F. Imbeaux

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...

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.

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.

Profile stiffness and global confinement

This paper analyses the properties of a critical gradient transport model based on a few assumptions: electrostatic gyroBohm scaling law, existence of an instability threshold and finite background transport below the threshold. A quantitative criterion of stiffness is proposed, which provides the means for a quantitative assessment and inter-machine comparison. It is also shown that this transport model is compatible with a two-term scaling law of global confinement, as proposed recently by the International Tokamak Physics Activity–Confinement Data Base and Modelling Topical Group. This model has also been applied to analyse a variety of experiments mostly using electron heat modulation on JET, ASDEX-Upgrade, TORE SUPRA and FTU. The thresholds are found to be in the expected domain for micro-instabilities in tokamaks. However, the stiffness factor is found to cover a broad range of variation.

Experimental studies of electron transport

Electron transport in tokamaks has many different features which are briefly reviewed. The paper is focused on electron heat transport in conventional tokamak plasmas. An inter-machine comparison indicates that the non-dimensional gradient length of the electron temperature profiles R/L Te is almost independent of the devices and varies little with plasma parameters. This strongly suggests that electron heat transport is governed by turbulence with a threshold in R/L Te . This is confirmed by modulation experiments using electron cyclotron heating. Simulations with empirical and physics-based transport models confirm this assumption.

Simulation of the hybrid and steady state advanced operating modes in ITER

Integrated simulations are performed to establish a physics basis, in conjunction with present tokamak experiments, for the operating modes in the International Thermonuclear Experimental Reactor (ITER). Simulations of the hybrid mode are done using both fixed and free-boundary 1.5D transport evolution codes including CRONOS, ONETWO, TSC/TRANSP, TOPICS and ASTRA. The hybrid operating mode is simulated using the GLF23 and CDBM05 energy transport models. The injected powers are limited to the negative ion neutral beam, ion cyclotron and electron cyclotron heating systems. Several plasma parameters and source parameters are specified for the hybrid cases to provide a comparison of 1.5D core transport modelling assumptions, source physics modelling assumptions, as well as numerous peripheral physics modelling. Initial results indicate that very strict guidelines will need to be imposed on the application of GLF23, for example, to make useful comparisons. Some of the variations among the simulations are due to source models which vary widely among the codes used. In addition, there are a number of peripheral physics models that should be examined, some of which include fusion power production, bootstrap current, treatment of fast particles and treatment of impurities. The hybrid simulations project to fusion gains of 5.6–8.3, βN values of 2.1–2.6 and fusion powers ranging from 350 to 500 MW, under the assumptions outlined in section 3. Simulations of the steady state operating mode are done with the same 1.5D transport evolution codes cited above, except the ASTRA code. In these cases the energy transport model is more difficult to prescribe, so that energy confinement models will range from theory based to empirically based. The injected powers include the same sources as used for the hybrid with the possible addition of lower hybrid. The simulations of the steady state mode project to fusion gains of 3.5–7, βN values of 2.3–3.0 and fusion powers of 290 to 415 MW, under the assumptions described in section 4. These simulations will be presented and compared with particular focus on the resulting temperature profiles, source profiles and peripheral physics profiles. The steady state simulations are at an early stage and are focused on developing a range of safety factor profiles with 100% non-inductive current.

Front propagation and critical gradient transport models

This paper analyzes the properties of a two-field critical gradient model that couples a heat equation to an evolution equation for the turbulence intensity. It is shown that the dynamics of a perturbation is ballistic or diffusive depending on the shape of the pulse and also on the distance of the temperature gradient to the instability threshold. This dual character appears in the linear response of this model for a wave packet. It is recovered when investigating the nonlinear solutions of this system. Both self-similar diffusive fronts and ballistic fronts are shown to exist. When the propagation is ballistic, it is found that the front velocity is the geometric mean between the turbulent diffusion coefficient and a microinstability growth rate.

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.

Integrated scenario in JET using real-time profile control

The recent development of real-time measurements and control tools in JET has enhanced the reliability and reproducibility of the relevant ITER scenarios. Diagnostics such as charge exchange, interfero-polarimetry, electron cyclotron emission have been upgraded for real-time measurements. In addition, real-time processes like magnetic equilibrium and q profile reconstruction have been developed and applied successfully in real-time q profile control experiments using model based control techniques. Plasma operation and control against magnetohydrodynamic instabilities are also benefiting from these new systems. The experience gained at JET in the field of real-time measurement and control experiments operation constitutes a very useful basis for the future operation of ITER scenarios.

Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model

The relevance of the assumption of critical gradient length in electron heat transport is tested against the results of electron cyclotron heating (ECH) modulation experiments carried out on ASDEX Upgrade, using time-dependent transport simulations. A general χe model based on a ∇Te/Te threshold is proposed, which can provide two different heat pulse (HP) propagation regimes, with respect to the power balance (PB) diffusion coefficient χePB: χeHP = χePB occurs if ∇Te/Te χePB if ∇Te/Te≥(∇Te/Te)c. By a careful choice of the model parameters, the experimental Te response to ECH modulations is simulated with excellent accuracy, and the transition between the two propagation regimes is, without ambiguity, ascribed to a ∇Te/Te threshold. Our findings are consistent with theoretical expectations, as well as with experimental observations made on TORE SUPRA. This global consistency shows the relevance of the main physical factors involved in our model, in particular the assumption of critical temperature gradient length.