L.-G. Eriksson

The CRONOS suite of codes for integrated tokamak modelling

CRONOS is a suite of numerical codes for the predictive/interpretative simulation of a full tokamak discharge. It integrates, in a modular structure, a 1D transport solver with general 2D magnetic equilibria, several heat, particle and impurities transport models, as well as heat, particle and momentum sources. This paper gives a first comprehensive description of the CRONOS suite: overall structure of the code, main available models, details on the simulation workflow and numerical implementation. Some examples of applications to the analysis of experimental discharges and the predictions of ITER scenarios are also given.

Inter-machine comparison of intrinsic toroidal rotation in tokamaks

Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M-A alpha beta(N), although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with beta(N) = 2.6, an intrinsic rotation Alfven Mach number of M-A similar or equal to 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input.

Toroidal rotation in ICRF-heated H-modes on JET

The first measurements of toroidal rotation of the bulk plasma during purely ion cyclotron resonance frequency (ICRF) heated H-modes on the JET tokamak are reported. Substantial toroidal acceleration in the direction of the plasma current occurs at the transition into H-mode. In the present paper the relationship between toroidal rotation and improved confinement of the H-mode is investigated. We conclude that the dominant driving mechanism for toroidal rotation is the ion pressure gradient.

Simulations of steady-state scenarios for Tore Supra using the CRONOS code

Scenarios of steady-state, fully non-inductive current in Tore Supra are predicted using a package of simulation codes (CRONOS). The plasma equilibrium and transport are consistently calculated with the deposition of power. The achievement of high injected energy discharges up to 1 GJ is shown. Two main scenarios are considered: a low density regime with 90% non-inductive current driven by lower hybrid waves-lower hybrid current drive (LHCD)-and a high density regime combining LHCD and ion cyclotron resonance heating with a bootstrap current fraction up to 25%. The predictive simulations of existing discharges are also reported.

Runaway acceleration during magnetic reconnection in tokamaks

In this paper, the basic theory of runaway electron production is reviewed and recent progress is discussed. The mechanisms of primary and secondary generation of runaway electrons are described and their dynamics during a tokamak disruption is analysed, both in a simple analytical model and through numerical Monte Carlo simulation. A simple criterion for when these mechanisms generate a significant runaway current is derived, and the first self-consistent simulations of the electron kinetics in a tokamak disruption are presented. Radial cross-field diffusion is shown to inhibit runaway avalanches, as indicated in recent experiments on JET and JT-60U. Finally, the physics of relativistic post-disruption runaway electrons is discussed, in particular their slowing down due to emission of synchrotron radiation, and their ability to produce electron–positron pairs in collisions with bulk plasma ions and electrons.

Suppression of runaway electron avalanches by radial diffusion

The kinetic theory of runaway electron avalanches caused by close Coulomb collisions is extended to account for radial diffusion. This is found to slow down the growth of avalanches. An approximate analytical formula for the growth rate is derived and is verified by a three-dimensional Monte Carlo code constructed for this purpose. As the poloidal magnetic flux that is available to induce an electric field in a tokamak is limited, avalanches can be prevented altogether by sufficiently strong radial diffusion. The requisite magnetic fluctuation level is sensitive to the mode structure and the speed of the disruption. It is estimated to be δB/B∼10−3 for parameters typical of large tokamaks.

Towards fully non-inductive current drive operation in JET

Quasi-steady operation has been achieved at JET in the high-confinement regime with internal transport barriers (ITBs). The ITB has been maintained up to 11 s. This duration, much larger than the energy confinement time, is already approaching a current resistive time. The high-performance phase is limited only by plant constraints. The radial profiles of the thermal electron and ion pressures have steep gradients typically at mid-plasma radius. A large fraction of non-inductive current (above 80%) is sustained throughout the high-performance phase with a poloidal beta exceeding unity. The safety factor profile plays an important role in sustaining the ITB characteristics. In this regime where the self-generated bootstrap current (up to 1.0 MA) represents 50% of the total current, the resistive evolution of the non-monotonic q-profile is slowed down by using off-axis lower-hybrid current drive.

A generic data structure for integrated modelling of tokamak physics and subsystems

The European Integrated Tokamak Modelling Task Force (ITM-TF) is developing a new type of fully modular and flexible integrated tokamak simulator, which will allow a large variety of simulation types. This ambitious goal requires new concepts of data structure and workflow organisation, which are described for the first time in this paper. The backbone of the system is a physics- and workflow-oriented data structure which allows for the deployment of a fully modular and flexible workflow organisation. The data structure is designed to be generic for any tokamak device and can be used to address physics simulation results, experimental data (including description of subsystem hardware) and engineering issues.

Theoretical analysis of ICRF heating in JET DT plasmas

A number of experiments with heating of DT plasmas using ICRF waves have been carried out at JET. The results of these experiments have been analysed by comparing experimentally measured quantities with the results of numerical simulations. In particular, four scenarios have been examined: (a) heating of minority (~5-20%) deuterons at the fundamental ion cyclotron frequency, ω = ωcD; (b) second harmonic heating of tritium, ω = 2ωcT; (c) fundamental minority heating of 3He with a few per cent of 3He; (d) second harmonic heating of deuterium, ω = 2ωcD. An important aim of the analysis was to assess whether the present understanding of the ICRF physics is adequate for predicting the performance of ICRF in DT plasmas. In general, good agreement between experimental results and simulations was found which increases the confidence in predictions of the impact of ICRF heating in future reactors. However, when a relatively high deuterium concentration was used in the ω = ωcD scenario, discrepancies were observed. In order to increase confidence in the simulations, the sensitivity of the simulation results to various plasma parameters has been studied.

On neutral-beam injection counter to the plasma current

It is well known that when neutral beams inject ions into trapped orbits in a tokamak, the transfer of momentum between the beam and the plasma occurs through the torque exerted by a radial return current. It is shown that this implies that the angular momentum transferred to the plasma can be larger than the angular momentum of the beam, if the injection is in the opposite direction to the plasma current and the beam ions suffer orbit losses. On the Mega-Ampere Spherical Tokamak (MAST) [R. J. Akers, J. W. Ahn, G. Y. Antar, L. C. Appel, D. Applegate, C. Brickley et al., Plasma Phys. Controlled Fusion 45, A175 (2003)], this results in up to 30% larger momentum deposition with counterinjection than with co-injection, with substantially increased plasma rotation as a result. It is also shown that heating of the plasma (most probably of the ions) can occur even when the beam ions are lost before they have had time to slow down in the plasma. This is the dominant heating mechanism in the outer 40% of the MAST ...