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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Intermittency effects and the associated multiscaling spectrum of exponents are investigated for impurities advection in tokamak edge plasmas. The two-dimensional Hasagawa-Wakatani model of resistive drift-wave turbulence is used as a paradigm to describe edge tokamak turbulence. Impurities are considered as a passive scalar advected by the plasma turbulent flow. The use of the extended self-similarity technique shows that the structure function relative scaling exponent of impurity density and vorticity follows the She-Leveque model. This confirms the intermittent character of the impurities advection in the turbulent plasma flow and suggests that impurities are advected by vorticity filaments.
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A ratchet-type average velocity is shown to appear for test particles moving in a stochastic potential and a magnetic field that is space dependent. This is a possible explanation for impurity behavior in tokamak plasmas.
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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.
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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.
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A statistical analysis of the advection of passive particles in a flow governed by driven two-dimensional Navier-Stokes equations (Kolmogorov flow) is presented. Different regimes are studied, all corresponding to a chaotic behavior of the flow. The diffusion is found to be strongly asymmetric with a very weak transport perpendicular to the forcing direction. The trajectories of the particles are characterized by the presence of traps and flights. The trapping time distributions show algebraic decrease, and strong anomalous diffusion is observed in transient phases. Different regimes lead to different types of diffusion, i.e., no universal behavior of diffusion is observed, and both time and space properties are needed to define anomalous transport. (c) 2001 American Institute of Physics.
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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.
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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.
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General physical features of the ion particle distribution function in the plasma sheath derived theoretically and observed experimentally are used for describing the dust shielding and charging in the sheath. It is shown that the shielding and charging of dust depend strongly on the degree of anisotropy of the ion distribution function and on the difference in the ion temperatures parallel and antiparallel with respect to the ion flow. Regions of "antishielding" appear both along the ion flow and perpendicular to it. The potential wells can be responsible for the attraction of other dust particles and for the creation of dust aggregates. This effect is related to the change of the sign of the dielectric function in the range of wave vectors corresponding to the strong Landau damping.
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Anomalous transport is investigated near threshold in the standard map. Very long time flights, and a large anomaly in the transport, are shown to be associated with a new form of multi-island structures causing orbit sticking. The phase space structure of these traps, and the exponents of the characteristic long time tails associated with them are determined. In general these structures are very complex, but some cases, consisting of layers of islands, allow simple modeling. (c) 1998 American Institute of Physics.
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We study the dynamics of charged particles in the presence of two electrostatic waves propagating obliquely to an ambient magnetic field. The presence of a second wave makes the problem a two-dimensional and time-dependent one with a complicated phase space behavior. We derive a set of difference equations (maps) for the nonrelativistic particle motion limit and numerically study them to elucidate the various aspects of the phase space dynamics. For the general case of oblique propagation, we observe synergistic effects leading to the lowering of the stochasticity threshold and the concomitant reduction in electric field amplitudes for particle heating applications. These results can be understood in terms of the resonance structures associated with the two waves and we obtain approximate analytic expressions for the thresholds. For the degenerate case of omega(1)=nOmega,omega(2)=mOmega (where omega(1),omega(2) are the frequencies of the two waves, Omega is the cyclotron frequency and n,m are integers) and strictly perpendicular propagation, the problem simplifies to a one-and-one-half-dimensional one. We observe the presence of stochastic webs in this situation. (c) 1996 American Institute of Physics.