Impurity Transport Coefficients Research Articles

Chapter 11: Impurity Transport in ASDEX Upgrade

In the core of a burning fusion plasma, the contamination by impurities has to be kept below a critical level. Understanding and control of impurity transport and accumulation are thus an essential issue. Impurity injection experiments have been performed to determine the impurity transport coefficients in the core and in the steep gradient region of H-mode plasmas. The measurements in the edge were edge-localized-mode resolved, and in the center, sawtooth-resolved transport coefficients were obtained for several species covering a wide range of ion charges. Comparison of the experimental values with impurity transport simulations revealed the contribution of anomalous and neoclassical transport in the different parts of the plasma. Discharge scenarios, which show impurity accumulation, were identified and control schemes were demonstrated.

Radiation power profiles and density limit with a divertor in the W7-AS stellarator

The addition of a divertor into the W7-AS stellarator has allowed access to a high density regime where the radiation profiles reach a steady state. In earlier limiter discharges, the plasma suffered a radiative collapse at high densities. In contrast to limiter experiments, where the impurity confinement time measured by Al laser blow-off increased with increasing line integrated density, in divertor discharges, above a density threshold, the impurity confinement time decreased with increasing line integrated density. The observation that the divertor plasma radiates mainly at the plasma edge rather than the plasma centre is a further indication that changes to the impurity transport coefficients at these high densities are the basis for the achievement of steady state discharges in the divertor configuration of W7-AS.The maximum line integrated density reached with a divertor is compared to that reached with a limiter. The previously derived scaling law for the density limit with a limiter shows that the achieved densities do not exceed those predicted when the higher deposited power is taken into account. In a divertor the radiated power is located at the plasma edge and increasing the density, cooling the plasma edge and radiating sufficient power to cause plasma detachment determines the density limit.

Radiation pattern and impurity transport in argon seeded ELMy H-mode discharges in JET

This paper addresses the issues of impurity behaviour during the argon seeding experiments in JET, in which argon and D2 have been simultaneously puffed in ELMy H-mode discharges to reach high density regimes, maintaining good confinement properties throughout the plasma discharge. The analysis is based mainly on a 1-D impurity diffusion model, which evaluates the impurity transport coefficients in three experimental scenarios.The available experimental data include, as a function of the time, the brightnesses of the soft x-rays and of several impurity lines, the effective charge Zeff, the profiles of the radiated power and the fully stripped Ar and C ion densities from charge-exchange recombination. From the simulation of these data it is possible to characterize the considered scenarios in terms of high-Z ion increase in the plasma centre and high radiation from the edge. In particular, it has been found that the configuration at high triangularity with continuous D2 puffing, characterized by an outward impurity pinch velocity, features flat or slightly hollow impurity ion profiles and high radiation from a narrow region at the edge, possibly associated to the presence of a significantneutral density. In this case an edge radiative mantle is established without high radiation from the plasma centre.

Experimental and simulatedargon spectra in the 2.3-3.4 nm region from tokamak plasmas

Experimental argon spectra in the 2.3-3.4 nm region from the Jettokamak on a single null divertor configuration have been simulated. Thespectra include lines from five ionization states, namely from Ar15+Li-like to Ar11+ N-like ions. Collisional-radiative models have beenconstructed for these five Ar ions, considering electron collisionalexcitation and radiative decay as the populating processes of the excitedstates. These models give photon emission coefficients for the emittedlines at electron density and temperature values corresponding to theexperimental situations. Impurity modelling is performed using aone-dimensional (1D) impurity transport code, calculating thesteady-state radial distribution of the Ar ions. The Ar line brightnessesare evaluated in a post-processing subroutine and simulated spectra areobtained. The parts of the spectra corresponding to a single-ionizationstate do not depend on the experimental conditions and show goodagreement except for the amplitude of the simulated 2s-3p Ar XVIline and the shape of the simulated 2.50 nm feature (composed of Ar XVI and Ar XV lines). On the other hand, the superpositionof these spectra depends on the experimental conditions, as aconsequence of the fact that the ion charge distributiondepends not only on the radial profiles of the electrondensity and temperature, but also of the impurity transportcoefficients. Simulations of the Ar spectra (includingtransport) give confidence in the atomic physics calculations;moreover, they allow the determination of the transportcoefficients in the plasma region emitting the consideredionization states, i.e. at the interior of the last closedmagnetic surface (LCMS). For a correct simulation of theamplitudes of the spectral features it is necessary to includea transport barrier inside the LCMS. As far as the atomicphysics is concerned, we report improved wavelengths forAr XV transitions and we benchmark photon emissioncoefficients for XUV transitions in highly ionizedargon.

Impurity toroidal rotation and transport in Alcator C-Mod ohmic high confinement mode plasmas

Central toroidal rotation and impurity transport coefficients have been determined in Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] Ohmic high confinement mode (H-mode) plasmas from observations of x-ray emission following impurity injection. Rotation velocities up to 3×104 m/sec in the co-current direction have been observed in the center of the best Ohmic H-mode plasmas. Purely ohmic H-mode plasmas display many characteristics similar to ion cyclotron range of frequencies (ICRF) heated H-mode plasmas, including the scaling of the rotation velocity with plasma parameters and the formation of edge pedestals in the electron density and temperature profiles. Very long impurity confinement times (∼1 sec) are seen in edge localized mode-free (ELM-free) Ohmic H-modes and the inward impurity convection velocity profile has been determined to be close to the calculated neoclassical profile.

Experimental and simulated neon spectra in the 10-nm wavelength region from tokamak and reversed field pinch plasmas

Experimental neon spectra (in the 10-nm region), from the tokamak Tore Supra and the reversed field pinch experiment RFX, have been simulated. The spectra include lines from three neon ionization states, namely Ne(7+), Ne(6+), and Ne(5+) ions. Collisional radiative models have been built for these three Ne ions, considering electron collisional excitation and radiative decay as populating processes of the excited states. These models give photon emission coefficients for the emitted lines at electron density and temperature values corresponding to the experimental situations. Impurity modelling is performed using a one-dimensional impurity transport code, calculating the steady-state radial distribution of the Ne ions. The Ne line brightnesses are evaluated in a post-process subroutine and simulated spectra are obtained. The parts of the spectra corresponding to a single ionization state do not depend on the experimental conditions and show good agreement with the simulated single ionization state spectra. On the other hand, the superposition of the three spectra depends on the experimental conditions, as a consequence of the fact that the ion charge distribution depends not only on the radial profiles of the electron density and temperature, but also of the impurity transport coefficients. Simulations of the Ne spectra (including transport) give confidence in the atomic physics calculations; moreover, they allow the determination of the transport coefficients in the plasma region emitting the considered ionization states.

Self-compensation in PbSe:Tl thin films

Processes of defect formation are investigated in epitaxial PbSe:Tl films prepared by vacuum evaporation from molecular beams at various condensation temperatures from mixtures with a thallium content of 0–1.6 at. %. It is established that an increase in the content of the acceptor impurity in the film is accompanied by a significant increase in the number of selenium donor vacancies through the self-compensation mechanism. The thallium concentrations in the films are determined, along with the impurity transport coefficients, which vary from 0.82 to 0.44 as the condensation temperature varies from 250 °C to 350 °C. The carrier densities are calculated theoretically as a function of the thallium content in the films. The noticeable discrepancy between theory and experiment for thallium concentrations in the film NTl 400 °C to obtain films having a low carrier density.

Derivation of local impurity transport quantities from soft-x radiation evolution during tracer injection at W7-AS

A frequently used method for determination of impurity transport coefficients is the analysis of the radial and temporal time evolution of the impurity density of injected tracer impurities. In cases when the impurity density cannot be measured directly, e.g., by active charge exchange recombination spectroscopy, the impurity density has to be reconstructed from impurity radiation as measured, e.g., by the soft-x camera. Due to the energy integrated information, assumption about the spatial ionization state distribution, e.g., coronal equilibrium, is necessary. This might not be valid in cases of large transport. Consequently, the transport quantities, derived under the preliminary assumption of radial coronal distribution, are used again in an iterative way to improve the density reconstruction in order to approach more realistic transport quantities. The procedure was applied to plasma discharges in the stellarator Wendelstein 7-AS.

Impurity transport in Alcator C-Mod plasmas

Trace non-recycling impurities have been injected into Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] plasmas in order to determine impurity transport coefficients. Subsequent impurity emission has been observed with spatially scanning x-ray and Vacuum Ultra-Violet (VUV) spectrometer systems. Measured time-resolved brightness profiles of helium- and lithium-like transitions have been compared with those calculated from a transport code which includes impurity diffusion and convection in conjunction with an atomic physics package for individual line emission. During Low-Confinement-Mode (L-mode) plasmas, the transport can be characterized by pure diffusion, with coefficients ∼5000 cm2/s, reflecting the ∼20 ms decay in the x-ray and VUV line brightnesses. During High-Confinement-Modes (H-modes), the impurity confinement times are much longer, and the modelling requires that there be a strong inward convection (of order 1000 cm/s) near the plasma edge, with greatly reduced diffusion (of order 100 cm2/s), also in the region of the edge transport barrier. These edge values of the transport coefficients during H-mode are qualitatively similar to the neo-classical values. Nitrogen has also been injected, and after the H- to L-mode transition, the inner shell satellite lines of lithium-like nitrogen dominate in intensity the resonance line of helium-like N5+ in a thin shell near the plasma edge.

Multiple plasma diagnoses from a five-chord, high energy resolution X-ray spectrometer array

X-ray spectra from Alcator C-Mod plasmas have been collected using a high wavelength resolution, five-spectrometer array during a wide range of operating conditions, providing a large variety of diagnostic information. Each independently scannable von Hamos-type spectrometer has a wavelength range of 2.6–4.1 Å and the complete Rydberg series of He- and H-like argon has been observed. Spectra of Δn = 1 ground state transitions and satellites taken along various chords have been simulated using the results from a collisional radiative model and the MIST transport code. Line ratios are used to infer the electron temperature profile and good agreement is found with electron cyclotron emission profiles. Line intensities have been used to obtain absolute argon densities and argon recycling coefficients, and up-down asymmetric density profiles are sometimes observed. The widths of the strongest lines have been used to deduce ion temperature profiles, and wavelength shifts have been used to determine toroidal rotation velocities. Transitions from around n = 9 to the ground state are populated by charge exchange in the outer regions of the plasma and these line intensities have been used to measure neutral hydrogen density profiles. Spectra from helium-like scandium have been obtained during injection experiments and time histories and line intensities have been used to determine impurity transport coefficients. Δn≥2 ground state transitions in molybdenum charge states around neon-like; have been observed and used to measure the absolute molybdenum density and to test atomic structure calculations.

X-ray and VUV observations of brightness profiles from Alcator C-Mod plasmas

Brightness profiles of x-ray and VUV lines from eight molybdenum charge states between and have been measured in Alcator C-Mod plasmas. These spatial profiles agree very well with those predicted by a model which includes ionization, recombination, excitation and transport. Comparison with the profiles of many different charge states provides severe constraints upon the rates used in the model. The charge state density profiles are calculated using measured impurity transport coefficients, measured electron density and temperature profiles and newly calculated ionization and recombination rate coefficients. These new rate coefficients include direct collisional ionization, excitation - autoionization, dielectronic and radiative recombination. Excitation - autoionization is shown to be an important process, since the excellent agreement between the measurements and predictions is obtained only with its inclusion. Fits to newly calculated excitation rate coefficients for the transitions are also presented.

Spectroscopic measurement of impurity transport coefficients and penetration efficiencies in Alcator C-Mod plasmas

Impurity transport coefficients and the penetration efficiencies of intrinsic and injected impurities through the separatrix of diverted Alcator C-Mod discharges have been measured using x-ray and vacuum ultraviolet (VUV) spectroscopic diagnostics. The dominant low Z intrinsic impurity in C-Mod is carbon which is found to be present in concentrations of less than 0.5%. Molybdenum, from the plasma facing components, is the dominant high Z impurity and is typically found in concentrations of about 0.02%. Trace amounts of medium and high Z nonrecycling impurities can be injected at the midplane using the laser blow-off technique and calibrated amounts of recycling, gaseous impurities can be introduced through fast valves either at the midplane or at various locations in the divertor chamber. A five chord crystal x-ray spectrometer array with high spectral resolution is used to provide spatial profiles of high charge state impurities. An absolutely calibrated, grazing incidence VUV spectrograph with high time resolution and a broad spectral range allows for the simultaneous measurement of many impurity lines. Various filtered soft x-ray diode arrays allow for spatial reconstructions of plasma emissivity. The observed brightnesses and emissivities from a number of impurity lines are used together with the mist transport code and a collisional-radiative atomic physics model to determine charge state density profiles and impurity transport coefficients. Comparisons of the deduced impurity content with the measured Zeff and total radiated power of the plasma are made.

Observations of Alcator C-Mod plasmas from a five chord high energy resolution x-ray spectrometer array

X-ray spectra from Alcator C-Mod plasmas have been collected using a high wavelength resolution, five spectrometer array during a wide range of operating conditions, providing a large variety of diagnostic information. Each independently scannable von Hamos type spectrometer has a wavelength range of 2.8–4.0 Å, and the complete Rydberg series of helium- and hydrogenlike argon have been observed. Spectra of Δn=1 ground state transitions and satellites taken along different chords have been simulated using the results from a collisional-radiative model and the mist transport code. Line ratios are very sensitive to the electron temperature and deduced profiles are in good agreement with ECE profiles. Line intensities have been utilized to obtain absolute argon densities. The widths of the strongest lines have been used to deduce ion temperature profiles. Transitions from around n=9 to the ground state are populated by charge exchange in the outer regions of the plasma and these line intensities have been used to determine the neutral hydrogen density profile. Spectra from heliumlike scandium have been obtained during injection experiments and time histories and line intensities have been utilized to determine impurity transport coefficients.

The impurity transport in HT-6B Tokamak

The quasi-stationary profiles of the impurity ionization stages in HT-6B Tokamak were absolutely determined by monitoring the VUV and visible line emissions. An impurity transport code was set up. The impurity transport coefficients and other parameters about impurities were determined. From the changes of impurity emission profiles, it was concluded that the impurity confinement was improved and the impurity recycling was reduced by the slow magnetic compression along the minor radius. Some characteristics about the impurity transport in this small device are discussed.

Impurity transport in the Advanced toroidal facility

The spectral line emissions from impurities injected using the laser ablation technique have been modelled in order to deduce impurity transport coefficients in the Advanced Toroidal Facility (ATF). The transport is found to be mainly diffusive, with little or no convective component. To reproduce the observed line emission it is necessary to postulate a radially dependent diffusion coefficient. For plasmas heated by electron cyclotron frequency waves the impurity transport is best fitted with a diffusion coefficient of 1000 cm2/s in the centre, increasing to 5000 cm2/s at the plasma edge. The global impurity particle confinement time for these plasmas is 65 ms and is considerably larger than the corresponding energy confinement time. Plasmas heated by high energy neutral particle beams display different impurity transport, with the best fit being a diffusion coefficient that is peaked on axis (5000 cm2/s) and that decreases towards larger minor radii (500 cm2/s at the plasma boundary). These transport coefficients have been successfully used to simulate the evolution of intrinsic impurities as well as laser ablated impurities in ATF

Power radiated from ITER by impurities

The MIST code has been used to model impurity radiation from the edge and core plasmas in ITER. A broad range of parameters have been varied, including Z eff, impurity species, impurity transport coefficients, and plasma temperature and density profiles. For a set of these parameters representative of the baseline ITER ignition scenario, it is seen that impurity radiation can make a major reduction in divertor power load without compromising core energy confinement. Scalings of impurity radiation with atomic number and machine size are also discussed.

Assessment of Atomic Data for Plasma Modelling and Effects of Difference in Atomic Data on Modelling Results

Of important atomic processes taking place in tokamak plasmas, rate coefficient formulas available for ionization and recombination are briefly reviewed and those for oxygen and iron ions are studied by comparison. As an example, assessment of rate coefficient formulas for an impurity transport modelling based on a one-dimensional tokamak model is made, and the remarkable dependence of the radial impurity distributions on the difference between two dielectronic recombination rate coefficient formulas is shown. This result suggests that considerably accurate atomic data would be necessary to derive reliable values of anomalous impurity transport coefficients from plasma modelling research.

Study of impurity radiation on the PLT and TFTR tokamaks with high-resolution, time-resolving spectrometers

Soft-x-ray (5–300 Å) spectra of intrinsic impurities have been recorded with a high-resolution multichannel XUV spectrometer (SOXMOS). Measurements of line intensity ratios as a function of time are applied to the determination of the impurity contribution to the energy balance. Results from TFTR Ohmic heated plasmas, including radiation due to carbon, oxygen, iron, nickel, chromium, titanium, and zirconium, are presented. The spatial ion distribution will be directly observed by a radial scanning spectrometer (FLOPSY). This instrument, under construction, will cover the spectral range from 1500 to 7000 Å and use mirrors and lenses for fast scanning. The spatial ion distribution, deduced from forbidden and allowed lines, will be compared to both theoretical models based on impurity concentrations and transport coefficients, as well as experimental data from bolometer measurements.

Effects of electrostatic trapping on neoclassical impurity transport in a collision-dominated plasma

It has been shown by Hazeltine and Ware that the existence of a reasonable high-Z impurity species can produce electrostatic trapping and drift comparable to the magnetic effects, assuming that the main plasma components are in the plateau regime. The calculation is extended to the collisional regime, modeling the edge region of the tokamak column and significant modification to the neoclassical impurity transport coefficients is found. A fluid approach is developed and the transport coefficients are found to be nonlinear in density and temperature gradients.

Impurity transport in the collisional regime for large poloidal variations

Impurity transport is studied in a toroidal plasma column with large poloidal variations of the plasma parameters (comparable to the variation of the magnetic field) near the edge. It is found that the highly collisional nature of the edge plasma can lead to such variations of density and electrostatic potential. The impurity transport coefficients are significantly modified by this effect, becoming non-linear in the gradients.