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We address the formation of Interface Transport Barriers using a generic turbulent transport model, reduced to 2D, and used to investigate interchange turbulence in magnetized plasmas. The generation of a transport barrier at the edge-scrape off layer (SOL) plasma interface is governed by a zonation regime in the edge region with closed-field lines. The barrier is triggered by a gap in the turbulent spectrum between zero, the zonal flow wave vector, and the wave vector of the spectrum maximum. This gap is controlled by the energy injection wave vector of the interchange instability and the Rhine scale that bounds the inverse cascade. Increasing the magnitude of the turbulence drive at a given gap reinforces the transport barrier. In the interface transport barrier regime, edge relaxation bursts of turbulence regenerate the zonal flows that are eroded by damping processes such as collisions. The duration of the quiescent phase between the quasi-periodic relaxation events is then governed by the ion collision frequency. Such an interface transport barrier can play the role of a seed barrier prior to a full bifurcation to improved confinement.

Turbulent plasmas notably self-organize to higher energy states upon application of additional free energy sources or modification of edge operating conditions. Mechanisms whereby such bifurcations occur have been actively debated for decades, mostly on the basis of reduced models. Here we unravel a surprising causal chain of events in the onset of an improved confinement state, by applying generic entropy-based and information theoretic measures to the primitive kinetic equations. Interfacial contamination of a large, stable region (the ‘dog’) by locally-borne peripheral turbulent fluctuations (the ‘tail’) is found to be central to explaining transport properties, globally. These results, highly relevant to the quest for magnetic fusion advocate the use of such data-driven methods to many problems in fluids and plasmas where interfacial turbulent contamination is active.

International audience; A model of E×B staircases is proposed, based on a wave kinetic equation coupled to a poloidal momentum equation. A staircase pattern is idealised as a periodic radial structure of zonal shear layers that bound regions of propagating wave packets, viewed as avalanches. Wave packets are trapped in shear flow layers due to refraction. In this model an E × B staircase motif emerges due to the interaction between propagating wave packets (avalanches) and trapped waves in presence of an instability drive. Amplitude, shape, and spatial period of the staircase E × B flow are predicted as functions of the background fluctuation spectrum and the growth rate of drift waves. The zonal flow velocity radial profile is found to peak near its maxima and to flatten near its minima. The optimum configuration for staircase formation is a growth rate that is maximum at zero radial wave number. A mean shear flow is responsible for a preferential propagation speed of avalanches. It is not a mandatory condition for the existence of staircase solutions, but has an impact on their spatial period.

The interplay between toroidal drift-wave turbulence and tokamak profiles is investigated using a wave-kinetic description. The coupled system is used to investigate the interplay between marginally stable toroidal drift-wave turbulence and geodesic acoustic modes (GAMs). The coupled system is found to be unstable. Notably, the most unstable mode corresponds to the resonance between the turbulent wave radial group velocity and the GAM phase velocity. For a low-field-side ballooned drift-wave growth, a background flow shear breaks the symmetry between inwards- and outwards-travelling instabilities. Although this turbulence–GAM coupling may not be the primary driver for avalanches in standard core ion temperature gradient simulations, this mechanism is generic and displays many of the expected features, and should be of interest in several other regimes, which include towards the edge or in the presence of energetic particles.

This paper presents a model for zonal flow generation based on a wave kinetic equation coupled to a poloidal momentum equation in a regime where wave trapping matters. Several models of the wave collision operator have been tested: Krook, diffusion and diffusion plus an instability growth rate. Conditions for zonal instability have been identified. It is found that a zonal instability is possible in all cases. However the force is a power law of the zonal velocity, so different from the quasi-linear case of random phases that produces a force that is linear in velocity. Also the zonal force may change sign, leading to flow radial profiles that are not sinusoidal.

International audience

International audience; A simple and comprehensive method is derived and used to quantify the impact of scaling laws on tokamak reactor dimensioning. Assuming prescribed geometrical coefficients, we find the ensemble of possible triplets $R$, $B$ and normalized beta $\beta _N$ which allow one to reach target fusion gain $Q$ and fusion power $P_{fus}$, at arbitrary Greenwald fraction. The model is generic and derived for any scaling law of the energy confinement time. Using the IPB98(y,2) scaling law [ITER Physics Basis Expert Groups on Confinement and Transport and Confinement Modelling and Database, ITER Physics Basis Editors 1999 $Nucl.\ Fusion$ 39 2175] leads to ITER specifications, as expected. The recently proposed new scaling law for H-mode plasmas (DS03, [A.C.C. Sips et al. 2018 $Nucl.\ Fusion$ 58 126010]) is shown to lead to modest changes to the dimensioning, except for $B$ which could be significantly smaller for the same target performance. The impact on the dimensioning of critical exponents of the scaling law-both regarding engineer and dimensionless variables-is assessed, pushing for their determination with refined accuracy. Finally, the method is applied to a DEMO-like machine. The DS03 scaling law is found to have favorable consequences on the dimensioning as compared to IPB98(y,2), provided one is able to operate at larger $\beta _N$ , which can reveal challenging in a reactor aiming at zero disruption. Importantly, the opposite scaling of both scaling laws with respect to the aspect ratio are shown to have significant consequences on the optimal choice of this critical parameter.

Barely trapped and passing electrons have been recently predicted to strongly enhance the damping rate of Geodesic Acoustic Modes (GAMs) in tokamak plasmas, while keeping their real frequency almost unchanged as compared to the case with adiabatic electrons. In this paper, dedicated gyrokinetic simulations are successfully compared with these analytical predictions. Specifically, the scaling of the GAM damping rate with respect to the ion to electron mass ratio, to the electron to ion temperature ratio, to the safety factor, and to the aspect ratio is recovered in most regions of the relevant parameter space.

Impurity transport is numerically investigated for different types of impurity, such as helium (He), argon (Ar), and tungsten (W). Both turbulent and neoclassical transports are treated self-consistently using the full-f gyrokinetic software GYSELA. For a light impurity (He), the transport is mainly controlled by turbulence, while neoclassical transport is found to be dominant in the case of a heavy impurity (W). The impact of a poloidal asymmetry of the impurity density is also studied in detail and it is found to be strong in case of a high charge impurity, due to its Boltzmann-type response. Such strong asymmetry might lead to a core accumulation of heavy impurities by reducing the thermal screening factor of neoclassical transport. The two main contributions to neoclassical transport—Pfirsch–Schlüter (PS) flux and banana–plateau (BP) flux—are also studied. Depending on their mass (A) and charge (Z), the magnitudes of each flux are determined accordingly. Tungsten shows a strong PS flux compared to the other impurities, while BP flux is dominant in the case of argon. An analytical model including the effect of poloidal asymmetry is compared with the numerical simulation and a good agreement is found between them.

Phase space structures are extracted from the time series of five dimensional distribution function data computed by the flux-driven full-f gyrokinetic code GT5D. Principal component analysis (PCA) is applied to reduce the dimensionality and the size of the data. Phase space bases in ( φ , v ∥ , w ) and the corresponding spatial coefficients (poloidal cross section) are constructed by PCA, where φ , v ∥, and w, respectively, mean the toroidal angle, the parallel velocity, and the perpendicular velocity. It is shown that 83% of the variance of the original five dimensional distribution function can be expressed with 64 principal components, i.e., the compression of the degrees of freedom from 1.3 × 1 0 12 to 1.4 × 10 9. One of the important findings—resulting from the detailed analysis of the contribution of each principal component to the energy flux—deals with avalanche events, which are found to be mostly driven by coherent structures in the phase space, indicating the key role of resonant particles. Another advantage of the proposed analysis is the decoupling of 6D (1D time and 5D phase space) data into the combinations of 3D data which are visible to the human eye.

This paper presents a calculation of the contribution of electrons to GAM damping. It appears that this contribution is usually not negligible due to a resonance between barely trapped/passing electrons bounce/transit frequency and the mode pulsation.

International audience; Hotspot generation by lower-hybrid (LH) launchers is found to be governed by a resonance in the plasma electric field response to the external drive. The kinetic analysis in 1D-1V in the parallel direction allows one to compute the amplification effect for small amplitude of the external drive. The resonant Lorentzian response distorts the distribution function. An island structure is formed in the suprathermal part at the phase velocity of the external electrostatic drive. The non-linear features enhance the plasma response, driving overlap effects between multiple waves at rather low amplitude. The onset of a plateau in the distribution function, with extent reaching one thermal velocity, is already obtained when the standard overlap condition is achieved. The sensitivity of the resonance to plasma parameters and large variation of the amplification magnitude can compensate the fast radial decay of the small-scale features generated by the LH launchers, which are responsible for the interaction with the cold electrons. This mechanism can trigger hotspot generation further in the scrape-off layer than otherwise expected.

International audience; Trace impurity transport is studied with the flux-driven gyrokinetic GYSELA code [V. Grandgirard et al., $Comp.\ Phys.\ Commun.$\ 207, 35 (2016)]. A reduced and linearized multi-species collision operator has been recently implemented, so that both neoclassical and turbulent transport channels can be treated self-consistently on an equal footing. In the Pfirsch-Schlüter regime likely relevant for tungsten, the standard expression of the neoclassical impurity flux is shown to be recovered from gyrokinetics with the employed collision operator. Purely neoclassical simulations of deuterium plasma with trace impurities of helium, carbon and tungsten lead to impurity diffusion coefficients, inward pinch velocities due to density peaking, and thermo-diffusion terms which quantitatively agree with neoclassical predictions and NEO simulations [E. Belli et al., $Plasma\ Phys.\ Control.\ Fusion$ 54, 015015 (2012)]. The thermal screening factor appears to be less than predicted analytically in the Pfirsch-Schlüter regime, which can be detrimental to fusion performance. Finally, self-consistent nonlinear simulations have revealed that the tungsten impurity flux is not the sum of turbulent and neoclassical fluxes computed separately, as usually assumed. The synergy mostly results from the turbulence-driven in-out poloidal asymmetry of tungsten density. This result puts forward the need for self-consistent simulations of impurity transport, i.e. including both turbulence and neoclassical physics, in view of quantitative predictions for ITER.

Heavy impurities, such as tungsten (W), can exhibit strongly poloidally asymmetric density profiles in rotating or radio frequency heated plasmas. In the metallic environment of JET, the poloidal asymmetry of tungsten enhances its neoclassical transport up to an order of magnitude, so that neoclassical convection dominates over turbulent transport in the core. Accounting for asymmetries in neoclassical transport is hence necessary in the integrated modeling framework. The neoclassical drift kinetic code, NEO [E. Belli and J. Candy, Plasma Phys. Controlled Fusion P50, 095010 (2008)], includes the impact of poloidal asymmetries on W transport. However, the computational cost required to run NEO slows down significantly integrated modeling. A previous analytical formulation to describe heavy impurity neoclassical transport in the presence of poloidal asymmetries in specific collisional regimes [C. Angioni and P. Helander, Plasma Phys. Controlled Fusion 56, 124001 (2014)] is compared in this work to numerical results from NEO. Within the domain of validity of the formula, the factor for reducing the temperature screening due to poloidal asymmetries had to be empirically adjusted. After adjustment, the modified formula can reproduce NEO results outside of its definition domain, with some limitations: When main ions are in the banana regime, the formula reproduces NEO results whatever the collisionality regime of impurities, provided that the poloidal asymmetry is not too large. However, for very strong poloidal asymmetries, agreement requires impurities in the Pfirsch-Schlüter regime. Within the JETTO integrated transport code, the analytical formula combined with the poloidally symmetric neoclassical code NCLASS [W. A. Houlberg et al., Phys. Plasmas 4, 3230 (1997)] predicts the same tungsten profile as NEO in certain cases, while saving a factor of one thousand in computer time, which can be useful in scoping studies. The parametric dependencies of the temperature screening reduction due to poloidal asymmetries would need to be better characterised for this faster model to be extended to a more general applicability.

International audience; Verification of a 1D-1V kinetic code with the PoPe method [1] is presented. Investigation of the impact of reducing the precision of the numerical scheme is analysed by following 3 indicators of the physics solved by the code, namely the plasma response to an external high frequency electric field wave. The response of the distribution function in the vicinity of the particle-wave resonance is found to be most sensitive to the resolution. Consistently, a rapid growth of the error indicator determined with PoPe is observed. However, no critical value of this indicator allowing us to retain the physics in a situation of degraded precision could be observed. The response of the amplitude of the electric potential fluctuations is characterised by a transient growth followed by a plateau. It is found that the loss of this plateau is governed by the resolution in v-space, but due to the generation of a symmetry in the problem rather than to errors in the numerical scheme. The analysis of the transient indicates that the growth rate of the amplitude of the electric potential is very robust down to very low resolution, step in velocity of 2 thermal velocities. However, a transition prior to this resolution, with step 0.5 thermal velocity, can be identified corresponding to a PoPe indicator of order zero, namely for errors of order 100 %.

Approximations for closing the kinetic equation for the one particle distribution function are calculated by using propagators. These provide the formal structure of the collision term in the Landau approximation. The method allows one to investigate the effect of inhomogeneities at the Debye scale and to analyse magnetised collisions, when the Larmor radius is smaller than the Debye length. This method also allows one developing a simple renormalisation scheme to derive the Lenard-Balescu collision operator.

Two full-F global gyrokinetic codes are benchmarked to compute flux-driven ion temperature gradient (ITG) turbulence in tokamak plasmas. For this purpose, the Semi-Lagrangian code GYrokinetic SEmi-LAgrangian and the Eulerian code GT5D are employed, which solve the full-F gyrokinetic equation with a realistic fixed flux condition. The equilibrium poloidal flow profile formation processes are benchmarked and compared against the local neoclassical theory. The simulations above are carried out without turbulence, which agree well with each other and with the theoretical estimates. Here, a lot of attention has been paid to the boundary conditions, which have huge impacts on the global shape of radial electric field. The behaviors of micro-instabilities are benchmarked for linear and nonlinear cases without a heat source, where we found good agreements in the linear growth rates and nonlinear critical gradient level. In the nonlinear case, initial conditions are chosen to be identical since they dominate the t...

International audience; Radial fluxes of parallel momentum due to E × B and curvature (and B) drifts are shown to be correlated in tokamak plasmas. This correlation comes from the onset of poloidal convective cells generated by turbulence. The entire process requires a symmetry breaking mechanism, e.g. a mean shear flow. An analytical calculation shows that anti-correlation between the poloidal and parallel components of the turbulent Reynolds stress results in anti-correlation of the fluxes of parallel momentum generated by E × B and curvature drifts.

Rapid Communications; International audience; Large-scale reactor-relevant fusion plasmas are likely to operate near marginal stability. In this regime, we show clear evidence of interplay between core and edge regions of the plasma. This result illustrates aspects of the controversial 'shortfall problem' in the far-core, near-edge so-called 'No Man's Land' region and a possible route to resolve this issue. More generally, it emphasises global-scale organisation of turbulence and relevance of edge dynamics to core confinement.

La neuvième édition du « Festival de Théorie » de physique des plasmas s’est tenue du 26 juin au 20 juillet 2017. Tous les deux ans depuis 2001, l’Institut de recherche sur la fusion par confinement magnétique (IRFM) du CEA/Cadarache [1] organise cette manifestation scientifique internationale à Aix-en-Provence – un clin d’oeil aux nombreux festivals qui rythment la saison estivale dans la région – avec le concours d’Aix-Marseille Université.

A connection is established between two classical problems: the non linear saturation of a bump-on tail instability in collisionless regime, and the decay of a zonal flow towards a finite amplitude residual. Reasons for this connection are given and commented.

International audience; This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic Gysela code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the Gysela code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.

Global gyrokinetic Vlasov simulations for trapped ion modes indicate that the ion temperature gradient (ITG) instability saturates via nonlinear toroidal coupling. Trapped Ion modes were studied by solving a Vlasov equation averaged over the cyclotron and bounce motion of trapped ions. The distribution function, for trapped ions, is then calculated in a two-dimensional phase space, parametrized by two adiabatic invariants, the longitudinal action and the magnetic moment, in presence of a magnetic shear. Our model can be viewed as a kinetic version of the standard one-field Hasegawa-Mima-type and a broad frequency spectrum can originate from model for trapped-ion driven turbulence. Some interesting new features, which appear in the nonlinear regime of the instability, are then discussed.

Proceedings of the 19th International Conference on Plasma-Surface Interactions in Controlled Fusion; International audience; We are interested here in modelling the electron and ion temperature fields, Te and Ti respectively, in order to understand the main trends that govern the ratio Ti/Te that is being better documented in the SOL with RFA probes and . The experimental evidence gathered from several devices indicates that this temperature ratio significantly exceeds unity in most data sets that have been analysed, including measurements in the SOL of limiter devices like Tore Supra. Several issues of interest have been addressed with this version of the SOLEDGE-2D code. First, we have analysed the width of the SOL heat channels to the wall components and compared these values to analytical expressions. The key control mechanism of the width of the SOL heat channel is given by a balance between the sheath boundary conditions and the transverse transport. More advanced simulations address the interplay between the edge and SOL plasma allowing one to recover regimes with Ti/Te > 1.

Proceedings of the 19th International Conference on Plasma-Surface Interactions in Controlled Fusion; International audience; The transition between the core and scrape-off layer of a tokamak corresponds to a marked momentum shear layer, owing to sheath acceleration on limiters which drives near-sonic flows along the plasma magnetic field in the scrape-off layer, and a parallel shear flow instability can possibly be triggered. The possibility of this instability driven by the velocity gradient is investigated numerically, using a minimum model of particle and parallel momentum transport in the edge of a tokamak, in a computational domain modelling a limiter plasma with background turbulence modelled as an effective diffusion. It is found that unstable regions can exist in the vicinity of a limiter, in agreement with experimental findings, when momentum radial transport - and therefore coupling between SOL and core flows - is sufficiently weak. Instability is reinforced by core rotation, and is found to be maximum downstream of the limiter (with respect to the core plasma flow).

International audience; The staircase transport regime reported in kinetic simulations of plasma turbulent transport in magnetic confinement is recovered with a simple 2D fluid model allowing for reduced damping of the zonal flows. Some of the complex dynamics of the kinetic zonation regime are recovered but the pattern of the corrugation appears to be sinusoidal with a characteristic scale comparable to that of turbulence modes with largest spectral energy, in contrast to regimes observed in global and flux-driven kinetic simulations. Enhanced zonal flows govern both an overall reduction of the SOL width and a gradual steepening of the gradients with distance to the separatrix.

International audience; The transport of particles in the presence of energetic geodesic acoustic modes (EGAMs) is analysed by means of full-f global gyro-kinetic simulations using the multi-species version of the Gysela code and a test-particle tracking post-treatment that solves the equations of motion of passive gyro-centres embedded in the self-consistent EGAM potential obtained from Gysela simulations. It is found that EGAMs induce transport of particles that eventually results in counter-passing particle losses modulated at the EGAM frequency. A detailed analysis of the trajectories of test gyro-centres is performed and evidences of the interaction between the EGAM island and the region of magnetically trapped particles (trapping cone) is observed. In particular, we report for the first time on the complex interaction between the stochastic separatrix of the EGAM island and the X-point of the trapping cone, creating a channel for the transport of particles from v < 0 to v > 0 regions. Therefore, for the cases analysed in this work, co-injection of energetic particles might lead to a significant reduction of EGAM-induced losses. This result opens up new perspectives for further studies of the selection of energetic particle injection in order to minimize the losses due to EGAMs. Particle transport due to energetic-particle-driven geodesic acoustic modes 2

We present a new code aiming at giving a global and coherent approach for transport and turbulence issues in the edge plasma of Tokamaks. The TOKAM-3D code solves 3D fluid drift equations in full-torus geometry including both closed field lines and SOL physics. No scale separation is assumed so that interactions between large scale flows and turbulence are coherently treated. Moreover, the code can be run in transport regimes ranging from purely anomalous diffusion to fully established turbulence. Specific numerical schemes have been developed which can solve the model equations whether the presence of a limiter in the plasma is taken into account or not. Example cases giving an overview of the field of application of the code as well as verification results are also presented.

The issue of parallel flows asymmetries in the edge plasma is tackled with a new first principle transport and turbulence code. TOKAM-3D is a 3D full-torus fluid code that can be used both in diffusive and turbulent regimes and covers either exclusively closed flux surfaces or both open and closed field lines in limiter geometry. Two independent mechanisms susceptible to lead to large amplitude asymmetric parallel flows are evidenced. Global ExB drifts coupled with the presence of the limiter break the poloidal symmetry and can generate large amplitude parallel flows even with poloidally uniform transport coefficients. On the other hand, turbulent transport in the edge exhibits a strong ballooning of the radial particle flux generating an up-down m = 1, n = 0 structure on the parallel velocity. The combination of both mechanisms in complete simulations leads to a poloidal and radial distribution of the parallel velocity comparable to experimental results.

Flux driven kinetic transport is analysed for deeply trapped ion turbulence with the code GYSELA. The main observation is the existence of a steady state situation with respect to the statistics, in particular the balance between the injected energy and the time averaged energy flowing out through the outer edge boundary layer. The temperature is characterised by a very bursty behaviour with a skewed PDF. Superimposed to these short time scale fluctuations, one finds a regime with a strong increase of the zonal flows and a quenching of the turbulent energy. During this phase of such a predator-prey cycle, the core temperature rapidly increases while the edge temperature gradually decreases. The end of this reduced transport regime is governed by the onset of turbulence that governs large relaxation events, and a strong modification of the zonal flow pattern.

International audience; The electric potential plays a key role in the confinement properties of tokamak plasmas, with the subsequent impact on the performances of fusion reactors. Understanding its structure in the peripheral plasma-interacting with solid materials-is of crucial importance, since it governs the boundary conditions for the burning core plasma. This paper aims at highlighting the dedicated impact of the plasma-wall boundary layer on this peripheral region. Especially, the physics of plasma-wall interactions leads to non-linear constraints along the magnetic field. In this framework, the existence and uniqueness of the electric potential profile are mathematically investigated. The working model is two-dimensional in space and time evolving.

Critical physical issues can be specifically tackled with the global full-f gyrokinetic code GYSELA. Three main results are presented. First, the self-consistent treatment of equilibrium and fluctuations highlights the competition between two compensation mechanisms for the curvature driven vertical charge separation, namely, parallel flow and polarization. The impact of the latter on the turbulent transport is discussed. In the non-linear regime, the benchmark with the Particle-In-Cell code ORB5 looks satisfactory. Second, the transport scaling with p. is found to depend both on p. itself and on the distance to the linear threshold. Finally, a statistical steady-state turbulent regime is achieved in a reduced version of GYSELA by prescribing a constant heat source.

Turbulence spreading, namely turbulent transport extending into a stable region is reported both for the flat density profiles in the far SOL and into a modeled H-mode barrier. It is shown that due to turbulence penetration, the pedestal width fluctuates and that its effective width is a factor 2 smaller than the linear predicted width. Turbulence overshooting throughout the pedestal leads to a non-vanishing turbulent transport within the barrier and provides a coupling of core and SOL turbulence despite the transport barrier.

A promising operational regime of future fusion reactors is characterized by an edge transport barrier, i.e. a localized steepening of density and temperature gradients. Typically, such a barrier is unstable and relaxes quasi-periodically. In this work, we show that complete barrier relaxation cycles can be reproduced by three-dimensional turbulence simulations. In these simulations, a barrier forms due to an imposed E × B shear flow. This barrier relaxes intermittently on the confinement time scale, even if fluctuations of the E × B flow are suppressed. It is found here that if the E × B shear increases faster than linearly with heating power, the relaxation frequency decreases with power. A relaxation event has a complex dynamical behaviour, characterized by the intermittent growth of a mode at the barrier centre. A crucial ingredient in this non-linear dynamics is a time delay for an effective E × B velocity shear stabilization.

Équipe 107 : Physique des plasmas chauds; International audience; This paper presents a reduced kinetic model, which describes simultaneously trapped-ion (TIM) and trapped-electron (TEM) driven modes. Interestingly, the model enables the study of a full f problem for ion and electron trapped particles at very low numerical cost. The linear growth rate obtained with the full f nonlinear code Trapped Element REduction in Semi Lagrangian Approach is successfully compared with analytical predictions. Moreover, nonlinear results show some basic properties of collisionless TEM and TIM turbulence in tokamaks. A competition between streamer-like structures and zonal flows is observed for TEM and TIM turbulence. Zonal flows are shown to play an important role in suppressing the nonlinear transport and strongly depend on the temperature ratio T-e/T-i.

Équipe 107 : Physique des plasmas chauds; International audience; One important issue in turbulence self-organization is the interplay between the Kelvin-Helmholtz (KH) instability and streamers and/or zonal flows. This question has been debated for a long time. The effects of the KH instability and its position in the sequence of events between streamers, turbulence, and zonal flows have been investigated with a reduced gyro-bounce averaged kinetic code devoted to study the primary ion temperature gradient (ITG) instability linked to trapped ion modes (TIM). In toroidal geometry, the specific dynamics of TIM linked to trapped particles becomes important when the frequency of ITG modes falls below the ion bounce frequency, allowing one to average on both the cyclotron and bounce motion fast time scales. This reduction of the number of degrees of freedom leads to a strong reduction of computer resources (memory and computation time). Bounce-averaged gyrokinetic code can be considered as a toy model able to describe basic structures of turbulent transport in tokamak devices. In particular, by means of this code, we have observed that the energy injected in the system by the TIM instability is exchanged between streamers and zonal flows by means of KH vortices that grow along these structures in the nonlinear phase. The energy transfer occurs throughout the relaxation phase of the streamer growth leading to a modification of the KH modes and to the generation of the zonal flows.

The Projection on Proper elements (PoPe) is a novel method of code control dedicated to (1) checking the correct implementation of models, (2) determining the convergence of numerical methods, and (3) characterizing the residual errors of any given solution at very low cost. The basic idea is to establish a bijection between a simulation and a set of equations that generate it. Recovering equations is direct and relies on a statistical measure of the weight of the various operators. This method can be used in any number of dimensions and any regime, including chaotic ones. This method also provides a procedure to design reduced models and quantify its ratio of cost to benefit. PoPe is applied to a kinetic and a fluid code of plasma turbulence.

Theoretical investigations are performed in order to explain the plasma rotation increments induced by lower hybrid current drive (LHCD) in Tore Supra and the results are compared to the experimental observations. The intrinsic toroidal rotation is governed by several mechanisms in concert. The impact of the LHCD on each involved mechanism is analyzed. The neoclassical toroidal rotation is always in the counter-current direction. The toroidal diamagnetic velocity is of the order of the experimental toroidal velocity. At high plasma current the rotation evolution in the lower hybrid (LH) phase is controlled by the neoclassical friction force due to the trapped ions in banana trajectories through the toroidal diamagnetic velocity. This force results in the counter-current increment as observed in the experimental measurement of toroidal rotation. At low plasma current the rotation is dominated by momentum turbulent transport when the LH waves are applied. The Reynolds stress grows strongly compared to the high plasma current case and acts as a co-current force through its residual stress contribution. Momentum transport simulations are also performed with CRONOS (Artaud et al 2010) in order to assess the rotation increments induced by LHCD.