Synergy of Turbulent Momentum Drive and Magnetic Braking

In absence of external torque, plasma rotation in tokamaks results from a balance between collisional magnetic braking and turbulent drive. The outcome of this competition and cooperation is essential to determine the plasma flow. A reduced model, supported by gyrokinetic simulations, is first used to explain and quantify the competition only. The ripple amplitude above which magnetic drag overcomes turbulent viscosity is obtained. The synergetic impact of ripple on the turbulent toroidal Reynolds stress is explored. Simulations show that the main effect comes from an enhancement of the radial electric field shear by the ripple, which in turn impacts the residual stress.

Finding the elusive E×B staircase in magnetized plasmas

Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation.

Resistive reduced MHD modeling of multi-edge-localized-mode cycles in Tokamak X-point plasmas

The full dynamics of a multi-edge-localized-mode (ELM) cycle is modeled for the first time in realistic tokamak X-point geometry with the nonlinear reduced MHD code jorek. The diamagnetic rotation is found to be instrumental to stabilize the plasma after an ELM crash and to model the cyclic reconstruction and collapse of the plasma pressure profile. ELM relaxations are cyclically initiated each time the pedestal gradient crosses a triggering threshold. Diamagnetic drifts are also found to yield a near-symmetric ELM power deposition on the inner and outer divertor target plates, consistent with experimental measurements.

Mechanism of edge localized mode mitigation by resonant magnetic perturbations

A possible mechanism of edge localized modes (ELMs) mitigation by resonant magnetic perturbations (RMPs) is proposed based on the results of nonlinear resistive magnetohydrodynamic modeling using the jorek code, realistic JET-like plasma parameters and an RMP spectrum of JET error-field correction coils (EFCC) with a main toroidal number n=2 were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-n ballooning mode. The externally imposed RMP drives nonlinearly the modes coupled to n=2 RMP which produce small multimode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearinglike structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures ("footprints") created by n=2 RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during a ELM phase mitigated by RMPs is reduced almost by a factor of 10. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small, much more frequent ELMs or magnetic turbulence. Total ELM suppression was also demonstrated in modeling at higher RMP amplitude.

Unraveling quasiperiodic relaxations of transport barriers with gyrokinetic simulations of tokamak plasmas

The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability--driven by the temperature anisotropy (T(∥)≠T(⊥)). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.

Impact of energetic-particle-driven geodesic acoustic modes on turbulence

The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.

Self-consistent dynamics of impurities in magnetically confined plasmas: turbulence intermittency and nondiffusive transport

Self-consistent turbulent transport of high-concentration impurities in magnetically confined fusion plasmas is studied using a three-dimensional nonlinear fluid global turbulence model which includes ion-temperature gradient and trapped electron mode instabilities. It is shown that the impurity concentration can have a dramatic feedback in the turbulence and, as a result, it can significantly change the transport properties of the plasma. High concentration impurities can trigger strong intermittency that manifests in non-Gaussian heavy tails of the probability density functions of the E × B fluctuations and of the ion-temperature flux fluctuations. At the heart of this self-consistent coupling is the existence of inward propagating ion-temperature fronts with a sharp gradient at the leading edge that give rise to instabilities and avalanchelike bursty transport. Numerical evidence of time nonlocality (i.e., history dependence) in the delayed response of the flux to the gradient is presented.

Generation and amplification of magnetic islands by drift interchange turbulence

We investigate the multiscale nonlinear dynamics of a linearly stable or unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small-scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island.

Existence of metastable kinetic modes

The nonlinear evolution of resonantly driven systems, such as suprathermal particle driven modes in magnetically confined plasmas, is shown to strongly depend on the existence and nature of an underlying damping mechanism. When background resonant damping is present, subcritical states can take place. In particular, purely nonlinear steady-state regimes are found, whose destabilization threshold and saturation levels are calculated and validated using numerical simulations. This nonlinear behavior can be of relevance for acoustic modes in magnetically confined plasmas.

On the validity of the local diffusive paradigm in turbulent plasma transport

A systematic, constructive and self-consistent procedure to quantify nonlocal, nondiffusive action at a distance in plasma turbulence is exposed and applied to turbulent heat fluxes computed from the state-of-the-art full- f, flux-driven gyrokinetic GYSELA and XGC1 codes. A striking commonality is found: heat transport below a dynamically selected mesoscale has the structure of a Lévy distribution, is strongly nonlocal, nondiffusive, scale-free, and avalanche mediated; at larger scales, we report the observation of a self-organized flow structure which we call the " E × B staircase" after its planetary analog.

Experimental electron temperature gradient dependence of heavy impurity transport in fusion devices

The turbulent impurity (nickel) transport dependence on the normalized electron temperature gradient has been analyzed in sawtooth-free electron cyclotron wave heated Tore Supra plasmas. In the core, our experimental analysis shows that the lower R/L((T)(e)), the lower the nickel diffusion coefficient. The latter decreases until the instability threshold is reached. The experimental threshold is in agreement with the one computed by a gyrokinetic model. Further out, R/L((T)(e)) plays no role in the impurity diffusion. This set of experimental results is consistent with a quasilinear gyrokinetic analysis.

Reversal of impurity pinch velocity in tokamaks plasma with a reversed magnetic shear configuration

Impurity transport in tokamak core plasmas is investigated with a three-dimensional fluid global code. It is shown that, in the presence of an internal transport barrier (ITB) created by a reversed magnetic shear configuration, one can obtain a reversal of the impurity pinch velocity which can change from the inward direction to the outward direction. This scenario is favorable for expelling impurities from the central region and decontaminating the core plasma. The mechanism of pinch reversal is attributed to a change of direction of the curvature pinch and to a modification of the dominant underlying instability caused by a change of the gradient of the ion temperature and consequently of the ITB formation.

Universal probability distribution function for bursty transport in plasma turbulence

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.

Nonlinear dynamics of magnetic islands imbedded in small-scale turbulence

The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the tearing instability are controlled by the properties of the pressure gradient. In these regimes, the interplay between the pressure and the magnetic flux determines the dynamics of the saturated state. A secondary instability can occur and strongly modify the magnetic island dynamics by triggering a poloidal rotation. It is shown that the complex nonlinear interaction between the islands and turbulence is nonlocal and involves small scales.

Interplay between gyrokinetic turbulence, flows, and collisions: perspectives on transport and poloidal rotation

The impact of ion-ion collisions on confinement is investigated with the full-f and global gyrokinetic Gysela code through a series of nonlinear turbulence simulations for tokamak parameters. A twofold scan in the turbulence drive and in collisionality is performed, highlighting (i) a heat transport expressed in terms of critical quantities-threshold and exponent, (ii) a first evidence of turbulent generation of poloidal momentum, and (iii) the dominance of mean flow shear, mediated through the turbulent corrugation of the mean profiles, with regard to the oft-invoked zonal flow shear.

Wave-number spectrum of drift-wave turbulence

A simple model for the evolution of turbulence fluctuation spectra, which includes neighboring interactions leading to the usual dual cascade as well as disparate scale interactions corresponding to refraction by large scale structures, is derived. The model recovers the usual Kraichnan-Kolmogorov picture in the case of exclusively local interactions and midrange drive. On the other hand, when disparate scale interactions are dominant, a simple spectrum for the density fluctuations of the form |nk|2 proportional to k(-3)/(1+k2)2 is obtained. This simple prediction is then compared to, and found to be in fair agreement with, Tore Supra CO2 laser scattering data.

Role of plasma elongation on turbulent transport in magnetically confined plasmas

The theoretical study of plasma turbulence is of central importance to fusion research. Experimental evidence indicates that the confinement time results mainly from the turbulent transport of energy, the magnitude of which depends on the turbulent state resulting from nonlinear saturation mechanisms, in particular, the self-generation of coherent macroscopic structures and large scale flows. Plasma geometry has a strong impact on the structure and magnitude of these flows and also modifies the mode linear growth rates. Nonlinear global gyrokinetic simulations in realistic tokamak magnetohydrodynamic equilibria show how plasma shape can control the turbulent transport. Results are best described in terms of an effective temperature gradient. With increasing plasma elongation, the nonlinear critical effective gradient is not modified while the stiffness of transport is decreasing.

Turbulence in the TORE SUPRA tokamak: measurements and validation of nonlinear simulations

Turbulence measurements in TORE SUPRA tokamak plasmas have been quantitatively compared to predictions by nonlinear gyrokinetic simulations. For the first time, numerical results simultaneously match within experimental uncertainty (a) the magnitude of effective heat diffusivity, (b) rms values of density fluctuations, and (c) wave-number spectra in both the directions perpendicular to the magnetic field. Moreover, the nonlinear simulations help to revise as an instrumental effect the apparent experimental evidence of strong turbulence anisotropy at spatial scales of the order of ion-sound Larmor radius.

Redistribution of suprathermal electrons due to fishbone frequency jumps

MHD instabilities driven by fast electrons identified as fishbonelike modes have been detected on Tore Supra during lower hybrid current drive discharges. Direct experimental evidence is reported of a novel feature: the regular redistribution of suprathermal electrons toward external tokamak regions which are correlated to periodic mode frequency jumps. Sharp drops of the electron temperature time trace are factually linked to the cyclical deterioration of the fast electron confinement.

Control of transport-barrier relaxations by resonant magnetic perturbations

Transport-barrier relaxation oscillations in the presence of resonant magnetic perturbations are investigated using three-dimensional global fluid turbulence simulations from first principles at the edge of a tokamak. It is shown that resonant magnetic perturbations have a stabilizing effect on these relaxation oscillations and that this effect is due mainly to a modification of the pressure profile linked to the presence of both residual magnetic island chains and a stochastic layer.

Evidence from numerical simulations of transport-barrier relaxations in tokamak edge plasmas in the presence of electromagnetic fluctuations

The dynamics of transport barriers in fusion plasmas is studied in the presence of electromagnetic fluctuations. The work is based on numerical simulations using a new three-dimensional electromagnetic fluid turbulence code (EMEDGE3D). In these simulations, the transport-barrier exhibits intermittent relaxation cycles. It is found that magnetic fluctuations have a negligible influence on the relaxation process while the magnetic activity is enhanced during these relaxations, in agreement with experimental observations.

Geodesic plasma compressibility effects on the magnetic islands in a tokamak

It is shown that the stability of rotating magnetic islands in a tokamak plasma is affected by plasma compressibility related to the geodesic curvature in an inhomogeneous magnetic field. A robust contribution has been found to the Rutherford evolution equation. It is shown that the sign of the geodesic curvature contribution is opposite to the sign of the polarization term. It is suggested that this mechanism plays a crucial role in the stability of small scale magnetic islands.

Probing internal transport barriers with heat pulses in JET

The first electron temperature modulation experiments in plasmas characterized by strong and long-lasting electron and ion internal transport barriers (ITB) have been performed in JET using ion cyclotron resonance heating in mode conversion scheme. The ITB is shown to be a well localized narrow layer with low heat diffusivity, characterized by subcritical transport and loss of stiffness. In addition, results from cold pulse propagation experiments suggest a second order transition process for ITB formation.

Nonlinear dynamics of transport barrier relaxations in tokamak edge plasmas

A new mechanism for intermittent relaxations of transport barriers is found by using three dimensional fluid turbulence simulations. This mechanism is generic since it only requires a stationary E x B shear flow. It is found here that if the flow shear increases faster than linearly with heating power, the relaxation frequency decreases with power. An analytical study reveals that this nonlinear dynamics is governed by a time delay for effective velocity shear stabilization.

Parametric dependence of turbulent particle transport in tore supra plasmas

Steady state full noninductive current tore supra plasmas offer a unique opportunity to study the local parametric dependence of particle pinch velocity, in order to discriminate among different theories. Magnetic field shear is found to generate an inward pinch which is dominant in the gradient region (normalized radius 0.3</=r/a</=0.6). In contrast, the direction of the pinch in the plasma core (r/a</=0.3) is correlated with the electron temperature gradient length. The results are in agreement with both the turbulent theoretical and computational predictions.

New tokamak plasma regime with stationary temperature oscillations

During noninductively driven discharges in the Tore Supra tokamak, steady sinusoidal oscillations of the central electron temperature, lasting as long as 2 min, have been observed for the first time. Having no helical structure, they cannot be ascribed to any known MHD instability. The most plausible explanation of this new phenomenon is that the plasma current density and the electron temperature evolve as a nonlinearly coupled predator-prey system. This interpretation is supported by the numerical solution of coupled resistive current diffusion and heat transport equations.

Turbulent particle transport in magnetized plasmas

Particle transport in magnetized plasmas is investigated with a fluid model of drift wave turbulence. An analytical calculation shows that magnetic field curvature and thermodiffusion drive an anomalous pinch. The curvature driven pinch velocity is consistent with the prediction of turbulence equipartition theory. The thermodiffusion flux is found to be directed inward for a small ratio of electron to ion pressure gradient, and it reverses its sign when increasing this ratio. Numerical simulations confirm that a turbulent particle pinch exists. It is mainly driven by curvature for equal ion and electron heat sources. The sign and relative weights of the curvature and thermodiffusion pinches are consistent with the analytical calculation.

Particle pinch with fully noninductive lower hybrid current drive in Tore Supra

Recently, plasmas exceeding 4 min have been obtained with lower hybrid current drive (LHCD) in Tore Supra. These LHCD plasmas extend for over 80 times the resistive current diffusion time with zero loop voltage. Under such unique conditions the neoclassical particle pinch driven by the toroidal electric field vanishes. Nevertheless, the density profile remains peaked for more than 4 min. For the first time, the existence of an inward particle pinch in steady-state plasma without toroidal electric field, much larger than the value predicted by the collisional neoclassical theory, is experimentally demonstrated.

Transport reduction by rotation shear in tokamak-edge turbulence

Effects of externally imposed and self-generated poloidal flows on turbulent transport in the edge region of a tokamak are investigated using 3D nonlinear global simulations of resistive pressure-gradient-driven turbulence. Transport reduction is found to be due to synergetic changes in the fluctuation amplitude and in the dephasing of the fluctuations. A scaling of the fluctuation level and turbulent diffusivity with E x B flow shear strength is deduced from these simulations. These scalings agree with recent experimental observations on edge biasing as well as with analytical models.

Discharges in the JET tokamak where the safety factor profile is identified as the critical factor for triggering internal transport barriers

Joint European Torus discharges which demonstrate the critical role the safety factor profile, q, can play in the formation of internal transport barriers (ITB) are examined. In these discharges, the target parameters, including the E x B flows, were kept virtually the same, except for the q profile. In a discharge with a nonmonotonic q, an ITB was triggered whereas a discharge with monotone q made no such transition. Thus, there is strong evidence that the q profile was the critical factor for the triggering of an ITB. Possible interpretations of this finding are discussed.

Experimental determination of critical threshold in electron transport on Tore Supra

In Tore Supra plasmas with fast wave electron heating, a critical threshold in the electron temperature gradient (inverted DeltaT(e)) is clearly observed, i.e., a finite value of inverted DeltaT(e) for which the turbulent heat diffusivity vanishes. The radial profile of this critical gradient is experimentally determined from a set of discharges characterized by similar plasma parameters with fast wave powers ranging from 0.75 to 7.4 MW. The dependence of the electron heat flux on the gradient length is found to be offset linearly. The offset term increases linearly with the ratio of the local magnetic shear to the safety factor.

Nondiffusive transport in tokamaks: three-dimensional structure of bursts and the role of zonal flows

Large scale transport events are studied in simulations of resistive ballooning turbulence in a tokamak plasma. The spatial structure of the turbulent flux is analyzed, indicating radially elongated structures (streamers) at the low field side which are distorted by magnetic shear at different toroidal positions. The interplay between self-generated zonal flows and transport events is investigated, resulting in significant modifications of the frequency and the amplitude of bursts. The propagation of bursts is studied in the presence of a transport barrier generated by a strong shear flow.

Internal transport barrier with ion-cyclotron-resonance minority heating on tore supra

Recently, reversed magnetic shear operation was performed using only ion-cyclotron-resonance frequency minority heating (ICRH) during current ramp-up. A wide region of reversed magnetic shear has been obtained. For the first time, an electron internal transport barrier sustained by ICRH is observed, with a dramatical drop of density fluctuations. This barrier was maintained, on the current flat top, for about 2 s.

Proper orthogonal decomposition and galerkin projection for a three-dimensional plasma dynamical system

A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of shear flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.