J Weiland

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.

Analysis of eta i mode by reactive and dissipative descriptions and the effects of magnetic q and negative shear on the transport

Ion temperature gradient driven modes are studied in the short wavelength region by using a three pole reactive fluid model and an adiabatic E*B convection model, as well as the gyro-Landau fluid model. In all of the above models the parallel ion dynamics is included and the results have been compared both analytically and numerically. Furthermore, the effects of the magnetic safety factor q on the growth rate and transport coefficient chi i have been investigated. The maximum of chi i as a function of the mode number is computed, and the stabilizing effect of the negative magnetic shear has been studied

The International Multi-Tokamak Profile Database

An international multi-tokamak profile database has been assembled, constituting a representative set of reference tokamak discharges for the purpose of testing local transport models against well documented data. In particular, it will allow one to measure the accuracy with which the models can reproduce experiments and draw confidence intervals for the predictions of the models outside the range covered in the database. This database is now available to the fusion community and may be accessed by anonymous ftp to iterphys.naka.go.jp; the purpose of this article is to describe the structure of the database and the discharges contributing to it so that all can take full advantage of this resource. Thus, after an introductory general discussion of the database, there is a more detailed description of its structure, with listings of variables emphasized and how to access the database. There is then a brief description of each contributing tokamak and information on the type of discharges available from that tokamak. This is followed by a more quantitative description of the data, giving the ranges of dimensional and dimensionless variables available. Some typical modelling results to illustrate the use of the database are given in the conclusion.

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.

Comparison of ITER performance predicted by semi-empirical and theory-based transport models

The values of Q = (fusion power)/(auxiliary heating power) predicted for ITER by three different methods are compared. The first method utilizes an empirical confinement-time scaling and prescribed radial profiles of transport coefficients; the second approach extrapolates from specially designed ITER similarity experiments, and the third approach is based on partly theory-based transport models. The energy confinement time given by the ITERH-98(y, 2) scaling for an inductive scenario with a plasma current of 15 MA and a plasma density 15% below the Greenwald density is 3.7 s with one estimated technical standard deviation of ±14%. This translates, in the first approach, for levels of helium removal, and impurity concentration, that, albeit rather stringent, are expected to be attainable, into an interval for Q of [6–15] at the auxiliary heating power, Paux = 40 MW, and [6–30] at the minimum heating power satisfying a good confinement ELMy H-mode. All theoretical transport-model calculations have been performed for the plasma core only, whereas the pedestal temperatures were taken as estimated from empirical scalings. Predictions of similarity experiments from JET and of theory-based transport models that we have considered—Weiland, MMM, and IFS/PPPL—overlap with the prediction using the empirical confinement-time scaling within its estimated margin of uncertainty.

A Perturbation Expansion for the Nonlinear Schrödinger Equation with Application to the Influence of Nonlinear Landau Damping

The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schrodinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method to those by Ott and Sudan on the KdV equation and to a recent paper by Pereira and Stenflo.

Radial extension of drift waves in the presence of velocity profiles

The effect of a radially varying poloidal velocity field on the recently found radially extended toroidal drift waves [Connor et al., Phys. Rev. Lett. 70, 1803 (1993)] is investigated analytically. The role of velocity curvature (Vθ‘) is found to have robust effects on the radial mode structure of the mode. For a positive value of the curvature [usually found in the high‐(H) mode edges] the radial mode envelope, similar to the sheared slab case, becomes fully outgoing. On the other hand, for a negative value of the curvature [usually observed in the low‐(L) mode edges] the characteristics of conventional drift waves return back. The radial mode envelope reduces to a localized Gaussian shape and the mode can be unstable again for typical (magnetic) shear values in tokamaks. Velocity shear (Vθ’) on the other hand is found to have a rather insignificant role both in determining the radial mode structure and the stability.

Simulation of a coupled dynamic system of temperature and density in a fusion plasma

Simulation studies of a coupled system of equations for the evolution of temperature and density have been performed. The results are presented in graphs displaying the evolution in time of the temperature and density profiles, as well as in phase-plane plots, relating the central values of temperature and density. Particular emphasis is devoted to the particle and heat pinch effects, which tend to counter-balance the ordinary diffusion, and to co-operate with the alpha particle heating in sustaining plasma equilibrium. Oscillatory approaches to equilibria are recorded.

Repetitive Explosive Instabilities

The saturation of explosive instabilities by third order terms is studied analytically and by means of computer in the coherent phase description. The combined effect of nonlinear frequency shifts and effective nonlinear dissipation is considered. The stabilized explosions are found to be repetitive in general.

Fluid description of electron temperature gradient driven drift modes

The electron temperature gradient (ETG) driven drift mode is studied using an advanced fluid model retaining effects of nonadiabatic ions, Debye shielding and the electron diamagnetic heat flow. The derived eigenmode equation is solved analytically in the strong ballooning limit. Both the toroidal and the slab branch of the ETG mode are included and the fluid growth rates are compared with gyrokinetic results. The role of nonadiabatic ion response is found to have a stabilizing effect on ETG-mode in the lower-hybrid regime. Strong stabilization is also found due to Debye shielding effect for λDe2/ρe2>1. In particular, it is shown that nonadiabatic ion response can result in inward flows of particles for peaked density profiles.