Hans Nordman

Simulation of toroidal drift mode turbulence driven by temperature gradients and electron trapping

Turbulence and transport due to fully toroidal ion temperature gradient driven drift waves and a collisionless trapped electron mode have been studied by mode coupling simulations and with the quasi-linear theory. Diffusion coefficients in good agreement with the simulations have been obtained. The observed tendency for equilibration of the temperature and density scale lengths leads to particle or heat pinch effects that are in agreement with experimental trends.

Diffusive particle and heat pinch effects in toroidal plasmas

A fully toroidal fluid description has been derived for electrostatic drift modes in plasmas with electron trapping. The system includes both a modified toroidal ion temperature gradient mode (ηi mode) and a new trapped electron mode. The transport, obtained both by quasi-linear theory and non-linear numerical simulations, shows several features that are in agreement with observations in tokamaks, such as particle or heat pinch effects. A general tendency for equilibration of the inhomogeneity scale lengths for the density and temperature is found.

Physics of transport in tokamaks

This paper is an overview of recent results relating to turbulent particle and heat transport, and to the triggering of internal transport barriers (ITBs). The dependence of the turbulent particle pinch velocity on plasma parameters has been clarified and compared with experiment. Magnetic shear and collisionality are found to play a central role. Analysis of heat transport has made progress along two directions: dimensionless scaling laws, which are found to agree with the prediction for electrostatic turbulence, and analysis of modulation experiments, which provide a stringent test of transport models. Finally the formation of ITBs has been addressed by analysing electron transport barriers. It is confirmed that negative magnetic shear, combined with the Shafranov shift, is a robust stabilizing mechanism. However, some well established features of internal barriers are not explained by theory.

Transport due to toroidal ηi mode turbulence in tokamaks

The ion temperature gradient driven drift mode turbulence (ηi mode) has been studied with a fully toroidal fluid model. The saturation amplitudes and ion energy transport have been obtained by numerical simulations. An analytical model for mode coupling saturation in combination with a quasi-linear approximation has been used to derive a simple diffusion coefficient which is in good agreement with the simulations. The scaling of the diffusion coefficient χI with Ln/LB indicates a considerably improved agreement with the experimental radial variation, and the scaling with Te/Tj has been found to favour tokamak operation in the hot ion regime. The diffusion coefficient is consistent both with the improved confinement for pellet injection experiments and with the H-mode results for very large ηi.

Impurity effects on ηi mode stability and transport

The effects of an impurity ion species on the linear stability of the toroidal ion temperature gradient driven mode (ηi mode) are investigated together with the scaling properties of the corresponding quasi-linear transport coefficients. A stabilizing influence of impurities is found for inwardly peaked or flat impurity density profiles except for small n (n = 2Ln/LB), in which case destabilization is found. However, new impurity driven instabilities are introduced also below the pure ηi mode stability threshold. The ηi mode still accounts for the major part of the quasi-linear ion energy transport, which is reduced accordingly. The direction of the ion particle transport is mainly determined by the shape of the the impurity density profile in relation to the background ion profile. With an inwardly peaked impurity profile, the impurity flow is usually directed towards the edge and the main ion flow is reversed owing to ambipolarity

Symmetry breaking effects of toroidicity on toroidal momentum transport

A derivation of symmetry breaking toroidicity effects on toroidal momentum transport has been made from the stress tensor. This effect is usually stronger than the symmetry breaking caused by the flowshear on the eigenfunction. The model obtained generalizes a recent derivation of diagonal transport elements from the stress tensor to convective elements of turbulent equipartition or thermoelectric types. This makes it possible to interpret the same type of effects previously obtained from a phase space conserving nonlinear gyrokinetic equation.

Zonal flow generation in ion temperature gradient mode turbulence

In the present work the zonal flow (ZF) growth rate in toroidal ion-temperature-gradient (ITG) mode turbulence including the effects of elongation is studied analytically. The scaling of the ZF growth with plasma parameters is examined for typical tokamak parameter values. The physical model used for the toroidal ITG driven mode is based on the ion continuity and ion temperature equations whereas the ZF evolution is described by the vorticity equation. The results indicate that a large ZF growth is found close to marginal stability and for peaked density profiles and these effects may be enhanced by elongation.

Drift wave model for inward energy transport in tokamak plasmas

Stationary inward flows of electron energy have been obtained in transport code simulations of reactive drift wave systems. The recent experimental results with off‐axis electron cyclotron heating in the DIII‐D tokamak [Phys. Rev. Lett. 68, 52 (1992)] have been recovered with peaked electron temperature profiles and strong profile consistency.

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)