Impurity Confinement Research Articles

Effect of rotation on negative triangularity plasmas in DIII-D

Abstract At the DIII-D tokamak, plasmas with negative triangularity (NT) have been found to have similar energy confinement times as H-mode plasmas with positive triangularity. These NT plasmas also have a stable edge that inhibits H-mode, lacks dangerous edge transients, and has naturally low impurity confinement. For these reasons, NT plasmas have the potential to be a transformative reactor scenario. To determine the importance of strong co-current neutral beam torque for NT performance at DIII-D, scans of neutral beam torque at constant neutral beam power have been performed. These scans have shown that the energy confinement time for a basic, inductive NT scenario ( q 95 ≈ 2.8 ) decreases by 16% when torque is reduced to reactor levels. This reduction in confinement can be replicated with gyrofluid modeling that isolates the role of E × B shear in the change in transport. In a separate set of discharges with lower plasma current ( q 95 ≈ 4.2 ), no significant correlation between confinement time and rotation was found. Throughout this investigation, excellent MHD stability was observed, even with very low toroidal rotation. Further, low impurity confinement was found at multiple rotation levels. Throughout the campaign, rotation near the edge was counter-current, consistent with the measurement of counter-current intrinsic edge rotation, and these observations agree with NT results from the TCV tokamak.

Design of a multi-energy soft X-ray diagnostic for profile measurements during long-pulse operation in the WEST tokamak

The W Environment in Steady-state Tokamakwas designed and built to test ITER-like tungsten plasma facing components in a long pulse (∼1000 s) scenario. Recently, a multi-energy soft x-ray diagnostic (MESXR) was installed in the WEST (W Environment in Steady-state Tokamak), to understand the sources, transport and confinement of high-Z impurities. The purpose of this work is to describe the engineering challenges posed by the long pulse scenario for the integration of the MESXR diagnostic and how they were addressed and solved. The calculations of vacuum and thermal stress as well as heat transfer are presented and discussed.

Overview of core impurity transport in the first divertor operation of Wendelstein 7-X

The impurity transport at Wendelstein 7-X during its most recent campaign is characterized and documented for a variety of different plasma scenarios. An overview of its dependence on several quantities is given, which allows identification of transport regimes and the major driver for impurity transport. Beyond this, a comparison with the impurity behavior in other fusion devices is now possible. In contrast to other stellarators, no density dependence of the impurity transport has been found. Additionally, the influence of the turbulence contribution to the overall transport is reflected in the dependence on various parameters, e.g. turbulent diffusion and density fluctuation amplitudes. With this database approach, one can now also apply scaling laws to make extrapolations about the impurity confinement in future plasma scenarios.

Increased radiation due to non-coronal effects on DIII-D and MAST-U with varying input power

Through SOLPS-ITER simulations of DIII-D and MAST-U, an X-divertor (XD) on DIII-D and a super X-divertor (SXD) on MAST-U were shown to have increased carbon emissivity (P Rad/n e n I) over corresponding standard divertors (SD) at similar degrees of partial detachment. The reasons behind the increased emissivity in the DIII-D XD and SXD are analyzed using a simple 0D transport model. From the transport model, it is seen that a major cause of the increased emissivity in the XD and SXD over the SDs is a shorter impurity confinement time. An additional cause (for the SXD) is an increase in the ratio of neutral hydrogen to electron density. The input power (P in) was varied and the XD had a higher emissivity at the higher P in, unlike the SDs which had the emissivity decrease with increasing P in. A basic geometrical reason is given to explain both the benefits of the XD over the SD as well as the increase in the XD’s emissivity with P in.

Investigation of core impurity transport in DIII-D diverted negative triangularity plasmas

Tokamak operation at negative triangularity has been shown to offer high energy confinement without the typical disadvantages of edge pedestals (Marinoni et al 2021 Nucl. Fusion 61 116010). In this paper, we examine impurity transport in DIII-D diverted negative triangularity experiments. Analysis of charge exchange recombination spectroscopy reveals flat or hollow carbon density profiles in the core, and impurity confinement times consistently shorter than energy confinement times. Bayesian inferences of impurity transport coefficients based on laser blow-off injections and forward modeling via the Aurora package (Sciortino et al 2021 Plasma Phys. Control. Fusion 63 112001) show core cross-field diffusion to be higher in L-mode than in H-mode. Impurity profile shapes remain flat or hollow in all cases. Inferred radial profiles of diffusion and convection are compared to neoclassical, quasilinear gyrofluid, and nonlinear gyrokinetic simulations. Heat transport is observed to be better captured by reduced turbulence models with respect to particle transport. State-of-the-art gyrokinetic modeling compares favorably with measurements across multiple transport channels. Overall, these results suggest that diverted negative triangularity discharges may offer a path to a highly-radiative L-mode scenario with high core performance.

Conductivity of Two-Dimensional Small Gap Semiconductors and Topological Insulators in Strong Coulomb Disorder

We are honored to dedicate this article to Emmanuel Rashba on the occasion of his 95 birthday. In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap, $\Delta$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $\Delta$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional narrow gap semiconductor on a substrate containing Coulomb impurities, mostly focusing on the case when amplitude of the random potential $\Gamma \gg \Delta$. We show that the conductivity generically exhibits three regimes and only the highest temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through nearest-neighbor or variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We arrive at a similar disorder driven steep insulator-metal transition in thin films of three-dimensional topological insulators with very large dielectric constant, where due to confinement of electric field internal Coulomb impurities create larger disorder potential. Away from neutrality point this unconventional insulator-to-metal transition is augmented by conventional metal-insulator transition at small impurity concentrations, so that we arrive at disorder-driven re-entrant metal-insulator-metal transition.

Experimental confirmation of efficient island divertor operation and successful neoclassical transport optimization in Wendelstein 7-X

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

Impurity transport in ion- and electron-root confinement scenarios at Wendelstein 7-X

This paper reports on the observation of enhanced Ar impurity confinement in high density, turbulence reduced ion-root confinement (IRC) scenarios in Wendelstein 7-X (W7-X). Compared to the central electron-root confinement (CERC), Ar densities are substantially increased up to one order of magnitude and Ar flux profiles switch from slightly positive to pronounced negative fluxes all along the plasma radius in IRC. Estimations of the diffusive D and convective V transport parameter profiles using the STRAHL impurity transport code suggest a fundamentally different behavior in CERC and IRC with, compared to neoclassical values, high diffusive D and typical V profiles in CERC versus strongly reduced D and pronounced negative V profiles in IRC.

Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

The general coupling between particle transport and ionization-recombination processes in hot plasma is considered on the key concept of equilibrium charge state (CS) transport. A theoretical interpretation of particle and CS transport is gained in terms of a two-dimensional (2D) Markovian stochastic (random) processes, a discrete 2D Fokker-Plank-Kolmogorov equation (in charge and space variables) and generalized 2D coronal equilibrium between atomic processes and particle transport. The basic tool for analysis of CS equilibrium and transport is the equilibrium cell (EC) (two states on charge and two on space), which presents simultaneously a unit phase volume, the characteristic scales (in space and time) of local equilibrium, and a comprehensive solution for the simplest nonlinear relations between transport and atomic processes. The space-time relationships between the equilibrium constant, transport rates, density distributions, and impurity confinement time are found. The subsequent direct calculation of the total and partial density profiles and the transport coefficients of argon impurity showed a strong dependence of the 2D CS equilibrium and transport on the atomic structure of ions. A model for recovering the recombination rate profiles of carbon impurity was developed basing on the CS equilibrium conditions, the derived relationships, the data about density profiles, plasma parameters and ionization rates.

Reduction of impurity confinement time by combined heating of LHW and ECRH in EAST* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2018YFE031110 and 2017YFE0301205), the National Natural Science Foundation of China (Grant Nos. 11905146, 11775269, and 11805113), the Users with Excellence Program of Hefei Science Center, Chinese Academy of Sciences (Grant No. 2019HSC-UE014),

The core impurity confinement properties are experimentally investigated in the Experimental Advanced Superconducting Tokamak (EAST) plasma heated by lower hybrid wave (LHW) and electron cyclotron resonance heating (ECRH) (LHW+ECRH). It is shown that the impurity confinement time (τ imp) in the L-mode plasma jointly heated by LHW and ECRH is weakly dependent on electron density but strongly dependent on the heating power, thus it is shorter than that in LHW-only heated L-mode plasma with the similar plasma parameters. The combined heating of LHW and ECRH can reduce the collisionality and indicates a more effective heating method for core τ imp reduction and normalized poloidal beta (β P) improvement. It should be emphasized that in this high β P operation window the small ELM regime can be accessed, and an L-mode level τ imp (40 ms–80 ms) and high β N (∼ 1.7) can be obtained simultaneously. It means that this typical small ELMy H-mode regime has an advantage in avoiding the serious tungsten accumulation, and will be competitive in future long-pulse steady-state and high-performance operation with high-Z material plasma-facing components.

Effects of an anisotropic parabolic potential and Coulomb's impurity potential on the energy characteristics of asymmetrical semi-exponential CsI quantum wells

Because of its unique optoelectronic properties, people have studied the characteristics of polarons in various quantum well (QW) models. Among them, the asymmetrical semi-exponential QW (ASEQW) is a new model for studying the structure of QWs in recent years. It is of great significance to study the influences of the impurity and anisotropic parabolic confinement potential (APCP) on the crystal’s properties, because some of the impurities, usually regarded as Coulomb’s impurity potential (CIP), will exist in the crystal more or less, and the APCP has flexible adjustment parameters. However, the energy characteristics of the ASEQW under the combined actions of impurities and APCP have not been studied, which is the motivation of this paper. Using the linear combination operation and Lee–Low–Pines unitary transformation methods, we investigate the vibrational frequency and the ground state energy of the strong coupling polaron in an ASEQW with the influences of the CIP at the origin of coordinates and APCP, and make a comparison between our results and previous literature’s. Our numerical results about the energy properties in the ASEQW influenced by the CIP and APCP may have important significances for experimental design and device preparation.

Investigation of argon transport by X-Ray imaging crystal spectrometer on J-TEXT

• A tangential XICS has been upgraded and the temporal evolution of Ar density were observed by XICS on J-TEXT. • The behavior of argon was investigated under different discharge conditions. • STRAHL simulation results showed that the convection velocity changed from negative to positive as the ne increased. A tangential X-ray imaging crystal spectrometer (XICS) has been upgraded in the J-TEXT tokamak. The XICS system has been used to measure ion and electron temperature, plasma rotation velocities, selected impurity densities, and can be used for impurity transport. The XICS on J-TEXT was designed to receive Ar XVII emissions from the -0.5 a to +0.5 a region with a spatial resolution of 1.8 cm in the vertical direction, a is the minor radius. The temporal evolution of argon impurity density profiles after an argon gas puffed were observed with a time resolution of up to 2 ms. The behaviour of argon was investigated under different discharge conditions. The experimental results show that, as the density increased, the impurity confinement time obviously increased. Simulation results obtained by STRAHL showed that the convection velocity changed from negative to positive as the electron density increased. This indicated that impurities moved more favourably toward the plasma boundary.

Impact of the temperature ratio on turbulent impurity transport in Wendelstein 7-X

First experimental observations in the Wendelstein 7-X stellarator indicate that the impurity confinement can be explained by turbulent processes. In particular, plasma discharges with increased ion to electron temperature ratio are accompanied by reduced electron density fluctuation amplitudes and anomalous impurity diffusion, suggesting a lower turbulent transport. Employing gyro-kinetic numerical simulations, we argue that the temperature ratio plays a key role for reducing the ion temperature gradient instability in Wendelstein 7-X, leading to an enhanced impurity confinement.

Impurity transport in the pedestal of H-mode plasmas with resonant magnetic perturbations

Experiments on DIII-D show that resonant magnetic perturbations (RMPs) reduce the impurity confinement time in the H-mode pedestal below that of naturally ELMy plasmas. STRAHL modeling of discharges with aluminum laser blow off (LBO) injection show increased diffusion in the pedestal of H-mode discharges with RMPs. The increased diffusion from the RMPs provides improved impurity control compared to the naturally ELMy discharges and prevents the buildup of impurities near the edge of the plasma. Tungsten LBO injection into discharges with and without RMPs led to striking differences in the evolution of the discharge. The naturally ELMy discharge became ELM free and showed an increase in edge radiation, leading to the eventual radiative collapse of the plasma. Injecting a similar number of W particles into discharges with RMPs, either with or without ELMs, led to a measurable accumulation of core W but did not significantly impact the evolution of the discharge. These results indicate that RMPs are beneficial for controlling the buildup of impurities in the pedestal region of the plasma.

Dependence of the impurity transport on the dominant turbulent regime in ELM-y H-mode discharges on the DIII-D tokamak

Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft x-ray measurements, and vacuum ultraviolet spectroscopy provides a detailed uncertainty quantification of transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal a threefold drop in the impurity confinement time and order of magnitude increase in midradius impurity diffusion, when additional electron heating is applied. Furthermore, the calculated stationary aluminum density profiles reverse from peaked in electron heated to hollow in the ion heated case, following a similar trend to electron and carbon density. Comparable values of a core diffusion have been observed for W and Al ions, while differences in the propagation dynamics of these impurities are attributed to pedestal and edge transport. Modeling of the core transport with non-linear gyrokinetics code CGYRO [J. Candy and E. Belly, J. Comput. Phys. 324, 73 (2016)], significantly underpredicts the magnitude of the variation in Al transport. Diffusion increases three-times steeper with additional electron heat flux, and 10-times lower diffusion is observed in ion heated case than predicted by the modeling. The CGYRO model quantitatively matches the increase in the Al diffusion when approaching the linear threshold for the transition from the ion temperature gradient to trapped electron mode.

Charge-state independent anomalous transport for a wide range of different impurity species observed at Wendelstein 7-X

In this paper, the plasma volume averaged impurity confinement of selected charge states and impurity species has been characterized for the Stellarator Wendelstein 7-X (W7-X), covering a wide range of atomic charges (Z = 12–44) and atomic masses (M = 28–184). A comparison of the experimental findings to theoretical neoclassical and turbulent transport expectations suggests, aside from/in addition to the neoclassical transport, an additional significant anomalous transport mechanism, which is not inconsistent with the predictions of a turbulence dominated impurity transport and is in agreement with the experimental results from recent transport studies based on the direct measurements of impurity diffusion profiles, performed at W7-X.

Integrated modelling of core and divertor plasmas for the DEMO Fusion Neutron Source hybrid facility

A steady state regime for the tokamak-based DEMO Fusion Neutron Source (DEMO-FNS) with parameters R/a = 3.2 m/1.0 m, B = 5 Т, Ipl = 4–5 MA, PNBI = 30 MW and РECR = 6 МW is studied using coupled simulations of the central and divertor plasma. In our analysis, the divertor plasma state is determined by the values of the heat flux PSOL, the pressure of the neutrals in the divertor p n and the total number of neon particles NNe outside the separatrix. As the boundary conditions for the core plasma, we use the values at the separatrix of the electron density, ne_sep, and temperatures of the ions, Ti_sep, and electrons, Te_sep, the concentration of the neon impurity normalized to the electron density at the separatrix, cNe = ∑ nNe/ne_sep and the hydrogen neutral influx into the core plasma, Γ0sep. In the divertor region, all the values are calculated using the SOLPS4.3 code for a number of operating points (~150 in our case) with different values of PSOL, p n and NNe. Then the calculation results are approximated by analytical formulas. Power balance in the core plasma is calculated using the ASTRA and NUBEAM codes. The hydrogen (deuterium and tritium) density is modelled taking into account the sources generated by the neutrals originating from the divertor region, as well as by injection of fast atoms and pellet injection. The neon density and radiation in the main plasma are simulated using the STRAHL code.As the result of the simulations, the operational regime of DEMO-FNS is determined, in which the heat loading onto the divertor targets remains at the acceptable level below 10 MW m−2, the divertor plasma does not transit into the ‘full detachment’ mode and the plasma in a double-null separatrix configuration is kept up–down symmetric. Variations of these conditions versus the impurity level and confinement parameters are investigated and discussed.

Absorption Spectra of Hydrogen-Like Donor Impurity in GaAs Quantum Well with Modified Pöschl-Teller Potential

Hydrogen-like donor impurity states in a quantum well with modified Poschl-Teller confinement potential have been considered. The dependence of binding energy on hydrogen-like donor impurity position and confinement potential parameters has been revealed. It has been shown that the dependence of binding energy on hydrogen-like donor impurity position has the bell-shaped character. The existence of binding energy maximum is explained by the concurrency of the size-quantization effect and the Coulomb interaction between electron and hydrogen-like donor impurity. The coefficient of an optical absorption in the presence of hydrogen-like donor impurity center has been computed. The absorption spectra for the quantum transitions between the hydrogen-like donor impurity ground state and conduction band ground state have been obtained.

Impurity transport studies at Wendelstein 7-X by means of x-ray imaging spectrometer measurements**Invited paper published as part of the Proceedings of the 45th Conference on Plasma Physics (EPS), Prague, Czech Republic, July, 2018.

This paper reports on the effect of on- and off-axis heating power deposition on the impurity confinement in purely electron cyclotron resonance heated He plasmas on the stellarator Wendelstein 7-X. Therefore, impurity transport times τI have been determined after Fe impurity injections by laser ablations and monitoring the temporal impurity emissivities by the x-ray imaging spectrometer HR-XIS. A significant increase of τI has been observed when changing the power deposition from on- to off-axis heating with energy confinement times τE being mainly unaffected. In addition, the scaling of impurity transport properties with respect to a variation of heating power PECRH and electron density ne has been investigated by keeping the heating power deposition on-axis. The observed τI scaling compares well to known τI scaling laws observed in other machines. A comparison of τI and τE yields an averaged ratio of τE/τI = 1.3 and transport times in the range of τI = 40–130 ms and τE = 40–190 ms. Comparing those absolute values to neoclassical predictions supports the recently observed nature of anomalous transport in Wendelstein 7-X, given within the up to now investigated operational parameters.

Tracer-Encapsulated Solid Pellet (TESPEL) injection system for Wendelstein 7-X.

Impurity confinement in fusion plasmas is mainly determined by transport mechanisms in the core region. For the Wendelstein 7-X stellarator, its island divertor is expected to screen effectively external impurity sources in the scrape-off layer at higher densities. However, the unique feature of Tracer-Encapsulated Solid Pellet (TESPEL) injection, releasing impurities at a well-localized radial position directly in the core plasma, enables investigating such transport mechanisms. This paper reports on the detailed design of a completely new TESPEL injection system, which has been designed by the National Institute for Fusion Science, Toki, Japan, and is currently being installed at Max-Planck-Institut für Plasmaphysik, Greifswald, Germany, for the Wendelstein 7-X. This injector consists of a storage and injection unit, attached to a system of guiding tubes which run through 3 successive differential pumping stages. A light-gate system and an optical observation system are used to determine the location of the deposited tracers. Laboratory tests carried out by shooting TESPELs onto a sample foil showed good performance after careful realignment of the guiding tubes.