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Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results. [ABSTRACT FROM AUTHOR]

A recent series of investigations on ion temperature gradient (ITG) drift instabilities based on multiscale gyrokinetic particle particle simulation have been carried out to address the questions concerning 1) the interactions between the global zonal flow modes and the mesoscale ITG turbulence, 2) the interplay between these instabilities and the resulting profile modifications and 3) the numerical noise issue in long time simulations. This purpose here is to review these results and to use them to shed some light on the question of steady state transport of ITG turbulence. [ABSTRACT FROM AUTHOR]

We use a linearized model of kinetic MHD for the perturbative calculation of growth rates of Alfvén eigenmodes. The numerical model, a code called CAS3D-K, is based on the three-dimensional ideal MHD stability code CAS3D and a numeric solution of the drift kinetic equation which avoids approximations to the magnetic geometry but neglects the drifts of the particles away from the flux surface. The approach is used to discuss stability boundaries in W7-X and W7-AS and considers both, passing and reflected particles. The limits of the applicability of the model will be discussed as well. It will be shown that gyro-kinetic PIC codes offer a very promising way to improve the model. The two-dimensional linear PIC code GYGLES is used to calculate gyro-kinetic counterparts of ideal MHD modes in cylindrical and in tokamak geometry. [ABSTRACT FROM AUTHOR]

The collisionless time evolution of zonal flows in stellarator systems is investigated. An analytical solution of the kinetic and quasineutrality equations describing the residual zonal flow is derived for arbitrary three-dimensional systems without approximations in the magnetic geometry. The theory allows for an arbitrary number of particle species. It has been found that in stellarators the residual zonal flows are not in general steady but oscillate with a certain frequency. This frequency is determined by the speed of the bounce-averaged radial drifts of the particles trapped in the magnetic field and vanishes in tokamaks, where such net drifts are absent. A reduction of the bounce-averaged radial drifts in configurations optimized with respect to neoclassical transport results in a smaller zonal-flow frequency. [ABSTRACT FROM AUTHOR]

A single particle tracking technique for studying nondiffusive transport is implemented in a new particle-in-cell gyrokinetic simulation of the entropy mode in a Z pinch geometry. Radial transport is characterized in terms of the time dependence of the variance of displacements. The vertical zonal flow dynamics of the nonlinear phase of the instability seem to cause subdiffusive transport for ions during the simulation lengths used here. Electrons follow subdiffusive transport, except for later times in the case of the largest gradient, where the transport becomes superdiffusive. The probability distribution of displacements shows a positive skew and long tails relative to the Gaussian distribution for both ions and electrons. [ABSTRACT FROM AUTHOR]

Global linear gyro-kinetic particle-in-cell (PIC) simulations of electromagnetic modes in pinch and tokamak geometries are reported. The Toroidal Alfvén Eigenmode and the Kinetic Ballooning Mode have been simulated. All plasma species have been treated kinetically (i.e. no hybrid fluid-kinetic or reduced-kinetic model has been applied). The main intention of the paper is to demonstrate that the global Alfvén modes can be treated with the gyro-kinetic PIC method. [ABSTRACT FROM AUTHOR]

Conventional neoclassical predictions are successfully recovered within a gyrokinetic framework using a minimal Fokker–Planck collision operator. This operator is shown to accurately describe some essential features of neoclassical theory, namely the neoclassical transport, the poloidal rotation and the linear damping of axisymmetric flows while interestingly preserving a high numerical efficiency. Its form makes it especially adapted to Eulerian or Semi–Lagrangian schemes. [ABSTRACT FROM AUTHOR]

High frequency gyrokinetic (HFGK) algorithm for particle-in-cell (PIC) simulation has been developed based on the gyrocenter-gauge kinetic theory. This new algorithm takes advantage of the separation of gyrocenter and gyrophase motions introduced by the gyrokinetic formalism. The 6D version of the algorithm is equivalent to the direct 6D Lorentz-force simulation in the limit of small gyroradius (compared to the ambient magnetic field). Since the gyrocenter dynamics is slow, one is allowed to use large time step for pushing gyrocenters in the 6D HFGK algorithm, which results in saving in computing time. Using simple electrostatic collisionless system in slab geometry, we perform nonlinear PIC simulation of the ion cyclotron instability and nonlinear ion perpendicular heating dynamics using new 6D HFGK algorithm. Comparisons with a conventional 6D Lorentz-force code are presented. [ABSTRACT FROM AUTHOR]

ITG and ETG turbulence is investigated with the nonlinear global PIC code ORB5. The large variety of numerical schemes and simulations domains used has sometimes lead to important discrepancies in the transport predictions. In order to discuss these disagreements, emphasis must be put on ways to check the numerical accuracy, such as energy conservation and numerical noise measurement. This paper therefore presents benchmarks, new algorithms and a noise diagnostic. After having demonstrated the numerical quality of our simulations, 2 topics are visited: the unclear role of the parallel nonlinearity and the transport level in ETG turbulence, for which predictions differing by one order of magnitude had been made elsewhere. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

The article highlights the importance of gyrokinetic theory in describing the Ion Temperature Gradient instability which may be important for stellarators. Linear simulations which include effects of trapped electrons and electromagnetic perturbations are important for tokamaks. In linear calculations the ballooning formalism or a flux tube is usually employed.

The article studies gyrokinetic global particle-in-cell (PIC) simulations using the method gyrokinetic solver. The article also studies the effect of the trapped electrons on fine-scale tokamak instabilities in the case of reduced mass ratio. The experiment shows that the Ion Temperature Gradient driven (ITG) instability and the Trapped Electron Mode (TEM) explain the fluctuation-driven transport in tokamak plasmas.

Collisionless time evolution of zonal flows in ion and electron temperature gradient turbulence in toroidal plasmas is investigated. The responses of the zonal-flow potential to the initial perturbation and to the turbulence source are determined from the gyrokinetic equations combined with the Poisson equation, A novel gyrofluid model is presented, which properly describes the zonal-flow time evolution and reproduces the same residual zonal-flow levels as predicted by the gyrokinetic model. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]