T. Vernay

Complete multi-field characterization of the geodesic acoustic mode in the TCV tokamak

The geodesic acoustic mode (GAM) is a coherently oscillating zonal flow that may regulate turbulence in toroidal plasmas. Uniquely, the complete poloidal and toroidal structure of the magnetic component of the turbulence-driven GAM has been mapped in the TCV tokamak. Radially localized measurements of the fluctuating density, ECE radiative temperature and poloidal flow show that the GAM is a fully coherent, radially propagating wave. These observations are consistent with electrostatic, gyrokinetic simulations.

Gyrokinetic simulations of turbulent transport: size scaling and chaotic behaviour

Important steps towards the understanding of turbulent transport have been made with the development of the gyrokinetic framework for describing turbulence and with the emergence of numerical codes able to solve the set of gyrokinetic equations. This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. Solving 5D gyrokinetic equations requires state-of-the-art high performance computing techniques involving massively parallel computers and parallel scalable algorithms. The various numerical schemes that have been explored until now, Lagrangian, Eulerian and semi-Lagrangian, each have their advantages and drawbacks. A past controversy regarding the finite size effect (finite ρ∗) in ITG turbulence has now been resolved. It has triggered an intensive benchmarking effort and careful examination of the convergence properties of the different numerical approaches. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the ρ∗ → 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary: inconsistent approximations that are sometimes used can lead to important discrepancies. Turbulent processes are characterized by a chaotic behaviour, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation. Further developments

Neoclassical equilibria as starting point for global gyrokinetic microturbulence simulations

The implementation of linearized operators describing inter- and like-species collisions in the global gyrokinetic particle-in-cell code ORB5 [ S. Jolliet, Comput. Phys. Commun. 177, 409 (2007) ] is presented. A neoclassical axisymmetric equilibrium with self-consistent electric field can be obtained with no assumption made on the radial width of the particle trajectories. The formulation thus makes it possible to study collisional transport in regions where the neoclassical approximation breaks down such as near the magnetic axis. The numerical model is validated against both analytical results as well as other simulation codes. The effects of the poloidally asymmetric Fourier modes of the electric field are discussed, and the contribution of collisional kinetic electrons is studied. In view of subsequent gyrokinetic simulations of turbulence started from a neoclassical equilibrium, the problem of numerical noise inherent to the particle-in-cell approach is addressed. A novel algorithm for collisional gyrokinetic simulation switching between a local and a canonical Maxwellian background for, respectively, carrying out the collisional and collisionless dynamics is proposed, and its beneficial effects together with a coarse graining procedure [ Y. Chen and S. E. Parker, Phys. Plasmas 14, 082301 (2007) ] on noise and weight spreading reduction are discussed.

Interaction of large scale flow structures with gyrokinetic turbulence

Shear flows have a profound influence on turbulence-driven transport in tokamaks. The introduction of arbitrary initial flow profiles into the code ORB5 [Jolliet et al., Comput. Phys. Commun. 177, 409 (2007)] allows the convenient study of how flows on all length scales both influence transport levels and self-consistently evolve. A formulation is presented which preserves the canonical structure of the background particle distribution when either toroidal or poloidal flows are introduced. Turbulence suppression is possible above a certain shearing rate magnitude for homogeneous shear flows, and little evolution of the shearing rate is seen. However, when a flow with a zone boundary, where the shearing rate reverses at mid-radius, is introduced, the shear flow evolves substantially during the simulation. E × B shear flows with a zone boundary of a positive sign decay to a saturation amplitude, consistent with the well known saturation of turbulently generated zonal flows. Unlike the E × B flow, the parall...

Synergy between ion temperature gradient turbulence and neoclassical processes in global gyrokinetic particle-in-cell simulations

Based on the CYCLONE case, simulations of collisional electrostatic ion temperature gradient (ITG) microturbulence carried out with the global gyrokinetic particle-in-cell (PIC) code ORB5 are presented. Considering adiabatic electrons, an increase in ion heat transport over the collisionless turbulent case due to ion-ion collisions is found to exceed the neoclassical contribution. This synergetic effect is due to interaction of collisions, turbulence, and zonal flows. When going from a collisionless to a collisional ITG turbulence simulation, a moderate reduction of the average zonal flow level is observed. The collisional zonal flow level turns out to be roughly independent of the finite collisionality considered. The Dimits shift softening by collisions [Z. Lin et al., Phys. Rev. Lett. 83, 3645 (1999)] is further characterized, and the shearing rate saturation mechanism is emphasized. Turbulence simulations start from a neoclassical equilibrium [T. Vernay et al., Phys. Plasmas 17, 122301 (2010)] and are...

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.

Global gyrokinetic simulations of TEM microturbulence

Global gyrokinetic simulations of electrostatic temperature-gradient-driven trapped-electron-mode (TEM) turbulence using the δf particle-in-cell code ORB5 are presented. The electron response is either fully kinetic or hybrid, i.e. considering kinetic trapped and adiabatic passing electrons. A linear benchmark in the TEM regime against the Eulerian-based code GENE is presented. Two different methods for controlling the numerical noise, based, respectively, on a Krook operator and a so-called coarse-graining approach, are discussed and successfully compared. Both linear and non-linear studies are carried out for addressing the issue of finite-ρ*-effects and finite electron collisionality on TEM turbulence. Electron collisions are found to damp TEMs through the detrapping process, while finite-ρ*-effects turn out to be important in the non-linear regime but very small in the linear regime. Finally, the effects of zonal flows on TEM turbulence are briefly considered as well and shown to be unimportant in the temperature-gradient-driven TEM regime. Consistently, basically no difference is found between linear and non-linear critical electron temperature gradients in the TEM regime.

Gyrokinetic transport relations for gyroscale turbulence

We derive explicit local transport relations for the global gyrokinetic formalism at arbitrary wavelength. This is an extension of the analysis in Scott et. al. 2010 where this was examined in the long-wavelength limit. Deriving a local expression for the fluxes requires that the gyroaveraging operator is symmetric, so that if point B is on the gyroring around A, point A is on the gyroring around B, for the same value of the magnetic moment. An algorithm for constructing a symmetric gyroring in a global code is described. Finally, using a simple 2D gyrokinetic code, we demonstrate the application of the momentum transport relation in a model problem with the full gyroaveraging operator without any long-wavelength approximation.

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.

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.