C. Bourdelle

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.

A new gyrokinetic quasilinear transport model applied to particle transport in tokamak plasmas

The scope of this paper is to present and benchmark the first version of a quasilinear calculation, QuaLiKiz, based on a fast linear gyrokinetic code, Kinezero [C. Bourdelle, X. Garbet, G. T. Hoang, J. Ongena, and R. V. Budny, Nucl. Fusion 42, 892 (2002)] accounting for all unstable modes and summing over a wave-number spectrum. The fluctuating electrostatic potential frequency and wave-number spectra are chosen based on turbulence measurements and nonlinear simulations results. A peculiar focus on particle transport is developed. The directions of compressibility and thermodiffusion convections of ions and electrons are analytically derived for passing and trapped particles in both ion and electron turbulence. Also, the charge and mass dependence of trace heavy impurity convection is analytically estimated. These results are compared with quasilinear simulations done by QuaLiKiz. Finally, the impact of accounting for all unstable modes and of summing over the wave-number spectrum is shown to reverse in s...

Global simulations of ion turbulence with magnetic shear reversal

This paper presents the results of three-dimensional fluid global simulations of electrostatic ion turbulence in tokamaks with reversed magnetic shear. It is found that a transport barrier appears at the location of magnetic shear reversal. This is due to a rarefaction of resonant surfaces in this region. For the same reason, the barrier is more pronounced when the minimum of the safety factor is a simple rational number. The barrier is broadened by velocity shear effects. It is also found that large-scale transport events hardly cross a transport barrier. Finally, a significant amount of toroidal rotation is generated by the turbulence. This rotation changes its sign at the position of magnetic shear reversal, as expected from a quasi-linear estimate of the Reynolds stresstensor.

Turbulent fluxes and entropy production rate

The entropy production rate is calculated for an interchange driven turbulence both in fluid and kinetic regimes. This calculation provides a rigorous way to define thermodynamical forces and fluxes. It is found that the forces are the gradients of density and temperature normalized to their “canonical” values, which are Lagrangian invariants of the flow. This formulation is equivalent to expressing the fluxes in terms of “curvature pinches,” where the curvature pinches are proportional to the logarithmic gradient of canonical profiles. Off diagonal terms in the transport matrix are found, which correspond to thermodiffusion and its Onsager symmetrical contribution to the heat flux. Hence, if thermodiffusion is significant, a heat pinch due to the density gradient also exists. The entropy production rate is found to be minimum when the profiles are equal to their canonical values. This property yields a generalized form of profile stiffness. However, a state where all profiles match their canonical values...

Residual parallel Reynolds stress due to turbulence intensity gradient in tokamak plasmas

A novel mechanism for driving residual stress in tokamak plasmas based on k∥ symmetry breaking by the turbulence intensity gradient is proposed. The physics of this mechanism is explained and its connection to the wave kinetic equation and the wave-momentum flux is described. Applications to the H-mode pedestal in particular to internal transport barriers, are discussed. Also, the effect of heat transport on the momentum flux is discussed.

Fluid simulations of turbulent impurity transport

Impurity transport in tokamak plasmas is studied with a fluid turbulence code, which has been upgraded to implement two ion species and electrons. The (fixed-flux) simulations are compared to the predictions of a quasilinear model. These simulations mostly agree with quasilinear estimates; they indicate that a turbulent impurity pinch exists. Moreover, this pinch is found to be dominated by curvature terms, as thermodiffusion pinches are found to decrease as 1∕Z and observed parallel velocity effects remain weak. The sign of the pinch is also investigated.

Stabilizing impact of high gradient of β on microturbulence

It is shown here that microturbulence can be stabilized in the presence of steep temperature and density profiles. Indeed in high β plasmas, pressure profile gradients are associated with high |β′|=−∂β/∂ρ, where β=P/(B2/2μ0) and ρ the square root of the toroidal flux normalized to its edge value. It is shown here that high values of |β′| have a stabilizing influence on drift modes. This may form the basis for a positive feedback loop in which high core beta values lead to improved confinement, and to further increase in β. A gyrokinetic electromagnetic flux tube code, GS2 [M. Kotschenreuther, G. Rewoldt, and W. M. Tang, Comput. Phys. Commun. 88, 128 (1995)], is used for analyzing the microstability. In high β spherical tokamak plasmas, high |β′| rather than low aspect ratio is a source of stabilization. Therefore, the effect of high |β′| should be stabilizing in the plasmas of the National Spherical Torus Experiment [Y.-K. Peng, M. G. Bell, R. E. Bell et al., Phys. Plasmas 7, 1681 (2000)].

Global and pedestal confinement in JET with a Be/W metallic wall

Type I ELMy H-mode operation in JET with the ITER-like Be/W wall (JET-ILW) generally occurs at lower pedestal pressures compared to those with the full carbon wall (JET-C). The pedestal density is similar but the pedestal temperature where type I ELMs occur is reduced and below to the so-called critical type I–type III transition temperature reported in JET-C experiments. Furthermore, the confinement factor H98(y,2) in type I ELMy H-mode baseline plasmas is generally lower in JET-ILW compared to JET-C at low power fractions Ploss/Pthr,08 2, the confinement in JET-ILW hybrid plasmas is similar to that in JET-C. A reduction in pedestal pressure is the main reason for the reduced confinement in JET-ILW baseline ELMy H-mode plasmas where typically H98(y,2) = 0.8 is obtained, compared to H98(y,2) = 1.0 in JET-C. In JET-ILW hybrid plasmas a similarly reduced pedestal pressure is compensated by an increased peaking of the core pressure profile resulting in H98(y,2) ≤ 1.25. The pedestal stability has significantly changed in high triangularity baseline plasmas where the confinement loss is also most apparent. Applying the same stability analysis for JET-C and JET-ILW, the measured pedestal in JET-ILW is stable with respect to the calculated peeling–ballooning stability limit and the ELM collapse time has increased to 2 ms from typically 200 µs in JET-C. This indicates that changes in the pedestal stability may have contributed to the reduced pedestal confinement in JET-ILW plasmas. A comparison of EPED1 pedestal pressure prediction with JET-ILW experimental data in over 500 JET-C and JET-ILW baseline and hybrid plasmas shows a good agreement with 0.8 < (measured pped)/(predicted pped,EPED) < 1.2, but that the role of triangularity is generally weaker in the JET-ILW experimental data than in the model predictions.

First scenario development with the JET new ITER-like wall

In the recent JET experimental campaigns with the new ITER-like wall (JET-ILW), major progress has been achieved in the characterization and operation of the H-mode regime in metallic environments: (i) plasma breakdown has been achieved at the first attempt and X-point L-mode operation recovered in a few days of operation; (ii) stationary and stable type-I ELMy H-modes with beta(N) similar to 1.4 have been achieved in low and high triangularity ITER-like shape plasmas and are showing that their operational domain at H = 1 is significantly reduced with the JET-ILW mainly because of the need to inject a large amount of gas (above 10(22) Ds(-1)) to control core radiation; (iii) in contrast, the hybrid H-mode scenario has reached an H factor of 1.2-1.3 at beta(N) of 3 for 2-3 s; and, (iv) in comparison to carbon equivalent discharges, total radiation is similar but the edge radiation is lower and Z(eff) of the order of 1.3-1.4. Strong core radiation peaking is observed in H-mode discharges at a low gas fuelling rate (i. e. below 0.5 x 10(22) Ds(-1)) and low ELM frequency (typically less than 10 Hz), even when the tungsten influx from the diverter is constant. High-Z impurity transport from the plasma edge to the core appears to be the dominant factor to explain these observations. This paper reviews the major physics and operational achievements and challenges that an ITER-like wall configuration has to face to produce stable plasma scenarios with maximized performance.

L–H power threshold studies in JET with Be/W and C wall

A comparison of the L?H power threshold (Pthr) in JET with all carbon, JET-C, and beryllium/tungsten wall (the ITER-like choice), JET-ILW, has been carried out in experiments with slow input power ramps and matched plasma shapes, divertor configuration and IP/BT pairs. The low density dependence of the L?H power threshold, namely an increase below a minimum density ne,min, which was first observed in JET with the MkII-GB divertor and C wall and subsequently not observed with the current MkII-HD geometry, is observed again with JET-ILW. At plasma densities above ne,min, Pthr is reduced by ?30%, and by ?40% when the radiation from the bulk plasma is subtracted (Psep), with JET-ILW compared to JET-C. At the L?H transition the electron temperature at the edge, where the pedestal later develops, is also lower with JET-ILW, for a given edge density. With JET-ILW the minimum density is found to increase roughly linearly with magnetic field, , while the power threshold at the minimum density scales as . The H-mode power threshold in JET-ILW is found to be sensitive both to variations in main plasma shape (Psep decreases with increasing lower triangularity and increases with upper triangularity) and in divertor configuration. When the data are recast in terms of Psep and Zeff or subdivertor neutral pressure a linear correlation is found, pointing to a possible role of Zeff and/or subdivertor neutral pressure in the L?H transition physics. Depending on the chosen divertor configuration, Pthr can be up to a factor of two lower than the ITPA scaling law for densities above ne,min. A shallow edge radial electric field well is observed at the L?H transition. The edge impurity ion poloidal velocity remains low, close to its L-mode values, ?5?km?s?1???2?3?km?s?1, at the L?H transition and throughout the H-mode phase, with no measureable increase within the experimental uncertainties. The edge toroidal rotation profile does not contribute to the depth of the negative Er well and thus may not be correlated with the formation of the edge transport barrier in JET.