P. Angelino

A global collisionless PIC code in magnetic coordinates

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.

Long global gyrokinetic simulations: Source terms and particle noise control

In global gyrokinetic simulations it takes a long time for the turbulence to reach a quasisteady state, and quantitative predictions about the quasisteady state turbulence have been difficult to obtain computationally. In particular, global particle-in-cell gyrokinetic simulations have been inefficient for long simulations due to the accumulation of noise. It is demonstrated that a simple Krook operator can effectively control noise; it also introduces an unphysical dissipation, which damps the zonal flows and can significantly affect simulation results even when the relaxation time is very long. However, it is possible to project out the effects of the Krook operator on the zonal flows. This permits noise accumulation to be controlled while preserving the physics of interest; simulations are then run to determine the level of quasisteady state transport and the variation across the ensemble of turbulent dynamics. Convergence is demonstrated both in the number of computational particles and the unphysical relaxation time.

Avalanchelike bursts in global gyrokinetic simulations

Highly variable flux surface averaged heat fluxes are resolved in gyrokinetic simulations of ion temperature gradient (ITG) turbulence, even in large systems. Radially propagating fronts or avalanches are also seen. Their propagation lengths in gyroradii and relative amplitude remain constant as simulation size is increased, so the avalanches appear to result from local dynamics, rather than global relaxation events. For the Cyclone [Dimits et al., Phys. Plasmas 7, 969 (2000)] case, the avalanche propagation direction is found to depend on the sign of the shearing rate. A mechanism for avalanche propagation based on the advection of turbulence tilted by the shear flows is proposed: The Cyclone linear ITG dispersion relation explains the propagation direction of tilted vortices. It also explains why there is no such preferred direction in a simulation with reduced magnetic shear. The paper explores several models for these bursts. First, certain types of models based on nonlinear heat diffusion equations a...

First principles based simulations of instabilities and turbulence

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.

Effects of plasma current on nonlinear interactions of ITG turbulence, zonal flows and geodesic acoustic modes

Reference CRPP-CONF-2005-073Afficher la publication dans Web of Science URL: http://www-fusion-magnetique.cea.fr/eftc11/index.html Notice creee le 2008-05-13, modifiee le 2017-05-12

A method for analysis and design of metabolism using metabolomics data and kinetic models: Application on lipidomics using a novel kinetic model of sphingolipid metabolism

We present a model-based method, designated Inverse Metabolic Control Analysis (IMCA), which can be used in conjunction with classical Metabolic Control Analysis for the analysis and design of cellular metabolism. We demonstrate the capabilities of the method by first developing a comprehensively curated kinetic model of sphingolipid biosynthesis in the yeast Saccharomyces cerevisiae. Next we apply IMCA using the model and integrating lipidomics data. The combinatorial complexity of the synthesis of sphingolipid molecules, along with the operational complexity of the participating enzymes of the pathway, presents an excellent case study for testing the capabilities of the IMCA. The exceptional agreement of the predictions of the method with genome-wide data highlights the importance and value of a comprehensive and consistent engineering approach for the development of such methods and models. Based on the analysis, we identified the class of enzymes regulating the distribution of sphingolipids among species and hydroxylation states, with the D-phospholipase SPO14 being one of the most prominent. The method and the applications presented here can be used for a broader, model-based inverse metabolic engineering approach.

Global gyrokinetic ion temperature gradient turbulence simulations of ITER

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.

Quasisteady and steady states in global gyrokinetic particle-in-cell simulations

Collisionless delta-f gyrokinetic particle-in-cell simulations suffer from the entropy paradox, in which the entropy grows linearly in time while low-order moments are saturated. As a consequence, these simulations do not reach a steady state and are unsuited to make quantitative predictions. A solution to this issue is the introduction of artificial dissipation. The notion of steady state in gyrokinetic simulations is studied by deriving an evolution equation for the fluctuation entropy and applying it to the global collisionless particle-in-cell code ORB5 [S. Jolliet , Comput. Phys. Commun. 177, 409 (2007)]. It is shown that a recently implemented noise-control algorithm [B. F. McMillan , Phys. Plasmas 15, 052308 (2008)] based on a W-stat provides the necessary dissipation to reach a steady state. The two interesting situations of decaying and driven turbulence are considered. In addition, it is shown that a separate heating algorithm, not based on a W-stat, does not lead to a statistical steady state.

Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poissons equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al., (2007) [5]), with a regular (non-field-aligned) mesh

Influence of the parallel nonlinearity on zonal flows and heat transport in global gyrokinetic particle-in-cell simulations

In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino , Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino , Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker , Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Koumlnies , Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino , Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.