Impurity Transport Coefficients Research Articles

High-n Rydberg transition spectroscopy for heavy impurity transport studies in W7-X (invited).

Here, we present a novel spectroscopy approach to investigate impurity transport by analyzing line-radiation following high-n Rydberg transitions. While high-n Rydberg states of impurity ions are unlikely to be populated via impact excitation, they can be accessed by charge exchange (CX) reactions along the neutral beams in high-temperature plasmas. Hence, localized radiation of highly ionized impurities, free of passive contributions, can be observed at multiple wavelengths in the visible range. For the analysis and modeling of the observed Rydberg transitions, a technique for calculating effective emission coefficients is presented that can well reproduce the energy dependence seen in datasets available on the OPEN-ADAS database. By using the rate coefficients and comparing modeling results with the new high-n Rydberg CX measurements, impurity transport coefficients are determined with well-documented 2σ confidence intervals for the first time. This demonstrates that high-n Rydberg spectroscopy provides important constraints on the determination of impurity transport coefficients. By additionally considering Bolometer measurements, which provide constraints on the overall impurity emissivity and, therefore, impurity densities, error bars can be reduced even further.

COREDIV simulations of D and D–T high current–high power Baseline pulses in JET-ITER like wall

The two best performing pulses of the so called ITER-Baseline scenario (I p = 3.5 MA and P in ≈ 35 MW) of JET-ITER like wall, one in deuterium (D) the other in deuterium–tritium (D–T) plasma are examined and compared in this study. Generally, the D–T Baseline pulses exhibit an electron density level higher than the D pulses and the plasma energy is higher than in the comparable D pulses by up to 20%, reaching about 12 MJ in the pulse studied here. In contrast with the D pulses, the D–T pulses are often characterised by the increase in time of the radiated power in the mantle region (0.70 < ρ < 0.95), which may lead to the loss of the edge localised mode activity when the threshold H–L transition power is approached and to the subsequent plasma disruption due to excessive radiation. In this study we try to identify the physical mechanisms responsible for this behaviour using the available experimental data (principally the total radiated power from the bolometry) and the results of the fluid COREDIV model (1D in the core, 2D in the scrape-off-layer (SOL)), self-consistent with respect to core-SOL and also to main plasma-impurities. In fact, the loss of power caused by impurity radiation affects the temperature profile and finally the power to the divertor plate. The electron density and temperature profiles are numerically reconstructed as well as the radiated power density profiles, indicating no major difference in impurity transport in D and D–T. Indeed, the impurity transport coefficients used in COREDIV to match the experimental radiated power profiles are similar in the two pulses. The computed tungsten sources and densities are lower in the D–T pulse and the divertor impurity retention capability is a little better in the D–T pulse, indicatinga stronger collisional drag force in the SOL. The higher electron density and the broadening of its profile are the main cause of the observed increase of the radiated power in the D–T pulse.

Parameter study of L–H transition for plasma operation scenario development in JA DEMO

We have investigated the L–H transition in JA DEMO, a design concept of the steady-state tokamak fusion demonstration reactor. We develop an L–H transition model, which determines the minimum pedestal growth time such that a power ratio, the net plasma loss power across the separatrix over the L–H threshold power, is maintained at a constant value during pedestal growth for a given external heating power. We conduct parameter studies using an integrated modeling code, considering impurity transport. The dependence of the heating power and time required for the L–H transition on the plasma density, temperature, threshold power, impurity density fraction, and impurity transport coefficients is clarified. We evaluate the appropriate impurity density fraction for the L–H transition and the divertor heat load reduction. The fraction depends on the impurity transport coefficients and external heating power. The obtained results are necessary to confirm the L–H transition feasibility and to develop the plasma operation scenario consistent with the various engineering constraints in a design-stage reactor. The heating power required for the L–H transition turns out to be lower than the power supposed to be installable in the current design activities of JA DEMO.

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.

Non-parametric inference of impurity transport coefficients in the ASDEX Upgrade tokamak

We present a non-parametric inference of impurity transport coefficients by using charge exchange recombination spectroscopy measurements of Ne X, Ne VIII, O VIII, and C VI lines. Due to their close atomic numbers, neon, oxygen and carbon impurity ions are assumed to have the same diffusion coefficient D and convection velocity v. Unlike conventional techniques that modulate or perturb the impurity contents, we employ a quasi-stationary plasma with static impurity profiles. Since the ratio of v to D only describes the equilibrated profile of the sum of all impurity charge states, steady-state measurements can still decouple D and v if different charge states are simultaneously observed. We have formulated a non-parametric analysis framework based on the Bayesian probability theory and conducted transport coefficient measurements for a Type III ELMy H-mode plasma at ASDEX Upgrade. The charge exchange reactions with the background neutrals, which are known to affect the impurity charge state balance, are taken into account by introducing additional free parameters. While D at the pedestal is close to the neoclassical level (1 m s−2), a large diffusion coefficient and a strong outward convection are inferred right inside the pedestal top.

Experimental inference of neutral and impurity transport in Alcator C-Mod using high-resolution x-ray and ultra-violet spectra

We present experimental inferences of cross-field impurity transport coefficients for AlcatorC-Mod plasmas without edge-localized modes, leveraging a novel forward model for the entire Ca K α spectrum, including satellite lines within the spectral range, to compare to high-resolution x-ray imaging crystal spectroscopy (XICS). These measurements are complemented by extreme ultra-violet (EUV) spectroscopy that constrains transport closer to the edge. Using new atomic data sets for both XICS and EUV analysis has enabled consideration of line ratios across both spectral ranges and has increased the accuracy of inferred transport coefficients. Inclusion of charge exchange between edge thermal neutrals and impurities is shown to be extremely important in C-Mod pedestals. Atomic D neutral densities from experimental D Ly α measurements at the midplane are compared to SOLPS-ITER simulations, finding good agreement. Bayesian inferences of impurity transport coefficients are presented for L-, EDA H-, and I-mode discharges, making use of the Aurora package for forward modeling and combining our spectroscopic constraints. Experimentally inferred diffusion profiles are found to match turbulent transport models at midradius within uncertainties, using both quasilinear gyro-fluid TGLF SAT-1 and nonlinear ion-scale gyrokinetic CGYRO simulations. Significant discrepancies in convection are observed in some cases, suggesting difficulties in predictions of flat or hollow impurity profiles.

Inference of experimental radial impurity transport on Alcator C-Mod: Bayesian parameter estimation and model selection

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian impurity transport inference (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code (Dux 2003 Fusion Sci Technol. 44 708–15), to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z = 20) laser blow-off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution x-ray imaging crystal spectroscopy and vacuum ultra-violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and non-linear) predictions are also obtained. We find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed.

Spectral diagnostic system for light impurity transport study in J-TEXT Tokamak

A light impurity diagnostic system is developed for the J-TEXT tokamak. This diagnostic system consists of carbon V (227.09 nm), carbon III (464.7 nm) and edge rotation diagnostics. The carbon V diagnostic consists of a 12-core fiber bundle for light collection, an aberration-corrected monochromator, and a 12-channel photomultiplier tube array. The carbon III diagnostic adopts three identical 18-channel Si photodiode arrays to cover the edge region of the high-field side (HFS), low-field side (LFS) and limiter regions at different toroidal positions, with a specified front filter. The carbon VI (529.26 nm) diagnostic consists of a 10-core fiber bundle, an aberration-corrected monochromator, and an electron-multiplying CCD camera. The system coverage range is 0.2 m to 0.07 m of the HFS. A high-resolution spectroscopic diagnostic can detect carbon III (229.69 nm) and carbon V (227.09 nm) radiation intensities in the LFS. An accurate absolute calibration is carried out by an integrating sphere light source, and a relative position calibration is developed for all diagnoses. Combining the impurity emission profile which derived from inversion and plasma parameter profile, the impurity density of each ion stage and impurity transport coefficients are obtained by a one-dimensional impurity transport code.

Study of impurity transport in HL-2A ECRH L-mode plasmas with radially different ECRH power depositions

In HL-2A, an inverse sawtooth oscillation is observed with a long-lasting m/n = 1/1 mode during ECRH phase with power deposition inside sawtooth inversion radius (inner-deposited ECRH), while a normal sawtooth instead appears when the ECRH power is deposited outside sawtooth inversion radius (outer-deposited ECRH). Aluminum is then injected as a trace impurity with laser blow-off (LBO) method into the inner- and outer-deposited ECRH phases of HL-2A discharges to investigate the effect of ECRH on impurity transport. Temporal behavior of soft x-ray (SXR) array signals is analyzed with a 1D impurity transport code, and radial structures of impurity transport coefficients are obtained. The result shows that the radial transport of Al ions is strongly enhanced during the inner-deposited ECRH phase. In particular, an outward convection velocity is developed with positive values of 0 ⩽ V(ρ) ⩽ 3.8 m s−1 in ρ ⩽ 0.5, while the convection velocity is inward in ρ ⩾ 0.6. In the outer-deposited ECRH discharge, on the other hand, the convection velocity takes a big negative value in ρ ⩽ 0.4 and close to zero at ρ ~ 0.6. In ohmic discharges, an inward V(ρ) always appears in the whole plasma radii and gradually increases toward the plasma edge (−3.2 m s−1 at ρ = 1). The simulation result also indicates that centrally-peaked Al ion density profiles presented in the outer-deposited ECRH discharge can be flattened by the inner-deposited ECRH. Modification of impurity transport is discussed in the presence of long-lasting m/n = 1/1 MHD mode.

Impact of the neoclassical distribution function on turbulent impurity and momentum fluxes: fluid model and gyrokinetic simulations

The impact of the neoclassical background on turbulent impurity transport is investigated by means of gyrokinetic simulations supported by fluid equations. The latter are derived, using a Laguerre polynomials expansion of the first order neoclassical distribution function, and analytical expressions of the turbulent momentum flux and impurity transport coefficients are assessed. Comparisons of gyrokinetic simulations including this neoclassical background (coupling between the codes GKW and NEO) and the fluid model are used to identify the main mechanisms behind the modification of the turbulent transport channels and benchmark the numerical implementation. These mechanisms include a modification of the parallel dynamics of the main ions and direct contributions stemming from the asymmetry in the parallel velocity space of the neoclassical distribution function. The latter which is found dominant for turbulent impurity transport, increases with increasing collisionality, , , impurity mass, safety factor and aspect ratio. These contributions to momentum and impurity fluxes are also found to depend on the directions of the toroidal magnetic field and plasma current.

Impurities in a non-axisymmetric plasma: Transport and effect on bootstrap current

Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21, 042503 (2014)] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations with theoretical asymptotes in the high collisionality limit. We observe and explain a 1/ν-scaling of the inter-species radial transport coefficient at low collisionality, arising due to the field term in the inter-species collision operator, and which is not found with simplified collision models even when momentum correction is applied. However, this type of scaling disappears if a radial electric field is present. We also use SFINCS to analyze how the impurity content affects the neoclassical impurity dynamics and the bootstrap current. We show that a change in plasma effective charge Zeff of order unity can affect the bootstrap current enough to cause a deviation in the divertor strike point locations.

Charge dependence of neoclassical and turbulent transport of light impurities on MAST

Carbon and nitrogen impurity transport coefficients are determined from gas puff experiments carried out during repeat L-mode discharges on the Mega-Amp Spherical Tokamak (MAST) and compared against a previous analysis of helium impurity transport on MAST. The impurity density profiles are measured on the low-field side of the plasma, therefore this paper focuses on light impurities where the impact of poloidal asymmetries on impurity transport is predicted to be negligible. A weak screening of carbon and nitrogen is found in the plasma core, whereas the helium density profile is peaked over the entire plasma radius. Both carbon and nitrogen experience a diffusivity of the order of 10 m2s−1 and a strong inward convective velocity of ∼40 m s−1 near the plasma edge, and a region of outward convective velocity at mid-radius. The measured impurity transport coefficients are consistent with neoclassical Banana-Plateau predictions within . Quasi-linear gyrokinetic predictions of the carbon and helium particle flux at two flux surfaces, and , suggest that trapped electron modes are responsible for the anomalous impurity transport observed in the outer regions of the plasma. The model, combining neoclassical transport with quasi-linear turbulence, is shown to provide reasonable estimates of the impurity transport coefficients and the impurity charge dependence.

Improved profile fitting and quantification of uncertainty in experimental measurements of impurity transport coefficients using Gaussian process regression

The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, but the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We show that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. We also discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.

Measurement of plasma current dependent changes in impurity transport and comparison with nonlinear gyrokinetic simulation

Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.

Fluid and gyrokinetic simulations of impurity transport at JET

Impurity transport coefficients due to ion-temperature-gradient (ITG) mode and trapped-electron mode turbulence are calculated using profile data from dedicated impurity injection experiments at JET. Results obtained with a multi-fluid model are compared with quasi-linear and nonlinear gyrokinetic simulation results obtained with the code GENE. The sign of the impurity convective velocity (pinch) and its various contributions are discussed. The dependence of the impurity transport coefficients and impurity peaking factor −∇n Z /n Z on plasma parameters such as impurity charge number Z, ion logarithmic temperature gradient, collisionality, E × B shearing, and charge fraction are investigated. It is found that for the studied ITG dominated JET discharges, both the fluid and gyrokinetic results show an increase in the impurity peaking factor for low Z-values followed by a saturation at moderate values of impurity peaking, much below the neoclassical predictions, for large values of Z. The results are in qualitative agreement with the experimental trends observed for the injected impurities (Ne, Ar, Ni) whereas for the background carbon species the observed flat or weakly hollow C profiles are not well reproduced by the simulations.

Core Impurity Transport Studies from Different Diagnostic Approaches in LHD

Impurity transport has been studied in the Large Helical Device (LHD) with different diagnostic approaches based on an active method that combine carbon pellet injection with visible bremsstrahlung measurement and three passive methods for radial profile measurements of Ar and Fe Kα X-ray lines, Zeff, and extreme ultraviolet (EUV, ≤500 Å) impurity line emissions, in addition to usual passive spectroscopy. The existence of an inward convective velocity is confirmed in the edge region (ρ > 0.6) using the active method, whereas no convection is required in the core region (ρ < 0.6). The electron density dependence is weak for the diffusion coefficient (typically D = 0.15 to 0.25 m2/s) for densities of 1 to 5 × 1013 cm-3 but is strong for the inward convective velocity, which varies in the range of V(a) = −0.2 to −1.5 m/s. The inward V in helium plasmas (−0.4 m/s at ρ = 0.8 and the central density, ne ~ 4.0 × 1013 cm−3) is nearly half that in hydrogen plasmas (−0.7 m/s). This difference suggests a charge state dependence of fuel ions predicted by the neoclassical theory. Radial profiles of impurity transport coefficients of argon and iron have been studied using spatially resolved soft X-ray pulse-height analyzers. The impurity transport has also been studied in extremely high density discharges achieved by H2 pellet injection based on the passive spectroscopy and Zeff profile measurement. A flat Zeff profile is obtained at ne = 2.5 × 1014 cm−3 with values of 1.1 ≤ Zeff ≤ 1.2, suggesting no existence of impurity accumulation and radially constant impurity partial pressure. Finally, radial profiles of impurity lines in the EUV range are analyzed with the transport coefficients.

Impurity Transport Study of Medium-Z Argon by Means of Soft X-Ray Pulse Height Analyzer in LHD

Radial profiles of impurity transport coefficients of argon have been successfully obtained in Large Helical Device, using an assembly equipped with conventional semiconductor detectors and soft x-ray pulse-height analyzers. Several fixed argon discharges have enabled the radial scanning of the assembly to measure the radial profiles of argon-Kα lines. The present experimental results indicate that the impurity transport study becomes possible with the soft x-ray pulse-height analyzers.

Effect of suprathermal electrons on the impurity ionization state

The effect of electron cyclotron resonance heating induced suprathermal electron tails on the ionization of iron impurities in magnetically confined plasmas is investigated. The behaviour of plasma emissivity immediately after injection provides evidence of a spatially localized ‘shift’ towards higher charge states of the impurity. Bearing in mind that the non-inductive plasma heating methods generate long lasting non-Maxwellian distribution functions, possible implications on the deduced impurity transport coefficients, when fast electrons are present, are discussed.

A dependence of carbon impurity transport coefficients on fuel ions in hydrogen and helium plasmas of Large Helical Device

Impurity transport of carbon has been studied using a new method combined carbon pellet injection with high-spatial resolution bremsstrahlung measurement on the Large Helical Device [A. Iiyoshi et al., Fusion Technol. 17, 169 (1990)]. The carbon pellets are injected into a steady phase in neutral beam heated discharges with a standard configuration of Rax=3.6m. The particle transport coefficients (diffusion coefficient D and convective velocity V) are inferred using a diffusive/convective model. The results are compared between hydrogen and helium plasmas. As a result, it is found that the analyzed D has a constant radial profile with almost closed values of 0.2m2∕s in both plasmas. On the other hand, the inward V is required only at the plasma outer region (ρ&amp;gt;0.6) where the electron density gradient exits, and the inward V in helium plasmas (−0.4m∕s at ρ=0.8 and ne∼4.0×1019m−3) is nearly half as much as that in hydrogen plasmas (−0.7m∕s). This difference of the inward V between hydrogen and helium plasmas suggests a dependence on the charge state of fuel ions predicted from neoclassical theory.

Experimental and simulated M-shell nickel spectra in the 14.4–18.0 nm region frommagnetic fusion devices

Experimental M-shell nickel spectra in the 14.4–16.5 nm region from the JET tokamak(from both divertor and limiter configurations) and from the reversed field pinch RFX havebeen simulated. These spectra include lines from five ionization states, namely from K-likeNi9+ to P-likeNi13+ ions.For the JET limiter configuration the spectrum upper wavelength limit was higher (18.0 nm) and lines fromSi-like Ni14+ ions were also observed. Collisional–radiative (CR) models have been built forthese six Ni ions, considering electron collisional excitation and radiative decayas the main populating processes for the excited states. These models givephoton emission coefficients (PECs) for the emitted lines at electron density(ne) andtemperature (Te) values corresponding to the experimental situations. Impurity modelling is performed using a1D impurity transport code, calculating the steady state radial distribution of the Ni ions. TheNi line brightnesses are evaluated in a post-processing subroutine and simulated spectra areobtained. The spectrum from a single ion, in the absence of blendings, depends only on theTe and ne values in the emitting shell of the ionization state considered. On the other hand, thesuperposition of these spectra depends on the experimental conditions, as a consequence ofthe fact that the ion charge distribution depends not only on the radial profiles ofTe and ne, but also on the chosen ionization and recombination rate coefficients and on the radialprofiles of the impurity transport coefficients in the region of the emitting shells. Since theaim of the paper is the investigation of the atomic physics of the M-shell ions, the sectiondiscussing the plasma physics phenomena is purposely limited. For each experimentalspectrum a few simulations are presented, since a unique choice has not beenfound by selecting the input parameters of the transport code. The effect of theTe and ne values on the emitting shells as well as the influence of line blendings on the single-ionization-degreespectra are stressed. These, in turn, are then compared with the predictions. For thene range considered the PECs are practically independent ofne.The Te dependence is much reduced due to the fact that the spectral fits performed are actuallycomparisons of line ratios. The agreement found between experimental and simulatedsingle-ionization-degree spectra gives confidence in the atomic data used in the CR models.