Search

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), delta f scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-1 line magnetic coordinates and a field-aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Another feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 109 marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests. (c) 2007 Elsevier B.V. All rights reserved.

It is now widely believed that low frequency turbulence developing from smallscale instabilities is responsible for the phenomenon of anomalous transport generally observed in magnetic confinement fusion experiments. The microinstabilities are driven by gradients of equilibrium density, ion and electron temperatures and magnetic field strength. Gyrokinetic theory is based on the Vlasov-Maxwell equations and, consistent with the ordering, averages out the fast particle gyromotion, reducing the phase space from 6 to 5 dimensions. Solving the resulting equations is a non-trivial task. Difficulties are associated with the magnetic confinement geometry, the strong disparities in space and time scales perpendicular and parallel to B, the different time scales of ion and electron dynamics, and the complex nonlinear behaviour of the system. The main numerical methods are briefly presented together with some recent developments and improvements to the basic algorithms. Recent results are shown, with emphasis on the roles of zonal E x B flows, of parallel nonlinearity and of toroidal coupling on the saturation of ion temperature gradient (ITG) driven turbulence in tokamaks.

Flux-driven global gyrokinetic codes are now mature enough to make predictions in terms of turbulence and transport in tokamak plasmas. Some of the recent breakthroughs of three such codes, namely GYSELA, ORB5 and XGC1, are reported and compared wherever appropriate. In all three codes, turbulent transport appears to be mediated by avalanche-like events, for a broad range of ρ* = ρi/a values, ratio of the gyro-radius over the minor radius. Still, the radial correlation length scales with ρi, leading to the gyro-Bohm scaling of the effective transport coefficient below ρ* ≈ 1/300. The possible explanation could be due to the fact that avalanches remain meso-scale due to the interaction with zonal flows, whose characteristic radial wavelength appears to be almost independent of the system size. As a result of the radial corrugation of the turbulence driven zonal and mean flows, the shear of the radial electric field can be significantly underestimated if poloidal rotation is assumed to be governed by the neoclassical theory, especially at low collisionality. Indeed, the turbulence contribution to the poloidal rotation increases when collisionality decreases. Finally, the numerical verification of toroidal momentum balance shows that both neoclassical and turbulent contributions to the Reynolds' stress tensor play the dominant role. The phase space analysis further reveals that barely passing supra-thermal particles mostly contribute to the toroidal flow generation, consistently with quasi-linear predictions.

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.

Drift wave turbulence is known to self-organize to form axisymmetric macroscopic flows. The basic mechanism for macroscopic flow generation is called inverse energy cascade. Essentially, it is an energy transfer from the short wavelengths to the long wavelengths in the turbulent spectrum due to nonlinear interactions. A class of macroscopic flows, the poloidally symmetric zonal flows, is widely recognized as a key constituent in nearly all cases and regimes of microturbulence, also because of the realization that zonal flows are a critical agent of self-regulation for turbulent transport. In tokamaks and other toroidal magnetic confinement systems, axisymmetric flows exist in two branches, a zero frequency branch and a finite frequency branch, named Geodesic Acoustic Modes (GAMs). The finite frequency is due to the geodesic curvature of the magnetic field. There is a growing body of evidence that suggests strong GAM activity in most devices. Theoretical investigation of the GAMs is still an open field of ...

International audience; This paper presents the results obtained with a set of gyrokinetic codes based on a semi-Lagrangian scheme. Several physics issues are addressed, namely, the comparison between fluid and kinetic descriptions, the intermittent behaviour of flux driven turbulence and the role of large scale flows in toroidal ITG turbulence. The question of the initialization of full-F simulations is also discussed.

The mutual interactions of ion temperature gradient (ITG) driven modes, zonal flows and geodesic acoustic modes (GAM) in tokamak plasmas are investigated using a global nonlinear gyrokinetic formulation with totally unconstrained evolution of temperature gradient and profile. A series of numerical simulations with the same initial temperature and density profile specifications is performed using a sequence of ideal MHD equilibria differing only in the value of the total plasma current, in particular with identical magnetic shear profiles and shapes of magnetic surfaces. On top of a bursty or quasi-steady state behaviour the zonal flows oscillate at the GAM frequency. The amplitude of these oscillations increases with the value of the safety factor q, resulting in a less effective suppression of ITG turbulence by zonal flows at a lower plasma current. The turbulence-driven volume-averaged radial heat transport is found to scale inversely with the total plasma current.

Geodesic acoustic mode (GAM) oscillations in tokamak plasmas are known to be sensitive to the value of the safety factor q. Through its linear and nonlinear interactions with ITG turbulence it has recently been shown in direct numerical global simulations that the turbulence driven heat transport is larger when GAM oscilations of large amplitude are present, resulting in an anomalous transport scaling with the inverse plasma current. GAM dispersion relations have been derived for circular, large aspect ratio configurations, and, recently, for helical configurations. Linear simulation results are presented using the global, PIC, finite element codes GYGLES and ORB5 for the GAM frequency, damping rate and Rosenbluth‐Hinton residual zonal flow for a scan in plasma elongation. It is found that CAM frequency slightly decreases, while GAM damping rate and residual zonal flows increase with elongation. Nonlinear ITG simulations using the ORB5 code show that elongation reduces heat transport and that this is related to the plasma current and not q alone.

Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and ExB zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric ExB flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of ExB flows. In addition, a revised delta f scheme is introduced and compared to the standard delta f method. (c) 2006 American Institute of Physics.

Global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence in an ideal MHD ITER equilibrium plasma are performed with the ORB5 code. The noise control and field-aligned Fourier filtering procedures implemented in ORB5 are essential in obtaining numerically healthy results with a reasonable amount of computational effort: typical simulations require 109 grid points, 109 particles and, despite a particle per cell ratio of unity, achieve a signal to noise ratio larger than 50. As compared with a circular concentric configuration with otherwise similar parameters (same ρ* = 1/720), the effective heat diffusivity is considerably reduced for the ITER MHD equilibrium. A self-organized radial structure appears, with long-lived zonal flows (ZF), modulating turbulence heat transport and resulting in a corrugated temperature gradient profile. The ratio of long-lived ZF to the fluctuating ZF is markedly higher for the ITER MHD equilibrium as compared with circular configurations, thereby producing a more effective ITG turbulence suppression, in spite of a higher linear growth rate. As a result, the nonlinear critical temperature gradient, R/LTcrit,NL, is about twice the linear critical temperature gradient, R/LTcrit,lin. Moreover, the heat transport stiffness above the nonlinear threshold is considerably reduced as compared with circular cases. Plasma elongation is probably one of the essential causes of this behaviour: indeed, undamped ZF residual levels and geodesic acoustic mode damping are both increasing with elongation. Other possible causes of the difference, such as magnetic shear profile effects, are also investigated.

Electrons whether adiabatic or non-adiabatic play important role in determining the stability properties of a global electrostatic mode. In the present analysis, the effect of non-adiabaticity of electrons with all its kinetic effects is investigated for ion temperature gradient driven mode in the presence of fast ions using a linear gyro-kinetic code EM-GLOGYSTO-F.

The effect of trapped electrons on the ion temperature gradient ITG mode in a regime where its wavelength is shorter than the conventional ITG mode k Li 1 has been studied. Such a mode propagates in the ion diamagnetic direction with a typical scale length k Li 1 and is termed as the short wavelength ITG SWITG mode. The effect of the trapped electrons on this SWITG mode is investigated, for the first time, using a global and local linear gyrokinetic model. The trapped electrons are observed to destabilize the mode strongly. Comparison of the various parameter scans for the SWITG mode with and without the trapped electrons is presented. One important result obtained is that, while in the absence of the trapped electrons the mode was found to subside with increasing value of n=Ln /R exhibiting the character of a slablike mode, the presence of the trapped electrons has been observed to enhance the n=Ln /R window of the existence of the SWITG mode making the mode more toroidal like. © 2009 American Institute of Physics.

It is believed that low frequency microinstabilities such as ion temperature gradient (ITG) driven modes and trapped electron modes (TEMs) are largely responsible for the experimentally observed anomalous transport via the ion and electron channels in a tokamak. In the present work, a comprehensive global linear gyrokinetic model incorporating fully kinetic (trapped and passing) electrons and ions, actual ion to electron mass ratio, radial coupling, and profile variation is used to investigate the ITG driven modes and pure TEMs. These modes are found to exhibit multiscale structures in the presence of nonadiabatic passing electrons. The multiscale structure is related to the large nonadiabaticity of electrons in the vicinity of mode rational magnetic surfaces and leads to reduced mixing length estimates of transport compared to those obtained from adiabatic electron models.

A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.

In this work, role of nonadiabatic untrapped electrons in the context of a global ion temperature gradient driven mode has been investigated. In past studies, untrapped electrons have been assumed to be able to respond "instantaneously" to a disturbance. It is proposed that such adiabatic electron models should be reexamined for two important reasons: (i) It is known that global modes with n in the range of 3

With the term microinstabilities, we indicate a class of plasma drift waves such as the ion temperature gradient (ITG) mode, the trapped electron mode (TEM), and the electromagnetic Alfvenic ion temperature gradient (AITG) mode. They are usually driven by spatial gradients in the plasma and they are held responsible for anomalous transport and enhanced heat flux in tokamaks. Their understanding is therefore crucial for the development of magnetically confined plasma fusion devices. Our approach is based on the gyrokinetic model (Hahm 1988) for particle dynamics. The gyrokinetic nonlinear Vlasov equation, in the presence of an electromagnetic perturbation (Brizard 1989, 1995), is derived using Lie perturbation theory (Cary and Littlejohn 1983) to average out the fast particle motion around the gyrocenter. We have linearized the gyrokinetic Vlasov equation and added the quasi-neutrality equation and Ampere's law, providing closure to the system. A temporal spectral formulation is used, ensuring the absence of numerical instabilities due to high frequency modes. The equations are simplified with a large aspect ratio approximation for an axisymmetric toroidal configuration. The fields are expanded in a Fourier series in the three spatial directions (radial, poloidal, and toroidal) reducing the problem in a matrix form. The code EM-GLOGYSTO (Brunner et al. 1998; Falchetto et al. 2003; Joint Varenna-Lausanne International Workshop 2002) has been developed to look at its solutions. Recently, we have included in the model an electrostatic equilibrium potential in order to provide E x B sheared flow. The code has been optimized for running in a parallel environment using MPI routines, and it allows us to study frequencies, growth rates, and mode structures of electromagnetic microinstabilities. Results on an AITG mode are shown to illustrate these features.