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Reduced quasilinear and nonlinear (gradient-driven) models with scale separations, commonly used to interpret experiments and to forecast turbulent transport levels in magnetised plasmas, are tested against nonlinear models without scale separations (flux-driven). Two distinct regimes of turbulence—either above threshold or near marginal stability—are investigated with Boltzmann electrons. The success of reduced models hinges in particular on the reproduction of nonlinear fluxes. Good agreement between models is found above threshold, whilst reduced models significantly underpredict fluxes near marginality, overlooking mesoscale flow organisation and turbulence self-advection. Constructive prescriptions whereby to improve reduced models are discussed.

Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian H e q ( ψ ) in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function F e q . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κ T , density κ n and equilibrium Hamiltonian κ Λ . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.

The effect of magnetic field ripple on tokamak plasma without turbulence is studied numerically and augmented with a reduced analytical model that includes neoclassical processes in the presence of non-axisymmetric perturbation and stochastic transport. For this study, a magnetic field ripple perturbation has been implemented in the GYSELA gyrokinetic code. This implementation has been verified thanks to a test of toroidal angular momentum conservation. The GYSELA code was then successfully benchmarked against the NEO code, which solves the drift kinetic equation, and against the reduced model in the collisionality range ν ⋆ ∈ [0.05–0.5] for several amplitudes of the magnetic ripple. An observation, shared by the model, the NEO code and GYSELA simulations is that the thermal drive of the mean poloidal velocity—measured by the k V P coefficient—decreases sharply for large yet experimentally relevant magnetic ripple amplitudes, and may even change sign.

Recent progress in experimental and theoretical studies of edge localized mode (ELM) physics is reviewed for the reactor relevant plasma regimes, namely the high confinement regimes, that is, H-modes and advanced scenarios.Theoretical approaches to ELM physics, from a linear ideal magnetohydrodynamic (MHD) stability analysis to non-linear transport models with ELMs are discussed with respect to experimental observations, in particular the fast collapse of pedestal pressure profiles, magnetic measurements and scrape-off layer transport during ELMs.High confinement regimes with different types of ELMs are addressed in this paper in the context of development of operational scenarios for ITER. The key parameters that have been identified at present to reduce the energy losses in Type I ELMs are operation at high density, high edge magnetic shear and high triangularity. However, according to the present experimental scaling for the energy losses in Type I ELMs, the extrapolation of such regimes for ITER leads to unacceptably large heat loads on the divertor target plates exceeding the material limits. High confinement H-mode scenarios at high triangularity and high density with small ELMs (Type II), mixed regimes (Type II and Type I) and combined advanced regimes at high βp are discussed for present-day tokamaks. The optimum combination of high confinement and small MHD activity at the edge in Type II ELM scenarios is of interest to ITER. However, to date, these regimes have been achieved in a rather narrow operational window and far from ITER parameters in terms of collisionality, edge safety factor and βp.The compatibility of the alternative internal transport barrier (ITB) scenario with edge pedestal formation and ELMs is also addressed. Edge physics issues related to the possible combination of small benign ELMs (Type III, Type II ELMs, quiescent double barrier) and high performance ITBs are discussed for present-day experiments (JET, JT-60U, DIII-D) in terms of their relevance for ITER. Successful plasma edge control, at high triangularity (~0.5) and high density (~0.7nGR), in ITB scenarios in JET is reported.Active control of ELMs by edge current, pellet injection, impurities and external magnetic perturbations creating an ergodic zone localized at the separatrix are discussed for present-day experiments and from the perspective of future reactors.

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.

Recent experimental results and plasma edge stability studies of ELMs are presented for both H-mode and optimized shear (OS) plasmas in JET. High triangularity (δ~0.5) ELMy \mbox{H-mode} experiments in JET achieved simultaneously high confinement (HIPB(y,2) = 1) and high density (~0.9 nGR). At high pedestal density (~1.1nGR), an anomalous decrease of type I ELMs frequency and energy losses per ELM was observed. A specific for high triangularity and high density (δ~0.5 and ne~1.1nGR) MHD activity with broad-band frequency spectrum (

Pressure driven curvature instabilities at the boundary of a tokamak plasma are studied. First, three-dimensional turbulence simulations are presented including the case where magnetic field lines are stochastic. Three main features are observed: (i) the level of pressure fluctuations decreases in the ergodic layer. (ii) This is essentially due to a suppression of large-scale structures. (iii) The turbulent heat diffusivity does not decrease in the stochastic layer due to an increase of electric field fluctuations. These observations are in agreement with turbulence measurements on Tore Supra. Second, particle flux driven turbulence in the scrape-off layer (SOL) is studied using a two-dimensional code. The transverse transport is found to be ballistic and intermittent. Bursts propagate outwards with a radial velocity of the order of one tenth of the parallel velocity. Test particles undergo outward and inward trajectories. The order of magnitude of the e-folding SOL length is in agreement with experimental data.

In this work, the flux-coordinate independent (FCI) approach to plasma turbulence simulations is formulated for the case of generic, static magnetic fields, including those possessing stochastic field lines. It is then demonstrated that FCI is applicable to nonlinear turbulent problems with and without X-point geometry. In particular, by means of simulations with the FENICIA code, it is shown that the standard features of ion temperature gradient (ITG) modes are recovered with reduced toroidal resolution. Finally, the impact of ITG turbulent transport on the temperature profile is studied under the influence of a static island, with ITER-like parameters. Results show the wide range of applicability of the method.

Perturbative transport experiments have been performed in JET low or reverse magnetic shear plasmas either in conditions of fully developed internal transport barrier (ITB) or during a phase where an ITB was not observed. Transient peripheral cooling was induced either by laser ablation or by shallow pellet injection, and the ensuing travelling cold pulse was used to probe the plasma transport in the electron and, for the first time, also in the ion channel. Cold pulses travelling through ITBs are observed to erode the ITB outer part, but, if the inner ITB portion survives, it strongly damps the propagating wave. The result is discussed in the context of proposed possible pictures for ITB formation. In the absence of an ITB, the cold pulse shows a fast propagation in the outer plasma half, which is consistent with a region of stiff transport, while in the inner half it slows down but shows the peculiar feature of amplitude growing while propagating. The data are powerful tests for the validation of theoretical transport models. This article was scheduled to appear in issue 7 of Plasma Phys. Control. Fusion. To access this Special issue please follow this link: http://stacks.iop.org/0741-3335/44/i=7

Important steps towards the understanding of turbulent transport have been made with the development of the gyrokinetic framework for describing turbulence and with the emergence of numerical codes able to solve the set of gyrokinetic equations. This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. Solving 5D gyrokinetic equations requires state-of-the-art high performance computing techniques involving massively parallel computers and parallel scalable algorithms. The various numerical schemes that have been explored until now, Lagrangian, Eulerian and semi-Lagrangian, each have their advantages and drawbacks. A past controversy regarding the finite size effect (finite rho-star) in ITG turbulence has now been resolved. It has triggered an intensive benchmarking effort and careful examination of the convergence properties of the different numerical approaches. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the rhostar going to 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary: inconsistent approximations that are sometimes used can lead to important discrepancies. Turbulent processes are characterized by a chaotic behaviour, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation. Further developments concerning non-adiabatic electron dynamics around mode-rational surfaces and electromagnetic effects are discussed.