Plasma Transport Code Research Articles

Dependence of divertor asymmetries on the toroidal magnetic field

A study of the effect of toroidal magnetic field (Bt) on the divertor asymmetries is carried out with a plasma transport code under BOUT++ framework with the magnetic equilibria from EAST and C-Mod. For the simulation cases with drifts, the density is larger at the inner divertor target, while the temperature and heat flux are larger at the outer divertor target. The ratio of the total particle flux at the outer target to that of the inner target increases with increasing Bt, while the ratio of the total heat flux at the outer target to that of the inner target decreases with increasing Bt. The in–out divertor asymmetries of both total particle and heat fluxes get weaker with increasing Bt. Further analysis shows that the edge radial transport induced by drifts is much weaker for the simulation case with higher Bt, indicating that drift-driven divertor asymmetries may be less important for future tokamaks with high Bt.

Modeling of tungsten impurity transport and distribution in EAST based on multi-fluid and kinetic Monte Carlo simulations

In recent years, the materials of plasma facing components, such as divertor target plates, domes, and outer walls of tokamaks, such as ASDEX Upgrade, WEST, JET, EAST, and ITER, have been changed from carbon to tungsten because of its lower erosion and tritium retention rates. Impurities are produced by interactions between the plasma and the first wall. This study provides an investigation to simulate the transport and distribution of tungsten impurities in the edge plasma on EAST. The 2D multi-fluid edge plasma transport code SOLPS-ITER and 2D kinetic Monte Carlo impurity transport code DIVIMP were used in the simulations. The multi-fluid model in SOLPS-ITER and the kinetic Monte Carlo model in DIVIMP were employed to treat tungsten impurity ions. The 2D density contour distributions in the computational region and the 1D density radial profiles at the inner and outer midplanes of tungsten impurity particles with ionization states (W0–W+74) and the total tungsten particles with all charge states were obtained. With the heating power 1.5 MW and the line-averaged plasma density 2 × 1019 m−3, the results from SOLPS-ITER and DIVIMP show that the maximum density of tungsten ion with single ionization state is about 1014 m−3 and the total density of tungsten impurities with all charge states is about 1015 m−3 at the core boundary. To the best of our knowledge, the simulation results from SOLPS-ITER and DIVIMP are compared for the first time to benchmark SOLPS-ITER with the multi-fluid mode and DIVIMP with the kinetic model for tungsten impurity transport. The density distributions of tungsten impurities with different ionization states from SOLPS-ITER and DIVIMP are highly similar, and good agreement can be found under similar conditions involved in the calculation. From the comparison benchmark between SOLPS-ITER and DIVIMP for tungsten impurity transport, it can be concluded that the impurity transport approximation used by DIVIMP is good.

Modeling transient edge plasma transport with dynamic recycling

The work presents numerical simulation studies of the role that dynamic plasma recycling on the main wall and divertor target surfaces plays in transient edge plasma transport phenomena, such as edge localized modes (ELMs). The studies are performed by coupling the edge plasma transport code UEDGE [Rognlien et al., J. Nucl. Mater. 196–198, 347 (1992)] and the wall reaction–diffusion transport code FACE [Smirnov et al., Fusion Sci. Technol. 71, 75 (2017)]. The two-dimensional, time-dependent, two-way coupling of the codes, in a realistic tokamak geometry, is accomplished using the Integrated Plasma Simulator framework [Elwasif et al., in 18th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP 2010), Pisa, Italy (IEEE, 2010), pp. 419–427] for all modeled material plasma boundaries. The simulations show that dynamic plasma recycling has substantially different characteristics on the main wall and on the divertor plates. It is demonstrated that during an ELM cycle the outer wall can dynamically absorb and release a number of particles comparable to that expelled by the ELM from the core plasma, by far exceeding the dynamic retention capacity of the divertor surfaces. The resulting evolution of the edge and divertor plasma conditions during an ELM cycle is analyzed.

Numerical study of divertor detachment in TCV H-mode scenarios

The effect of divertor closure and nitrogen seeding on the detachment process has been studied by performing 2D numerical simulations of tokamak à configuration variable (TCV) H-mode divertor scenarios with the SOLEDGE3X-EIRENE edge plasma transport code. The simulations reveal that, in the cases with only deuterium gas fuelling, detachment occurs at a similar level of divertor neutral pressure (0.76 Pa), despite the difference in divertor closure achieved by changing the length of the outer baffle. Nitrogen reduces the target temperature with little effect on the upstream density and momentum loss but drops the upstream pressure, leading to a decrease in the target particle flux and divertor neutral pressure. Furthermore, when the radiation front starts to move up from the outer target, the peak parallel heat flux level at the outer target remains approximately the same ( MW m−2), regardless of whether it is a deuterium fuelling scan, a nitrogen seeding scan at a fixed fuelling rate, or a change in the length of the outer baffle. An empirical partial detachment qualifier calibrated on AUG experimental data was compared with the TCV simulations. The results show good agreement in detachment state prediction, indicating the potential of this detachment qualifier to be applied in devices of different sizes, emphasizing the combined influence of input power entering the divertor, neutral pressure, and the concentration and species of impurity in achieving divertor detachment.

Efficient data acquisition and training of collisional-radiative model artificial neural network surrogates through adaptive parameter space sampling

Effective plasma transport modeling of magnetically confined fusion devices relies on having an accurate understanding of the ion composition and radiative power losses of the plasma. Generally, these quantities can be obtained from solutions of a collisional-radiative (CR) model at each time step within a plasma transport simulation. However, even compact, approximate CR models can be computationally onerous to evaluate, and in-situ evaluation of these models within a larger plasma transport code can lead to a rigid bottleneck. As a way to bypass this bottleneck, we propose deploying artificial neural network (ANN) surrogates to allow rapid evaluation of the necessary plasma quantities. However, one issue with training an accurate ANN surrogate is the reliance on a sufficiently large and representative training and validation data set, which can be time-consuming to generate. In this work we explore a data-driven active learning and training routine to allow autonomous adaptive sampling of the problem parameter space to ensure a sufficiently large and meaningful set of training data is assembled for the network training. As a result, we can demonstrate approximately order-of-magnitude savings in required training data samples to produce an accurate surrogate.

Edge Transport Barrier Models for Simulating H-Mode Operation Scenarios in DEMO with Integrated Plasma Transport Code TOTAL

Edge Transport Barrier Models for Simulating H-Mode Operation Scenarios in DEMO with Integrated Plasma Transport Code TOTAL

Estimation and Uncertainties of Profiles and Equilibria for Fusion Modeling Codes

The results of transport modeling codes, e.g., GENE for the plasma core or SOLPS-ITER for the plasma edge, depend critically on reliable profile and equilibrium estimates. The propagation of uncertainties (UP) of input quantities to the results of modeling codes, e.g., power and particle exhaust and plasma stability, is frequently neglected because of the costs of running the codes as well as because of the missing uncertainty quantification of input quantities. The situation becomes even more cumbersome if profile gradients and their uncertainties are of major concern for transport analyses. Two different techniques are presented to estimate profiles, profile gradients, their uncertainties, and candidate profiles for UP in modeling codes. Markov Chain Monte Carlo sampling of the posterior probability density of an integrated data analysis approach is applied to estimate electron density and temperature profiles. Nonstationary Gaussian process regression is applied to estimate ion temperature and angular velocity profiles. Both methods provide in a natural way profile gradients, profile logarithmic gradients, and their uncertainties. Modeling codes benefit also from reliable equilibrium reconstructions and quantification of the uncertainty of various equilibrium parameters. For the analysis of diagnostics data, the position and uncertainty of flux surfaces as well as of the magnetic axis are important. For plasma transport and stability codes, the estimation of uncertainties of current and q-profiles is presented. For plasma edge codes the position of the separatrix contour and its uncertainty at various poloidal positions is of primary interest especially if steep profile gradients are present. Examples of uncertainties and their sources in magnetic scalar quantities, profiles, and separatrix contours are shown.

Simulations of divertor plasmas with inverse sheaths

The effect of strong electron emission from material surfaces has been proposed to form an “inverse sheath”: a region with a positive potential relative to the near-wall plasma which prevents the flow of ions to the wall [M. D. Campanell, “Negative plasma potential relative to electron-emitting surfaces,” Phys. Rev. E. 88, 033103 (2013); M. D. Campanell and M. V. Umansky, “Strongly emitting surfaces unable to float below plasma potential,” Phys. Rev. Lett. 116, 1–5 (2016); M. D. Campanell and G. R. Johnson, “Thermionic cooling of the target plasma to a sub-ev temperature,” Phys. Rev. Lett. 122, 1–5 (2019)]. We assess the viability of this regime in a tokamak device using the 2D edge plasma transport code UEDGE [T. Rognlien et al., “A fully implicit, time dependent 2-D fluid code for modeling tokamak edge plasmas,” J. Nucl. Mater. 196–198, 347–351 (1992)]. Since the UEDGE code does not consider the sheath region directly, we apply boundary conditions at the divertor targets which emulate the physics of both “standard” and “inverse” sheath regimes [R. Masline et al., “Influence of the inverse sheath on divertor plasma performance in tokamak edge plasma simulations,” Contrib. Plasma Phys. 60, e201900097 (2020)]. Using these boundary conditions, we perform scoping studies to assess plasma parameters near the target by varying the density at the core-edge interface. We observe a smooth transition in the resultant profiles of plasma parameters for the standard sheath, and a bifurcation across the simulation set for plasmas with an inverse sheath. The cause of this bifurcation is assessed by performing the parameter scan both with and without impurity radiation; we observe that the bifurcation persists in both cases, indicating that this bifurcation is caused by plasma recombination.

Simulation of divertor heat flux width on EAST by BOUT++ transport code

The BOUT++ edge plasma transport code is applied to study the effects of neutral recycling, drifts and heating scheme on edge plasma profiles and the divertor heat flux width of two discharges of the experimental advanced superconducting tokamak (EAST) steady-state H-mode plasmas heated by low hybrid wave (LHW) and neutral beam (NB), respectively. Neutral recycling seems to have played an important role in the plasma density profile. The edge plasma density drops dramatically for the case w/o neutral recycling, while it can be sustained for the case w/ neutral recycling. Drifts are found to have significant influences on edge plasma profiles. Both the amplitude and width of the divertor heat flux are found to have increased a lot due to drifts. The simulated heat flux width w/ drifts for the two discharges shows reasonable agreement with the experiments. However, the width from the simulation and experiment for the LHW heated discharge is much larger than that of the NB heated discharge. Comparison with Goldston’s drift-based model and more detailed analysis on the heat flux contributions from drifts versus turbulence show that drifts are the dominant factor in edge plasma transport for both LHW and NB heated discharges, while turbulence may have played a more important role in determining the heat flux width in LHW heated discharges than that in NB heated discharges. This may account for the larger heat flux width in the LHW heated discharge. The magnetic topology and the equilibrium change by the LHW power may also be a potential reason for the larger heat flux width in the LHW heated discharges, which still needs more evidence and studies to support it. Additional SOLPS simulation w/o drifts for the two discharges show reasonable agreement with the counterpart from the BOUT++ simulation, suggesting the two are both suitable codes for EAST edge plasma simulation.

Influence of the inverse sheath on divertor plasma performance in tokamak edge plasma simulations

AbstractRecently, it was shown that strong electron thermionic emission from material walls could result in the formation of an “inverse sheath,” which prevents the flow of cold ions to the wall.[1–3] Such regimes look very favourably from the point of view of plasma–material interactions at the edge of magnetic fusion devices, where the problem of the erosion of plasma‐facing components under ion irradiation is one of the key issues for the development of future magnetic fusion reactors. However, it is not clear whether such regimes are compatible with edge plasma parameters and heat removal requirements in fusion reactors. To address the issue of practicality of the “inverse sheath” regime for edge tokamak plasma conditions, we perform a set of numerical simulations with 2D edge plasma transport code UEDGE[4] for a DIII‐D‐like geometry and magnetic configuration. To describe both “standard” and “inverse sheath” conditions within the framework of the UEDGE code (which does not consider the sheath region per se), at the material surfaces, we apply effective boundary conditions that emulate both “standard” and “inverse sheath” regimes. We demonstrate that, for the same input parameters, spatial distributions of edge plasma parameters corresponding to detached divertor and “inverse sheath” regimes are similar, with only a few minor differences. We discuss the compatibility of “inverse sheath” regimes with core plasma parameters.

IMPGYRO: The full-orbit impurity transport code for SOL/divertor and its successful application to tungsten impurities

In future fusion reactors, tungsten (W) is currently regarded as one of the most feasible candidates for the plasma-facing components (PFCs). Once the W impurities sputtered from the PFCs penetrate into the core plasma, the large radiation cooling and fuel dilution, which leads to the deterioration of the core plasma performance, take place. To understand and to control W impurity transport are indispensable for future fusion reactors. In order to understand W transport, we are continuing to develop the kinetic impurity transport code IMPGYRO for SOL/divertor in fusion reactors. The IMPGYRO has obtained following unique features compared to other existing kinetic impurity transport codes through the 15-years development activity; (i) the exact Larmor motion of impurity ions are computed so that the effects of drifts are automatically taken into account, (ii) the Coulomb collision between impurities and background plasma ions are modelled by the Binary Collision Method which kinetically calculates more precise friction and thermal forces, and (iii) the background plasma transport and impurity transport are computed self-consistently by the coupled calculation with SOL/divertor plasma transport code such as SOLPS-ITER. Although the IMPGYRO transport model has significantly improved from the initial development phase, the modelling improvement of the IMPGYRO has never been described in detail. In this paper, (a) the current W generation/transport model, and (b) the coupling strategy between the SOLPS-ITER and the IMPGYRO are summarized. The new results (c) the check of the prompt re-deposition model of the IMPGYRO, and (d) the further extension of the Coulomb collision modelling of the IMPGYRO towards the neoclassical (NC) transport handling capability has been performed. The effects of the NC transport processes on a simple circular tokamak geometry are compared with the anomalous diffusion by means of the extended IMPGYRO to obtain better understanding of cross-field transport process of W. The results show that the NC transport process may become non-negligible compared to the anomalous diffusion at least in this configuration. Based on these recent improvements, the present version of the IMPGYRO is very useful tool for understanding and prediction of W transport in SOL/divertor regions of fusion devices.

Active Recycling Control Through Lithium Injection in EAST

The coating of tokamak walls with thin layers of lithium has been demonstrated to reduce plasma recycling from the plasma-facing surfaces and to improve overall plasma performance. These effects, including reduced divertor $D_{\alpha }$ emission, the elimination of edge-localized modes, and increased energy confinement have been observed in multiple experiments when lithium coatings are applied before plasma discharges. However, this coating technology does not extrapolate to future long-pulse devices, since the lithium coatings will be passivated by the continual plasma flux onto the surface. In order to provide active conditioning capability, a new technology has been developed that is capable of injecting lithium powder into the scrape-off layer plasma during plasma discharges, where it quickly liquefies and turns into an aerosol. The use of this “lithium dropper” is under study at the Experimental Advanced Superconducting Tokamak (EAST), where the potential benefits of real-time wall conditioning via lithium injection are being tested. Here, we present an analysis of the recycling characteristics during EAST experiments testing active lithium injection in order to assess recycling reduction and control. Lithium aerosol was injected from the top of the machine, with one system dropping lithium near the $X$ -point and another into the low-field side divertor leg. The injection of lithium into the SOL reduced divertor recycling, as evidenced by reduced $D_{\alpha }$ emission with ion flux measured by probes relatively unchanged. This effect is strongest in the active divertor, confirming the lithium is transported to strongly plasma-wetted areas. Quantitative analysis of the recycling changes using the SOLPS edge plasma and neutral transport code indicated a ~20% reduction in recycling coefficient with lithium injection.

Simulation of the gas puffing fueling on the HL-2A tokamak using SOLPS

Plasma fueling by gas puffing on HL-2A tokamak is studied by using the SOLPS code package. The injected molecular D2 is simulated by the kinetic neutral transport code Eirene and the plasma is modeled by the multi-fluid plasma transport code B2.5. By adjusting the radial transport coefficients D⊥ and χ⊥, the HL-2A experimental upstream plasma is well reproduced, which is taken as the initial state before gas puffing. The plasma and neutral evolution during the gas puffing and its impact on the divertor plasma are studied. It is found that the D2 can only penetrate into a very shallow region, however, the atomic D produced mainly by the dissociation can enhance the neutral D penetration depth, thus fuels the core plasma. Moreover, the impact of the gas puffing rate on the plasma is presented and discussed.

VITALS: A Surrogate-Based Optimization Framework for the Accelerated Validation of Plasma Transport Codes

Understanding transport in magnetically confined plasmas is critical for developing predictive models for future devices such as ITER. Thanks to recent progress in simulation and theory, along with enhanced computational power and better diagnostic systems, direct and quantitative comparisons between experimental results and models is possible. However, validating transport models using additional constraints and accounting for experimental uncertainties still remains a formidable task. In this work, a new optimization framework is developed to address the issue of constrained validation of transport models. The Validation via Iterative Training of Active Learning Surrogates (VITALS) framework exploits surrogate-based strategies using Gaussian processes and sequential parameter updates to achieve the combination of plasma parameters that matches experimental transport measurements within diagnostic error bars. VITALS is successfully implemented to study L-mode plasmas in the Alcator C-Mod tokamak, and for the first time, additional measurable quantities, such as incremental diffusivity and fluctuation levels, are used during the validation process of the quasi-linear transport models TGLF-SAT1 and TGLF-SAT0. First results indicate that these machine-learning algorithms are very suitable and adaptable as a self-consistent, fast, and comprehensive validation methodology for plasma transport codes.

Radiative detached divertor with acceptable separatrix Zeff

The feasibility study is performed for the radiative detached divertor (RDD) concept, which characterizes a variety of detached plasmas with impurity amounts providing the highest levels of divertor radiation without X-point MARFE (XPM), based on a set of restrictive criteria for the leading plasma parameters (LPPs) including, e.g., tolerable peak power loads below 1 MW/m2, low separatrix densities, allowable impurity concentrations, and acceptable Zeff values for a DIII-D like tokamak. For this, extensive simulations with the 2-D edge plasma transport code were done scanning the deuterium and impurity inventories practically for all impurity elements from beryllium to neon and the analysis of LPP variations in these scans is presented. It is shown that, for a given D inventory, the total radiation fraction with an increase in the impurity inventory reaches a flat top level, frad = 0.85 ± 0.01, whereas the higher frad corresponds to XPM. This critical fraction is the same for all elements and values of the D inventory. Successful RDD solutions with a flat top radiation meeting all ad hoc LPP criteria are found for some elements. Boron and nitrogen are shown to be the most promising elements for seeding, since they are capable of providing alone the successful RDD at the lowest concentrations. Several important effects on impurity radiation are considered including: cross-field impurity transport in regions with strong temperature gradients, multi-species thermal force, charge-exchange of impurity ions with D atoms originating from recombination, impurity entrainment by parallel flows, flows caused by inner/outer divertor asymmetries, and Mach ∼ 1 flows reached inside radiation-ionization fronts. The impurity radiation profiles of various elements are analyzed suggesting three patterns differing in the radiation front position with respect to the D ionization source. The modeled relocation of D from the pedestal into divertor regions; an enhanced pedestal enrichment for impurities with high first ionization potential; and RDD capability of confining inside the divertors the large D inventories as neutral atoms, are considered as effects of increasing impurity inventory. The responses of a flat-top RDD to the input parameters variation are studied. For instance, dependencies of LPPs on the input power increase, which express the sharp and even bifurcation transitions between two distinct branches corresponding to the detached and attached divertors, are discussed.

Exploring drift effects in TCV single-null plasmas with the UEDGE code

This paper explores the effects of particle drifts across the magnetic field in TCV single-null plasmas using the two-dimensional edge plasma transport code UEDGE. In particular, it aims to reproduce a double-peaked density target profile, a feature which has been observed both at JET and in a TCV forward-field ( drift of core ions towards the X-point) discharge. Initial simulations are performed with drift effects turned off. This allows identification of the input parameters that strongly influence the computed steady-state but are not well known from the experiment. Including cross-field drifts self-consistently in the simulations brings computed profiles at the inner target closer to the experiment, with the double peak being reproduced for the density. In agreement with the experiment, simulations of a similar reversed-field shot yield lower ne and higher Te at the inner target, as well as unchanged temperatures at the outer plate. However, several discrepancies remain. In the forward field case, the inner target density peak near the separatrix is much sharper than seen experimentally. Furthermore, simulations show a strong dependence of the outer plate density and of the outer/inner power sharing on toroidal field direction. Experimentally, no such dependencies are observed. In the simulations, the changes of target profiles with field direction are mainly due to E × B drifts in the divertor region. While these simulations highlight the importance of E × B drifts in these TCV plasmas, the remaining differences with the experiment indicate that their role is overestimated in the simulations.

Simulation of impurity transport in the peripheral plasma due to the emission of dust in long pulse discharges on the Large Helical Device

Two different plasma termination processes by dust emission were observed in long pulse discharges in the Large Helical Device. One is a plasma termination caused by large amounts of carbon dust released from a lower divertor region. The other is termination caused by stainless steel (iron) dust emission from the surface of a helical coil can. The effect of the dust emission on the sustainment of the long pulse discharges are investigated using a three-dimensional edge plasma transport code (EMC3-EIRENE) coupled with a dust transport code (DUSTT). The simulation shows that the plasma is more influenced by the iron dust emission from the helical coil can than by the carbon dust emission from the divertor region. The simulation revealed that the plasma flow in divertor legs is quite effective for preventing dust from terminating the long pulse discharges.

H-mode WEST tungsten divertor operation: deuterium and nitrogen seeded simulations with SOLEDGE2D-EIRENE

Simulations of WEST H-mode divertor scenarios have been performed with SOLEDGE2D-EIRENE edge plasma transport code, both for pure deuterium and nitrogen seeded discharge. In the pure deuterium case, a target heat flux of 8 MW/m2 is reached, but misalignment between heat and the particle outflux yields 50 eV plasma temperature at the target plates. With nitrogen seeding, the heat and particle outflux are observed to be aligned so that lower plasma temperatures at the target plates are achieved together with the required high heat fluxes. This change in heat and particle outflux alignment is analysed with respect to the role of divertor geometry and the impact of vertical vs horizontal target plates on neutrals spreading.

Sensitivity of the Boundary Plasma to the Plasma-Material Interface

While the sensitivity of the scrape-off layer and divertor plasma to the highly uncertain cross-field transport assumptions is widely recognized, the plasma is also sensitive to the details of the plasma-material interface (PMI) models used as part of comprehensive predictive simulations. Here, these PMI sensitivities are studied by varying the relevant submodels within the SOLPS plasma transport code. Two aspects are explored: the sheath model used as a boundary condition in SOLPS, and fast particle reflection rates for ions impinging on a material surface. Both of these have been the study of recent high-fidelity simulation efforts aimed at improving the understanding and prediction of these phenomena. It is found that in both cases quantitative changes to the plasma solution result from modification of the PMI model, with a larger impact in the case of the reflection coefficient variation. This indicates the necessities to better quantify the uncertainties within the PMI models themselves and to perform thorough sensitivity analysis to propagate these throughout the boundary model; this is especially important for validation against experiment, where the error in the simulation is a critical and less-studied piece of the code-experiment comparison.

Interchange Turbulence Model for the Edge Plasma in SOLEDGE2D‐EIRENE

AbstractCross‐field transport in edge tokamak plasmas is known to be dominated by turbulent transport. A dedicated effort has been made to simulate this turbulent transport from first principle models but the numerical cost to run these simulations on the ITER scale remains prohibitive. Edge plasma transport study relies mostly nowadays on so‐called transport codes where the turbulent transport is taken into account using effective ad‐hoc diffusion coeffecients. In this contribution, we propose to introduce a transport equation for the turbulence intensity in SOLEDGE2D‐EIRENE to describe the interchange turbulence properties. Going beyond the empirical diffusive model, this system automatically generates profiles for the turbulent transport and hence reduces the number of degrees of freedom for edge plasma transport codes. We draw inspiration from the k‐epsilon model widely used in the neutral fluid community. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)