and much smaller horizontal bunches (upper left panel). The CFC divertor armor erodes mainly along the PAN fiber bunches under action of ELMs. After formation of characteristic surface profile with valleys along the PAN fiber bunches the erosion proceeds everywhere due to ‘undermining’ of pitch ridges from the valleys. Shown are the CFC sample surface after hundreds of plasma shots in the QSPA-T facility (lower left panel) and the PEGASUS-3D simulation result (right panel).

The sequence of events leading to the crack formation in tungsten is as follows. During surface heating a compressive thermostress is developed under the surface due to the temperature gradient, which reaches its maximum at the surface,5 but this compressive thermostress does not cause cracking. Melting of the surface completely relaxes the thermostress inside the melt and the molten tungsten expands perpendicular to the surface. Re-solidification of the melt after ELM goes with very fast rate, and the re-solidified layer of smaller density arises almost without stress on the top of the deformed solid tungsten with maximum stress at the interface between the solid and the former melt. So, after fast resolidification the re-solidified layer is stress-less at the melting temperature and under this layer the compressive thermostress in un-molten solid is maximal, decreasing perpendicular to the surface. During cooling down of this layered structure the unmolten tungsten, which has been compressed during heating, relaxes, so the compressive thermostress relaxes also, but this relaxation of the ‘floor’ of the former melted pool causes expansion of the re-solidified layer thus generating tensile stress inside the re-solidified layer. The tensile stress increased during cooling down of tungsten surface and causes cracking. The force from the main component of the stress tensor sxx directed along the heated surface5 causes formation of cracks perpendicular to the surface. Again, the main reason of the tensile thermostress generation in this case is fast re-solidification of the molten tungsten layer with decreased density. Let us assume that melting does not occur and all the deformations are elastic. Then the compressive thermostress arises during heating with ELM 152

and then fully relaxes during cooling down after ELM. The tensile thermostress does not appear at all and the cracking is absent in this case. II.C. W Erosion Mechanism due to Plastic Deformation

If tungsten surface heating is not enough to melt its surface then the cracks generated by tensile stress due to plastic deformation of tungsten. As in the previous case, the dust is produced due to particles split from the crack sides, but the thermostress, which causes cracking, is different. During heating of tungsten surface thermal expansion leads to the compressive thermostress generation. The thermostress grows with increase of the temperature gradient during heating with ELM. Compressive thermostress does not produce cracks, but when the thermostress tensor reaches the threshold value for plasticity (von Mises criterion) the plastic deformations start. Under action of the stress the sample surface is plastically deformed with compressive deformations in the surface plane and tensile deformation in the direction perpendicular to the plane. The deformations proceeds all the time when the von Mises criterion is fulfilled.2 The compressive deformation stops because of the thermostress relaxation due to cooling down of the sample surface then the compressive stress relaxes to zero and afterwards turns to tensile one. The tensile stress arises at the cooling down phase of ELM similarly to the previous case due to compressive deformation of the surface layers, but in this case deformations are plastic, not due to fast resolidification. Without plastic deformation of the surface the compressive thermostress reverses to zero during


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cooling down, the tensile stress does not arise and the cracking does not exist. III. SIMULATION OF W EROSION UNDER ACTION OF REPETITIVE ELMs

Simulations of the crack network evolution and the tungsten dust production under action of repetitive ELMlike surface heating have been performed using the PEGASUS-3D code. The conditions of real experiment in the QSPA-Kh50 plasma gun have been chosen for the simulations. The gun shot of the energy deposition E 5 0.75 MJ/m2 during t 5 0.25 ms provides tungsten surface melting of *7 mm and then the surface cracks after re-solidification. In the experiment the crack network has been analyzed after 5 shots. The crack pattern consists of the cracks of two characteristic sizes: large cracks of a few hundred micrometers depth with 0.5-1mm mesh size; small cracks of a few tens micrometers depth with 50–100 mm mesh size, see Fig. 2. The crack mesh is

Fig. 2. Crack pattern arising at the tungsten sample surface after 10 shots of 0.75 MJ/m2 energy deposition and 0.25 ms time duration in the QSPA-Kh50 facility. Upper panel shows the surface crack pattern, which consist of a large crack and small cracks, covering each closed mesh of the large crack. Lower panel is a perpendicular cut showing the depth of the large and the small cracks. To be compared with the simulation results in Fig. 3. FUSION SCIENCE AND TECHNOLOGY

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stable: the surface mesh pattern does not change under action of further hundred shots. In the PEGASUS-3D simulations it is assumed that the dust particle splits from the bulk tungsten when crack surrounds some volume from all sides. Grain structure of tungsten reproduced in the code on 3D array of cubic cells of 1 mm size. Depending of each cell position the thermophysical properties of the grain bulk or the grain boundary is prescribed to the cell. The boundary between neighboring cells is breached if thermostress there exceeds local tensile strengths value.6 No other artificial assumptions on the dust production mechanism are made. Simulations of the QSPA-Kh50 plasma shots have been performed under the following assumptions: the tungsten sample is cooled down to initial temperature after each plasma shot; then the sample is heated with the same shot. When the surface melts, the cracks inside the melt layer are healed, so the re-solidified layer is crackles, but the cracks deeper in the sample remain unhealed. The simulated crack pattern shown in Fig. 3 illustrates good agreement with the pattern of the simulated experiment. Strictly speaking the cracks are evolved, but the most important features of the crack pattern: two different characteristic mesh sizes and depths are in good agreement. The simulation results show that during first stage of the sample heating the cracks are closed due to thermal expansion of tungsten. Then the sample surface with closed, but not healed cracks melts. The cracks in the molten layer are healed. After re-solidification the layer is crackles at the solidification temperature. The re-solidified layer starts to crack in course of cooling down of the sample after the shot, thus producing the dust.

Fig. 3. Crack pattern arising at the numerical tungsten sample after 1 shot simulating the QSPA-Kh50 shot of 0.75 MJ/m2 energy deposition and 0.25 ms time duration using the PEGASUS-3D code. Upper left panel shows the surface crack pattern, which consist of both large and small cracks, the upper right panel shows the crack pattern at the depth of 100 mm, that is the large cracks only. Lower panel is a perpendicular cut showing the depth of the large and the small cracks.

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Fig. 4. Evolution of surface crack pattern under action of consequent ELMs simulated with the PEGASUS-3D code. Shown are the patterns after first ELM (left panel), after 4 and 7 identical ELMs. Each ELM melts tungsten surface and bridges the surface cracks. But, the cracks are much deeper than the melt depth, so after re-solidification of the melt the cracks arise approximately at the positions of the healed cracks.

The thermostress inside the layer is concentrated at the ‘bridges’ above the cracks, which still exist deep inside the sample. No wonder that the cracks in the healed layer arise nearly at the same positions as they were before healing. The simulation results confirm this assumption. Figure 4 illustrates that the surface crack pattern slightly changes during first 2–3 shots and then stabilized. The crack pattern deeper inside the sample, at the depth of 100 mm, shown in Fig. 2 evolutes so negligibly that it is worthless to show the difference. Despite the large scale crack pattern stabilization the microstructure of cracks evolutes: dust particles are split from the edges. Besides, dust particles are produced during cracking of the melted and re-solidified surface layer of tungsten. Dust particles, produced in numerical simulation, have an exponential size distribution shown in Fig. 5. The size distribution is in qualitative agreement with the distribution of dust particles found in experiment in QSPA-Kh50, see Fig. 3 of Ref. 7. The resolution of the numerical simulations

Fig. 5. Simulated size distribution of the dust particles produced after 7 shots of the QSPA-Kh50 facility of 0.75 MJ/m2 energy deposition and 0.25 ms time duration using the PEGASUS-3D code. 154

does not allow simulating the particles with size less than 1 mm. Taking into account this limitation the agreement is satisfactory.

IV. CONCLUSIONS

Results of comprehensive investigations of the divertor armor erosion under action of ELM-like surface heat loads performed earlier using the PEGASUS-3D code and the experimental results obtained in QSPAKh50 and QSPA-T plasma guns have been analyzed. Comparison of the erosion process for two different armor materials – CFC and tungsten has revealed qualitative difference in erosion mechanisms. CFC eroded the whole surface, heated with ELMs. In contrast with CFC tungsten produces dust from linear cracks, forming a network at the sample surface, so the dust production rate is proportional to the total crack length. The length of the crack inside the unit surface area is inverse proportional to the mean size of the crack mesh, so the rate depends of the mean mesh size. The dust is produced due to particles split from the crack sides. Tungsten surface inside each crack mesh does not eroded. This is why the erosion rate of tungsten is much smaller comparing with that of CFC. For example, sustained W dust production rate during 250 shots of 0.75 MJ/m2 the QSPA-Kh50 facility is 0.8?105 mm3 of dust per pulse from cm2. This value is at least three orders of the magnitude smaller in comparison with the CFC erosion rate of 0.5–2?108 mm3/pulse/cm2 measured in QSPA-T facility8 under the action of plasma pulses of comparable heat load. Additional investigation of the crack pattern evolution under repetitive ELM-like surface heat load has been performed using the PEGASUS-3D code. The heat pulse simulated with PEGASUS-3D code corresponds to the one of 0.75 MJ/m2 in the QSPA-Kh50 facility. The simulation results have been compared with the experimental measurements and good agreement has been


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Fig. 6. Crack sides roughening under action of plasma shots of 0.75 MJ/m2, 0.25 ms time duration in QSPA-Kh50 facility. Shown are the cracks after one shot (left panel) and after 350 shots (right panel).

found. Tungsten surface is melted under action of the surface heating and the melt depth is *7 mm in agreement with the value measured in the experiment as well as the main features of the crack pattern: two characteristic mesh sizes and depths are in good agreement. In the simulation the crack pattern slightly changes during first 2–3 shots and then stabilized. In the experiment the tungsten target has been analyzed after 5, 10, 50, 100 pulses and the crack pattern didn’t changed. Besides, an important feature of the dust production has been found – the erosion rate in few first pulses is 10–30 times larger than the sustained erosion rate later on.9 The same difference in erosion rate has been found in experiments in QSPA-Kh50 and QSPA-T. This large dust production rate in first pulses can be explained by simulations: after first cracking of virgin tungsten surface a very rough crack sides are appeared. Then, after few closing and opening of each crack the rough sides are smoothed away by split of the spikes. This sides roughening is illustrated in Fig. 6. Taking into account this peculiarity, one can propose the following tungsten tiles processing before using as tokamak armor. The tiles should be irradiated with 1–2 intense plasma shots causing surface melting of *5 mm, which produces a crack network, which consists of cracks, running mainly perpendicular to the heated surface. This initial crack network should be tested with stationary heat load to reveal the overheated regions due to the cracks, occasionally running parallel to the surface. These samples should be sorted out, but it is a priori clear that the number of such defective tiles should be relatively small due to elongation of the W grains perpendicular to the heated surface. Tungsten dust, produced during such processing shots should be removed. The divertor armor, produced from tiles processed in such a way should produce at least one order of the magnitude less dust during heating with ITER ELMs. The crack pattern produced in such a way is similar to the tiles castellation, but the castellation does not prevent the tiles cracking. FUSION SCIENCE AND TECHNOLOGY

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Processing the tiles with plasma shots generates natural ‘castellation’ with inherent pattern, so this ‘castellation’ does not evolutes further and does not deteriorate the thermoconductivity because the cracks are perpendicular to the tiles surface, so parallel to the heat flux.

ACKNOWLEDGMENTS This work, supported by the European Communities under the EFDA Task Agreement WP13-IPH-A11-P1-01 between EURATOM and Karlsruhe Institute of Technology, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

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