Pär Strand

Physics of confinement improvement of plasmas with impurity injection in DIII-D

External impurity injection into L mode edge discharges in DIII-D has produced clear confinement improvement (a factor of 2 in energy confinement and neutron emission), reduction in all transport channels (particularly ion thermal diffusivity to the neoclassical level), and simultaneous reduction of long wavelength turbulence. Suppression of the long wavelength turbulence and transport reduction are attributed to synergistic effects of impurity induced enhancement of E × B shearing rate and reduction of toroidal drift wave turbulence growth rate. A prompt reduction of density fluctuations and local transport at the beginning of impurity injection appears to result from an increased gradient of toroidal rotation enhancing the E × B shearing. Transport simulations carried out using the National Transport Code Collaboration demonstration code with a gyro-Landau fluid model, GLF23, indicate that E × B shearing suppression is the dominant transport suppression mechanism.

The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results

A selection of achievements and first physics results are presented of the European Integrated Tokamak Modelling Task Force (EFDA ITM-TF) simulation framework, which aims to provide a standardized platform and an integrated modelling suite of validated numerical codes for the simulation and prediction of a complete plasma discharge of an arbitrary tokamak. The framework developed by the ITM-TF, based on a generic data structure including both simulated and experimental data, allows for the development of sophisticated integrated simulations (workflows) for physics application.The equilibrium reconstruction and linear magnetohydrodynamic (MHD) stability simulation chain was applied, in particular, to the analysis of the edgeMHDstability of ASDEX Upgrade type-I ELMy H-mode discharges and ITER hybrid scenario, demonstrating the stabilizing effect of an increased Shafranov shift on edge modes. Interpretive simulations of a JET hybrid discharge were performed with two electromagnetic turbulence codes within ITM infrastructure showing the signature of trapped-electron assisted ITG turbulence. A successful benchmark among five EC beam/ray-tracing codes was performed in the ITM framework for an ITER inductive scenario for different launching conditions from the equatorial and upper launcher, showing good agreement of the computed absorbed power and driven current. Selected achievements and scientific workflow applications targeting key modelling topics and physics problems are also presented, showing the current status of the ITM-TF modelling suite.

Particle transport and density profile analysis of different JET plasmas

Over the last two years, several experiments relevant for the study of particle transport and density profile evolution, have been performed at JET. They can be classified as stationary discharges with and without central particle source due to the beams, quasi-stationary discharges with deuterium gas puffing, deep pellet fuelled discharges and discharges perturbed by cold pulses obtained by shallow pellet injection. All these experimental scenarios have been simulated by means of the JETTO transport code, employing different transport models: purely empirical models and the semi-empirical mixed Bohm/gyro-Bohm transport model, both with the addition of different theory-based expressions for the anomalous particle pinch and the first principle Weiland transport model. The coefficients used to scale the pinch velocity in the purely empirical and in the mixed Bohm/gyro-Bohm model have been varied from shot to shot. In this paper, the results of the simulations are presented. The main conclusions are that, for the cases studied in this paper, the sawtooth activity is the main particle transport mechanism in the plasma centre (r/a ≤ 0.5). Nevertheless, to reproduce the density profile in the gradient zone (0.5 ≤ r/a ≤ 0.9), an anomalous pinch seems to be necessary, at least for L-mode plasmas. This anomalous convective flux is well reproduced by the off-diagonal elements of the transport matrix given by the Weiland model.

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 −∇nZ/nZ 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. (Some figures in this article are in colour only in the electronic version)

Influence of the radio frequency ponderomotive force on anomalous impurity transport in tokamaks

Trace impurity transport in tokamaks is studied using an electrostatic, collisionless fluid model for ion-temperature-gradient and trapped-electron mode driven turbulence in the presence of radio frequency (rf) fields, and the results are compared with neoclassical predictions. It is shown that the inward impurity convective velocity (pinch) that is usually obtained can be reduced by the rf fields, in particular close to the wave resonance location where the rf ponderomotive force may be significant. However, the impurity diffusivity and convective velocity are usually similarly affected by the ponderomotive force, and hence the steady-state impurity density peaking factor −∇nz∕nz is only moderately affected by the rf fields.Trace impurity transport in tokamaks is studied using an electrostatic, collisionless fluid model for ion-temperature-gradient and trapped-electron mode driven turbulence in the presence of radio frequency (rf) fields, and the results are compared with neoclassical predictions. It is shown that the inward impurity convective velocity (pinch) that is usually obtained can be reduced by the rf fields, in particular close to the wave resonance location where the rf ponderomotive force may be significant. However, the impurity diffusivity and convective velocity are usually similarly affected by the ponderomotive force, and hence the steady-state impurity density peaking factor −∇nz∕nz is only moderately affected by the rf fields.

Performance of distributed multiscale simulations

Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources. We find that the first mode has the apparent benefit of increasing simulation speed, and the second mode can increase simulation speed if local resources are limited. Depending on resource reservation and model coupling topology, the third mode may result in a reduction of resource consumption.

Toroidal and poloidal momentum transport studies in JET

This paper reports on the recent studies of toroidal and poloidal momentum transport in JET. The ratio of the global energy confinement time to the momentum confinement is found to be close to τE/τφ=1 except for the low density discharges where the ratio is τE/τφ=2-3. On the other hand, local transport analysis of tens of discharges shows that the ratio of the local effective momentum diffusivity to the ion heat diffusivity is χφ/χi�0.1-0.4 rather than unity, as expected from the global confinement times and used in ITER predictions. The apparent discrepancy in the global and local momentum versus ion heat transport is explained by the fact that momentum confinement within edge pedestal is worse than that of the ion heat and thus, momentum pedes- tal is weaker than that of ion temperature. Another observation is that while the Ti has a threshold in R/LTi and profiles are stiff, the gradient in vφ increases with increasing torque and no threshold is found. Predictive trans- port simulations also confirm that χφ/χi�0.1-0.4 reproduce the core toroidal velocity profiles well. Concerning poloidal velocities on JET, the experimental measurements show that the carbon poloidal velocity can be an or- der of magnitude above the neo-classical estimate within the ITB. This significantly affects the calculated radial electric field and therefore, the E◊B flow shear used for example in transport simulations. The Weiland model reproduces the onset, location and strength of the ITB well when the experimental poloidal rotation is used while it does not predict an ITB using the neo-classical poloidal velocity. The most plausible explanation for the gen- eration of the anomalous poloidal velocity is the turbulence driven flow through the Reynolds stress. Both TRB and CUTIE turbulence codes show the existence of an anomalous poloidal velocity, being significantly larger than the neo-classical values. And similarly to experiments, the poloidal velocity profiles peak in the vicinity of the ITB and is caused by flow due to the Reynolds stress.

Toroidal and poloidal momentum transport studies in tokamaks

The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. tau(E)/tau(phi)approximate to 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity chi(phi eff)/chi(i.eff) among different tokamaks can be found. For example, the value of effective Prandtl number is typically around chi(phi eff)/chi(i.eff)approximate to 0.2 on JET while still tau(E)/tau(phi)approximate to 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number chi(phi)/chi(i) of around 1 is valid if there is an additional, significant inward momentum pinch which is required to explain the amplitude and phase behaviour of the momentum perturbation. The experimental results, i.e. the high Prandtl number and pinch, are in good qualitative and to some extent also in quantitative agreement with linear gyro-kinetic simulations. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E x B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynolds stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.

Influence of magnetic shear on impurity transport

The magnetic shear dependence of impurity transport in tokamaks is studied using a quasilinear fluid model for ion temperature gradient (ITG) and trapped electron (TE) mode driven turbulence in the collisionless limit and the results are compared with nonlinear gyrokinetic results using GYRO [J. Candy and R. E. Waltz, J. Comput. Phys 186, 545 (2003)]. It is shown that the impurity transport is sensitive to the magnetic shear, in particular for weak, negative, and large positive shear where a strong reduction of the effective impurity diffusivity is obtained. The fluid and gyrokinetic results are in qualitative agreement, with the gyrokinetic diffusivities typically a factor 2 larger than the fluid diffusivities. The steady state impurity profiles in source-free plasmas are found to be considerably less peaked than the electron density profiles for moderate shear. Comparisons between anomalous and neoclassical transport predictions are performed for ITER-like profiles [R. Aymar, P. Barabaschi, and Y. Shimo...

Impurity transport in temperature gradient driven turbulence

In the present paper, the transport of impurities driven by trapped electron (TE) mode turbulence is studied. Non-linear (NL) gyrokinetic simulations using the code GENE are compared with results from quasilinear (QL) gyrokinetic simulations and a computationally efficient fluid model. The main focus is on model comparisons for electron temperature gradient driven turbulence regarding the sign of the convective impurity velocity (pinch) and the impurity density gradient R/LnZ (peaking factor) for zero impurity flux. In particular, the scaling of the impurity peaking factors with impurity charge Z and with driving temperature gradient is investigated and compared with results for the more studied ion temperature gradient (ITG) driven turbulence. The question of helium ash removal in TE mode turbulence is also investigated. In addition, the impurity peaking is compared to the main ion peaking obtained by a self-consistent fluid calculation of the density gradients corresponding to zero particle fluxes. For the scaling of the peaking factor with impurity charge Z, a weak dependence is obtained from NL GENE and fluid simulations. The QL GENE results show a stronger dependence for low Z impurities and overestimates the peaking factor by up to a factor of two in this region. As in the case of ITG dominated turbulence, the peaking factors saturate as Z increases, at a level much below neoclassical predictions. The scaling with Z is, however, weak or reversed as compared to the ITG case. The results indicate that TE mode turbulence is as efficient as ITG turbulence at removing He ash, with DHe/χeff>1.0. The scaling of impurity peaking with the background temperature gradients is found to be weak in the NL GENE and fluid simulations. The QL results are also here found to significantly overestimate the peaking factor for low Z values. For the parameters considered, the background density gradient for zero particle flux is found to be slightly larger than the corresponding impurity zero flux gradient.