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Assessing the performance of the ITER design for the tungsten (W) divertor Plasma Facing Units (PFUs) in a tokamak environment is a high priority issue to ensure efficient plasma operation. This paper reviews the most recent results derived from experiments and post-mortem analysis of the ITER-grade PFUs exposed in the WEST tokamak and the associated modelling, with a focus on understanding heat loading and damage evolution. Several shaping options, sharp or chamfered leading edge (LE), unshaped or shaped blocks with a toroidal bevel as foreseen in ITER, were investigated, under steady state heat fluxes of up to 120 MW⋅m−2 and 6 MW⋅m−2 on the sharp LE and top surface of the block, respectively. A very high spatial resolution (VHR) infrared (IR) camera (0.1 mm/pixel) was used to derive the temporal and surface distribution of the temperature and heat load on the castellated tungsten blocks for different geometric alignment and plasma conditions. Photonic modelling was required to reproduce the IR measurements in particular in the toroidal and poloidal gaps of the mono-block (MB) stacks where high apparent temperatures are observed. Specular reflection is found to be the dominant emitter in these parts of the blocks. W-cracking was observed on the leading edge of the blocks already within the first phase of plasma operation, during which the divertor was equipped with unshaped PFUs, including some intentionally misaligned blocks. Numerical analysis taking into account softening processes and mechanical stresses, revealed brittle failure due to transients as the dominant failure mechanisms. Ductile failure was observed in one particular block used for the melting experiment, therefore under extremely high steady state heat load conditions. W-melting achieved on actively cooled PFU exhibits specific features: shallow melting and slow melt displacement. Plasma exposure of pre-damaged PFUs at various damage levels (crack network and melted droplets) was carried out under, QC 20231201

The consequences of tungsten (W) damaging processes, such as cracking and melting, on divertor lifetime and plasma operation are high priority issues for ITER. A sustained melting experiment was conducted in WEST using a 2 mm deep groove geometry on the upstream mono-block (MB) to overexpose the sharp leading edge (LE) of the downstream MB. W-cracking has been evidenced for the first time with a very high spatial resolution infrared camera before tungsten melting was reached. These cracks develop when the monoblock temperature is about 2600 degrees C, thus higher than both ductile to brittle transition and softening threshold of tungsten, suggesting that these cracks are different from the ones observed in previous campaigns where brittle failure was involved, because of transient events on cold monoblock. Post-exposure analyses have been performed on the damaged monoblock, highlighting 12 main cracks on the LE, with a width varying from 33 mu m to 77 mu m, and an average spacing of 0.45 mm. Parallel heat flux about 90 MW/m2 has been derived from infrared temperature measurements, with a heat flux decay length on the target of 4 mm. The T-REX modelling code suggest here that with these thermal inputs, a crack can initiates due to thermal cycling without disruption, with a ductile failure, under 1 to 5 cycles for a tungsten DBTT varying from 400 degrees C to 500 degrees C., QC 20231215

We summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-called Multi-particle collision (MPC) method, alternative to Fokker-Planck and Monte Carlo approaches. MPC is related to particle-mesh approaches for the computation of self consistent long-range fields, ensuring that simulation time scales with $N\log N$ in the number of particles, as opposed to $N^2$ for direct $N$-body. The collisional relaxation effects are modelled by computing particle interactions based on a collision operator approach that ensures rigorous conservation of energy and momenta and depends only on particles velocities and cell-based integrated quantities., Comment: 7 pages, 2 figures. To appear in the proceedings of the 362 IAU symposium "Predictive Power of Computational Astrophysics as a Discovery Tool". Chamonix, France 8-12 Nov. 2021

We summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-called Multi-particle collision (MPC) method, alternative to Fokker-Planck and Monte Carlo approaches. MPC is related to particle-mesh approaches for the computation of self consistent long-range fields, ensuring that simulation time scales with $N\log N$ in the number of particles, as opposed to $N^2$ for direct $N$-body. The collisional relaxation effects are modelled by computing particle interactions based on a collision operator approach that ensures rigorous conservation of energy and momenta and depends only on particles velocities and cell-based integrated quantities., Comment: 7 pages, 2 figures. To appear in the proceedings of the 362 IAU symposium "Predictive Power of Computational Astrophysics as a Discovery Tool". Chamonix, France 8-12 Nov. 2021

Plasma-facing components receive enormous heat fluxes under steady state and especially during transient conditions that can even lead to tungsten (W) melting. Under these conditions, the unimpeded thermionic current density emitted from the W surfaces can exceed the incident plasma current densities by several orders of magnitude triggering a replacement current which drives melt layer motion via the J x B force. However, in tokamaks, the thermionic current is suppressed by space-charge effects and prompt re-deposition due to gyro-rotation. We present comprehensive results of particle-in-cell modelling using the 2D3V code SPICE2 for the thermionic emissive sheath of tungsten. Simulations have been performed for various surface temperatures and selected inclinations of the magnetic field corresponding to the leading edge and sloped exposures. The surface temperature dependence of the escaping thermionic current and its limiting value are determined for various plasma parameters; for the leading edge geometry, the results agree remarkably well with the Takamura analytical model. For the sloped geometry, the limiting value is observed to be proportional to the thermal electron current and a simple analytical expression is proposed that accurately reproduces the numerical results., QC 20180115

The first results of particle-in-cell simulations of the electrostatic sheath and magnetic pre-sheath of thermionically emitting planar tungsten surfaces in fusion plasmas are presented. Plasma conditions during edge localized modes (ELMs) and during inter-ELM periods have been considered for various inclinations of the magnetic field and for selected surface temperatures. All runs have been performed under two assumptions for the sheath potential drop; fixed or floating. The primary focus lies on the evaluation of the escaping thermionic current and the quantification of the suppression due to the combined effects of space-charge and Larmor gyration. When applicable, the results are compared with the predictions of analytical models. The heat balance in the presence of thermionic emission as well as the contribution of the escaping thermionic current to surface cooling are also investigated. Regimes are identified where emission needs to be considered in the energy budget., QC 20170815

A series of experiments has been performed on JET to investigate the dynamics of transient melting due to edge localized modes (ELMs). The experiment employs a deliberately misaligned lamella in one module of the JET bulk tungsten outer divertor, allowing the combination of stationary power flux and ELMs to transiently melt the misaligned edge. During the design of the experiment a number of calculations were performed using 2D particle-in-cell simulations and a heat transfer code to investigate the influence on the deposited power flux of finite Larmor radius effects associated with the energetic ELM ions. This has been performed using parameter scans inside a range of pedestal temperatures and densities to scope different experimentally expected ELM energies. On the one hand, we observe optimistic results, with smoothing of the heat flux due to the Larmor gyration on the protruding side of the lamella which sees the direct parallel flux-the deposited power tends to be lower than the nominal value expected from geometric magnetic field line impact over a distance smaller than 2 Larmor radii, a finding which is always valid during ELMs for such a geometry. On the other hand, the fraction of the flux not reaching the directly wetted side is transferred and spread to the top surface of the lamella. The hottest point of the lamella (corner side/top) does not always benefit from the gain from the Larmor smoothing effect because of an enhanced power deposition from the second contribution., QC 20150109

This paper presents an analysis of the carbon-deuterium circulation and the resulting balance in Tore Supra over the period 2002-2007. Carbon balance combines the estimation of carbon gross erosion from spectroscopy, net erosion and deposition using confocal microscopy, lock-in thermography and SEM, and a measure of the amount of deposits collected in the vacuum chamber. Fuel retention is determined from post-mortem (PM) analyses and gas balance (GB) measurements. Special attention was paid to the deuterium outgassed during the nights and weekends of the experimental campaign (vessel under vacuum, Plasma Facing Components at 120 degrees C) and during vents (vessel at atmospheric pressure, PFCs at room temperature). It is shown that this outgassing is the main process reconciling the PM and GB estimations of fuel retention, closing the coupled carbon-deuterium balance. In particular, it explains why the deuterium concentration in deposits decreases with increasing depth. (C) 2013 Elsevier B.V. All rights reserved.

This paper presents an analysis of the carbon-deuterium circulation and the resulting balance in Tore Supra over the period 2002-2007. Carbon balance combines the estimation of carbon gross erosion from spectroscopy, net erosion and deposition using confocal microscopy, lock-in thermography and SEM, and a measure of the amount of deposits collected in the vacuum chamber. Fuel retention is determined from post-mortem (PM) analyses and gas balance (GB) measurements. Special attention was paid to the deuterium outgassed during the nights and weekends of the experimental campaign (vessel under vacuum, Plasma Facing Components at 120 degrees C) and during vents (vessel at atmospheric pressure, PFCs at room temperature). It is shown that this outgassing is the main process reconciling the PM and GB estimations of fuel retention, closing the coupled carbon-deuterium balance. In particular, it explains why the deuterium concentration in deposits decreases with increasing depth., QC 20140311

Experiments in the tokamaks TEXTOR, CASTOR, T-10 and ISTTOK, as well as in the reversed field pinch RFX have provided new and complementary evidence on the physics of the universal mechanism of E x B velocity shear stabilization of turbulence, concomitant transport barrier formation and radial conductivity by using various edge biasing techniques. In TEXTOR the causality between transport reduction and induced electric fields in the edge has been for the first time clearly demonstrated. The high electric field gradients have been identified as the cause for the quenching of turbulent cells. A quantitative analysis of the measured transport reduction is in good agreement with theoretical predictions. The scaling of plasma turbulence suppression with velocity shear has been established, revealing the density-potential cross-phase as a key element. Reduction in poloidal electric field, temperature, and density fluctuations across the shear layer lead to a reduction of the anomalous conducted and convected heat fluxes resulting in an energy transport barrier that is measured directly. In CASTOR the biasing electrode is placed at the separatrix in a non-intrusive configuration which has demonstrated strongly sheared electric fields and consequent improvement of the global particle confinement, as predicted by theory. The impact of sheared E x B flow on edge turbulent structures has been measured directly using a comprehensive set of electrostatic probe arrays as well as emissive probes. Measurements with a full poloidal Langmuir probe array have revealed quasi-coherent electrostatic waves in the SOL with a dominant mode number equal to the edge safety factor. In T-10 edge biasing is clearly improving the global performance of ECR heated discharges. Reflectometry and heavy ion beam probe measurements show the existence of a narrow plasma layer with strong suppression of turbulence. On ISTTOK, the influence of alternating positive and negative electrode and (non-intrusive), QC 20100525

Radial electric fields (E-r) and their role in the establishment of edge transport barriers and improved confinement have been studied in the tokamaks TEXTOR-94 and CASTOR, where E-r is externally applied to the plasma in a controlled way using a biased electrode, as well as in the tokamak T-10 where an edge transport barrier (H-mode) is obtained during electron-cyclotron resonance heating (ECRH) of the plasma. The physics of radial currents was studied and the radial conductivity in the edge of TEXTOR-94 (R = 1.75 m, a = 0.46 m) was found to be dominated by recycling (ion-neutral collisions) at the last closed flux surface (LCFS) and by parallel viscosity inside the LCFS. From a performance point of view (edge engineering), such electrode biasing was shown to induce a particle transport barrier, a reduction of particle transport, and a concomitant increase in energy confinement. An H-mode-like behaviour can be induced both with positive and negative electric fields. Positive as well as negative electric fields were shown to strongly affect the exhaust of hydrogen, helium, and impurities, not only in the H-mode-like regime. The impact of sheared radial electric fields on turbulent structures and flows at the plasma edge is investigated on the CASTOR tokamak (R = 0.4 m, a = 0.085 m). A non-intrusive biasing scheme that we call separatrix biasing is applied whereby the electrode is located in the scrape-off layer (SOL) with its tip just touching the LCFS. There is evidence of strongly sheared radial electric field and E x B flow, resulting in the formation of a transport barrier at the separatrix. Advanced probe diagnosis of the edge region has shown that the E x B shear rate that arises during separatrix biasing is larger than for standard edge plasma biasing. The plasma flows, especially the poloidal E x B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates (approximate to5, QC 20100525