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At least 181 records · Page 10

Tungsten–carbon surface evolution and erosion modeling for a small angle slot divertor in DIII-D

Abstract We modeled tungsten–carbon mixed surface evolution, sputtering erosion, and transport for the tungsten coated region of a small angle slot (SAS) divertor design for the DIII-D tokamak. This divertor concept aims to achieve a closed slot dissipative plasma to minimize heat load and surface erosion, and to study high- Z material performance. Our advanced simulations use coupled ITMC-DYN material mixing/response and 3D full kinetic REDEP/WBC erosion/redeposition code packages, with divertor plasma solution from the SOLPS-ITER package with 4 MW power input. The SAS design geometry and resulting in-slot plasma parameters cause significant differences in predicted sputter/transport from a conventional divertor. For 2% C/D incident plasma ratio, an equilibrium mixed C/W surface is attained at ∼30 s of discharge, from wall sputtered carbon transported to the 10 cm long tungsten divertor region. Tungsten remains exposed to the plasma, but the evolved surface composition varies with different C/D ratios. Tungsten is primarily sputtered from the mixed surface by impinging carbon ions in the +1 to +4 charge states, with some self-sputtering. Redeposition of sputtered tungsten to the divertor is significant, ∼80% along the higher plasma temperature attached plasma SAS entrance region, but this is less than the typically near-unity values for a conventional divertor. Plasma-incident carbon is highly backscattered (∼50%) from the mixed surface, with little redeposition (<10%); this helps maintain tungsten in the surface sputter zone. Carbon is mainly sputtered from the mixed surface by D + ions, also with low redeposition (∼10%–30%). Finally, the modeling shows non-zero but low sputtered tungsten current from the divertor to the core plasma direction. These results appear favorable for effective testing of a tungsten-containing SAS divertor in DIII-D, and extrapolation of mixed-material evolution/response findings to the analogous low- Z /high- Z , Be/W, ITER plasma facing system.

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Hyperdiffusion of dust particles in a turbulent tokamak plasma

In this work, the effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number St∝a d /n 0 , with a d the dust radius and n 0 the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories Δr 2 is shown to depend on the ratio Ku/St, with Ku∝u rms the Kubo number and urms the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting Δr 2 ∝(Ku/St) 2 t 3 , or Δr 2 ∝(u rms n 0 /a d ) 2 t 3 . As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible and drives the transition from a hyperdiffusive regime toward a ballistic one.

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Hyperdiffusion of dust particles in a turbulent tokamak plasma

The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number $St\propto a_d/n_0$, with $a_d$ the dust radius and $n_0$ the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories $\Delta r^2$ is shown to depend on the ratio $Ku/St$, with $Ku\propto u_{rms}$ the Kubo number and $u_{rms}$ the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting $\Delta r^2\propto (Ku/St)^2t^3$, or $\Delta r^2\propto (u_{rms}n_0/a_d)^2t^3$. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.

dust↗

Ion cyclotron heating at high plasma density in Proto-MPEX

The physics of ion cyclotron heating (ICH) relevant to the steady-state linear machine MPEX (Material Plasma Exposure eXperiment) has been explored in its predecessor, short-pulse device: Proto-MPEX. MPEX will utilize fundamental ICH to increase heat flux at the target and produce ion temperatures and velocity distributions with improved fidelity to those found in a tokamak divertor region, in comparison to those produced by substrate biasing. In the experiments on Proto-MPEX described here, bulk ion temperatures up to ~15 eV have been achieved with 20 kW net ICH power at 6.5 MHz, using ICH heating of a deuterium plasma produced by a helicon plasma source. The heat flux at the target has been observed to increase throughout the plasma cross section, including in the core region. Core $T_i$ and target heat flux are observed to scale linearly with injected ICH power. Further, measurements of plasma loading and target heat flux as a function of the magnetic field strength at the antenna, together with modeling of the wave propagation from the antenna to the ion cyclotron resonance using the ANTENA and COMSOL codes with a warm plasma dielectric tensor, indicate that power is coupled to the core plasma via fast wave excitation of a kinetic Alfvén wave.

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Isotope dependence of transport in ST40 hot ion mode plasmas

The ST40 compact, high-field spherical tokamak, operating at 2.1 T and with 1.8 MW of neutral beam heating, achieved central carbon impurity ion temperatures in excess of 10 keV, surpassing their business milestone of 100 M °C (8.6 keV). The high temperature discharges were in the hot ion mode, with $T_i \gg T_e$, and they were achieved in both hydrogen and deuterium plasmas with deuterium neutral beam injection. In order to achieve the high temperature scenarios, careful wall conditioning and scenario optimization was carried out in $H^0 \rightarrow H^+$, $D^0 \rightarrow H^+$, and finally in $D^0 \rightarrow D^+$ plasmas. The TRANSP transport code was employed to study the dependence of confinement and transport on isotopic mass, and the conditions that led to the high measured central ion temperatures in the $D^0 \rightarrow H^+$ and $D^0 \rightarrow D^+$ plasmas. The kinetic profiles input into TRANSP were inferred from line-of-sight and limited radial measurements as well as consistency with a number of other experimental constraints. The TRANSP results first showed that the main species central ion temperature was only 0.5–1 keV lower than the measured carbon impurity temperature, and thus in the high performance plasmas also surpassed the 100 M °C level. TRANSP also showed that while the electron thermal conduction loss was dominant, reductions in central ion transport, and an effective decoupling of the ions from the electrons, led to an increase in central ion temperatures with increasing plasma mass. In fact, the associated confinement times exhibited a strong dependence on the isotopic mass of the thermal plasma. These preliminary results are foundations for dedicated experiments with full kinetic profile measurements on ST40 in the next run campaign.

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Simulation of electron Bernstein waves using FullWave with a 2D non-local hot plasma model

Hot plasma wave simulation capability is expanded in the FullWave code by updating the hybrid iterative solver in the code with a semi-implicit time stepping method. The new approach is used to simulate Electron Bernstein Wave (EBW) heating in over-dense spherical tokamak plasmas. The code’s hybrid iterative solver circumvents the prohibitive memory cost of direct methods by combining a time evolution of Maxwell’s equations with frequency-domain relaxation, while the conductivity kernel, calculated via 3D particle tracking, captures the essential non-local wave–particle interactions. One-dimensional EBW simulations verify the algorithm’s accuracy by demonstrating mode conversion from X-mode wave to EBW at the upper hybrid resonance and a strong cyclotron damping near the plasma core. Two-dimensional simulation reproduces the predicted short EBW wavelength and quantitatively matches the hot-plasma dispersion relation. This study demonstrates the fidelity of the hybrid solver for the electron cyclotron frequency range.

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Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC

The global total-f gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas or to couple with a core gyrokinetic code while functioning as an edge gyrokinetic code, implements a 5-dimensional (5D) continuum grid to perform the dissipative operations, such as plasma collisions, or to exchange the particle distribution function information with a core code. To transfer the distribution function between marker particles and a rectangular 2D velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large and cause non-negligible numerical heating in a steep edge pedestal. In the present work we update XGC to use a novel mapping technique, based on the calculation of a pseudo-inverse, to exactly preserve moments up to the order of the discretization space. We describe the details of the implementation and we demonstrate the reduced interpolation error for a tokamak test plasma by using 1st- and 2nd-order elements with the pseudo-inverse method and comparing to the bilinear mapping.

Fusion Plasma↗

Modelling the nonlinear plasma response to externally applied three-dimensional fields with the Stepped Pressure Equilibrium Code

Small-amplitude, symmetry-breaking magnetic field perturbations, including resonant magnetic perturbations (RMPs) and error fields, can profoundly impact plasma properties in both tokamaks and stellarators. In this work, we perform the first comparison between the Stepped Pressure Equilibrium Code (SPEC) (a comparatively fast and efficient equilibrium code based on energy-minimisation principles) and M3D-C 1 (a high-fidelity albeit computationally expensive initial-value extended-magnetohydro-dynamic (MHD) code) to assess the conditions under which SPEC can be used to model the nonlinear, non-ideal plasma response to an externally applied (m = 2,n = 1) RMP field in an experimentally relevant geometry. We find that SPEC is able to capture the plasma response in the weakly nonlinear regime – meaning perturbation amplitudes below the threshold for break up of the separatrix and onset of secondary magnetic island formation – when around half of the total toroidal flux is enclosed in the volume containing the q = 2 resonant surface. Further, the observed dependence of SPEC solutions on input parameters, including toroidal flux and the number of volumes into which the plasma is partitioned, indicates that additional exploration of the underlying Multi-Region Relaxed MHD physics model is needed to constrain the choice of parameters. Nonetheless, this work suggests promising applications of SPEC to optimisation and fusion plasma design.

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Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC

The global total-f gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas or to couple with a core gyrokinetic code while functioning as an edge gyrokinetic code, implements a five-dimensional continuum grid to perform the dissipative operations, such as plasma collisions, or to exchange the particle distribution function information with a core code. To transfer the distribution function between marker particles and a rectangular two-dimensional velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large and cause non-negligible numerical heating in a steep edge pedestal. In the present work we update XGC to use a novel mapping technique, based on the calculation of a pseudo-inverse, to exactly preserve moments up to the order of the discretization space. Here we describe the details of the implementation and we demonstrate the reduced interpolation error for a tokamak test plasma using first- and second-order elements with the pseudo-inverse method and comparing with the bilinear mapping.

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Improved analytic modeling of the linear Rayleigh–Taylor instability with plasma transport

The Rayleigh–Taylor (R–T) instability with transport effects has long been studied analytically in the neutral fluid regime. How this picture may differ in plasmas has been given less consideration, however. Leveraging previous numerical simulations with plasma viscosity and diffusion of R–T at a binary plasma interface, we show how plasma transport and kinetic effects alter the linear R–T dispersion relation. Our insight informs a much improved analytical dispersion relation, which better matches the simulation data than previously established models. Additionally, we demonstrate the importance of employing asymptotically correct viscosity coefficients in fluid codes for accurately capturing plasma R–T growth.

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TRANSP Workshop Summary - September 27-28, 2024, Princeton Plasma Physics Laboratory, NJ

The TRANSP Code Workshop provided a platform for in-depth discussions on advancing the capabilities of the TRANSP code, focusing on key areas such as predictive capabilities, interpretive frameworks, core-edge coupling, and integration with engineering components. More than 25 scientists from PPPL and around the world contributed to the workshop by making presentations and participating in discussions. The workshop covered a range of topics including: (1) Current Status of TRANSP; (2) Code Infrastructure, Core-Edge Coupling, and Engineering Integration; (3) Enhancing Interpretive Capabilities, and (4) Predictive Capabilities for Discharge Optimization

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ELM sputter erosion modeling of a tungsten coated small angle slot divertor in DIII-D

We modeled plasma edge localized mode (ELM) sputter erosion for a Small Angle Slot divertor with a tungsten coated region (SAS-VW), designed for experiments in the DIII-D tokamak, and proposed for use in future advanced tokamaks. The simulations use a free-streaming, 1000 eV, C +6 and D +1 ELM impingement model, with SOLPS-ITER, ITMC-DYN, and REDEP/WBC code packages for background plasma, material response, and erosion/redeposition respectively. The results show ELM'ing plasma gross and net tungsten erosion fluxes of the mixed-material C/W surface peaking at the slot entrance region, and an order of magnitude higher than for non-ELMs. The per-pulse erosion, however, remains low, of order 0.5 nm, due to expected moderate ELM frequencies and duration in DIII-D. Here, the ELMs result in a ~25x higher peak sputtered W current leaving the divertor slot region, towards the core plasma, compared to the ELM-free plasma case. The time-integrated escape current, however, may not significantly affect core plasma high-Z contamination concerns, for a 1% ELM duty factor, but may be an issue for higher frequency ELMs. In general, the modeling results appear favorable for effective testing of the SAS-VW divertor in DIII-D, and extrapolation to innovative divertor designs in future ITER-like and DEMO fusion devices.

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Gyrokinetic GENE simulations of DIII-D near-edge L-mode plasmas

We present gyrokinetic simulations with the GENE code addressing the near-edge region of an L-mode plasma in the DIII-D tokamak. At radial position ρ = 0.80, simulations with the ion temperature gradient (ITG) increased by 40% above the nominal value give electron and ion heat fluxes that are in simultaneous agreement with the experiment. This gradient increase is consistent with the combined statistical and systematic uncertainty σ of the charge exchange recombination spectroscopy measurements at the 1.6σ level. Multiscale simulations are carried out with a realistic mass ratio and geometry for the first time in the near-edge. These multiscale simulations suggest that the highly unstable ion temperature gradient (ITG) modes of the flux-matched ion-scale simulations suppress electron-scale transport, such that ion-scale simulations are sufficient at this location. At radial position ρ = 0.90, nonlinear simulations show a hybrid state of ITG and trapped electron modes, which was not expected from linear simulations. The nonlinear simulations reproduce the total experimental heat flux with the inclusion of E × B shear effects and an increase in the electron temperature gradient by ∼23%. This gradient increase is compatible with the combined statistical and systematic uncertainty of the Thomson scattering data at the 1.3σ level. These results are consistent with previous findings that gyrokinetic simulations are able to reproduce the experimental heat fluxes by varying input parameters close to their experimental uncertainties, pushing the validation frontier closer to the edge region.

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Screening of resonant magnetic perturbation fields assuming various plasma flow models

A recently updated version of the MARS-F code [Y. Q. Liu et al., Phys. Plasmas 7, 3681 (2000); L. Li et al., Phys. Plasmas 25, 082512 (2018); and G. L. Xia et al., Nucl. Fusion 59, 126035 (2019)] is utilized to numerically investigate the plasma screening effect on the applied resonant magnetic perturbation (RMP) field, assuming various equilibrium flow models, including the toroidal flow, the parallel flow and their combinations, and poloidal and toroidal projections of the parallel flow. A parallel equilibrium flow with a uniform radial profile is found to have no effect on plasma screening of the RMP field. A sheared parallel flow, however, does change plasma screening. The poloidal projection of the parallel flow weakens plasma screening in the resistive-inertial regime. The effect on the favorable average curvature regime is found, however, to be non-monotonic. With the increasing flow speed, the poloidal projection first weakens Glasser-Green-Johnson (GGJ)-screening. Further increase in the flow speed results in enhanced GGJ-screening again. This non-monotonic behavior is related to the perturbed parallel shielding current, which appears also off the mode rational surface at fast flow due to additional resonances between the RMP perturbation and the sound wave continuum. These results indicate that flow induced plasma screening to the RMP field can have complicated characteristics, which, in turn, can have implications on the RMP field penetration into the plasma in experiments for controlling the edge localized modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulations of tokamak boundary plasma turbulence transport in setting the divertor heat flux width

The BOUT++ code has been used to simulate edge plasma electromagnetic (EM) turbulence and transport, and to study the role of EM turbulence in setting the scrape-off layer (SOL) heat flux width λ q . More than a dozen tokamak discharges from C-Mod, DIII-D, EAST, ITER and CFETR have been simulated with encouraging success. The parallel electron heat fluxes onto the target from the BOUT++ simulations of C-Mod, DIII-D, and EAST follow the experimental heat flux width scaling of the inverse dependence on the poloidal magnetic field. Further turbulence statistics analysis shows that the blobs are generated near the pedestal pressure peak gradient region inside the separatrix and contribute to the transport of the particle and heat in the SOL region. Transport simulations indicate two distinct regimes: drift dominant regime and turbulence dominant regime. Goldston's heuristic drift-based (HD) model yields a consistent divertor heat flux width in the drift dominant regime. For C-Mod enhanced D α H-mode discharges, drifts and turbulence are competing in setting the divertor heat flux width, possibly due to its compact machine size and good pedestal confinement. The simulations for ITER and CFETR indicate that divertor heat flux width λ q of the future machines may no longer follows the 1/B pol,OMP HD-based empirical (Eich) scalings and the HD model gives a pessimistic limit of divertor heat flux width. The simulation results show a transition from a drift dominant regime to a turbulence dominant regime from current machines to future machines such as ITER and CFETR for two reasons. (1) The magnetic drift-based radial transport decreases due to large CFETR and ITER machine sizes. (2) The SOL turbulence thermal diffusivity increases due to larger turbulent fluxes ejected from the pedestal into the SOL when operating in a different pedestal structure, from an ELM-free H-mode pedestal regime to a small and grassy ELM regime.

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Effects of external kink and fishbone-like modes on energetic particle transport in tokamak plasmas

Transport and loss of beam injected energetic particles (EPs) due to three-dimensional perturbations, associated with the external kink (XK) instability and fishbone-like mode (FLM), are numerically investigated utilizing the guiding center following code ORBIT for static toroidal plasmas in HL-2A. The perturbation structure for the XK is computed by the MARS-F code and then mapped to the Boozer coordinates as defined in ORBIT. The simulation shows that the EP profile experiences a significant change in the middle of the plasma column, when the XK-induced radial magnetic field perturbation amplitude, normalized by the equilibrium field, exceeds a threshold value of about 10 -2 . The EP transport is found to be dominated by a diffusion process instead of convection. Furthermore, by scanning the perturbation frequency as a free parameter while maintaining the XK mode structure (thus mimicking the FLM as observed in DIII-D and JT-60U tokamaks), redistribution and loss of EPs are found to be substantially enhanced due to strong resonances between the FLM and EPs, when the mode frequency exceeds a threshold value of ~2 kHz for the case considered. For either XK or FLM, the response of passing EPs to the perturbation is dominant due to the assumed tangential neutral beam injection. Most lost EPs due to these instabilities are initially passing particles but are eventually lost through trapped orbits.

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