J. Abiteboul

An overview of intrinsic torque and momentum transport bifurcations in toroidal plasmas

An overview of the physics of intrinsic torque is presented, with special emphasis on the phenomenology of intrinsic toroidal rotation in tokamaks, its theoretical understanding, and the variety of momentum transport bifurcation dynamics. Ohmic reversals and electron cyclotron heating-driven counter torque are discussed in some detail. Symmetry breaking by lower single null versus upper single null asymmetry is related to the origin of intrinsic torque at the separatrix. (Some figures may appear in colour only in the online journal)

Large scale dynamics in flux driven gyrokinetic turbulence

The turbulent transport governed by the toroidal ion temperature gradient driven instability is analysed with the full-f global gyrokinetic code GYSELA (Grandgirard et al 2007 Plasma Phys. Control. Fusion 49 B173) when the system is driven by a prescribed heat source. Weak, yet finite, collisionality governs a neoclassical ion heat flux that can compete with the turbulent driven transport. In turn, the ratio of turbulent to neoclassical transport increases with the source magnitude, resulting in the degradation of confinement with additional power. The turbulent flux exhibits avalanche-like events, characterized by intermittent outbursts which propagate ballistically roughly at the diamagnetic velocity. Locally, the temperature gradient can drop well below the linear stability threshold. Large outbursts are found to correlate with streamer-like structures of the convection cells albeit their Fourier spectrum departs significantly from that of the most unstable linear modes. Last, the poloidal rotation of turbulent eddies is essentially governed by the radial electric field at moderate density gradient.

Conservation equations and calculation of mean flows in gyrokinetics

Conservation equations are derived for the gyrocenter toroidal momentum density and the polarization field. These equations are derived from the gyrokinetic model as it is implemented in simulation codes. In view of predicting the toroidal rotation in future fusion devices such as ITER, where external momentum input will be small, accurate simulations of momentum transport are crucial. The evolution equation for gyrocenter toroidal momentum density involves the divergence of the off-diagonal components of the Reynolds and generalized Maxwell stress, while the source term is the radial current of gyrocenters. The time evolution of the polarization field is the opposite of the gyrocenter current. Hence, an evolution equation for the total momentum density, i.e., the sum of gyrocenter and polarization field toroidal momentum density can be written. The force balance equation and the toroidal momentum conservation equations have been numerically tested with the gysela code. They are satisfied with a high leve...

Physics of intrinsic rotation in flux-driven ITG turbulence

Global, heat flux-driven ITG gyrokinetic simulations which manifest the formation of macroscopic, mean toroidal flow profiles with peak thermal Mach number 0.05, are reported. Both a particle-in-cell (XGC1p) and a semi-Lagrangian (GYSELA) approach are utilized without a priori assumptions of scale separation between turbulence and mean fields. Flux-driven ITG simulations with different edge flow boundary conditions show in both approaches the development of net unidirectional intrinsic rotation in the co-current direction. Intrinsic torque is shown to scale approximately linearly with the inverse scale length of the ion temperature gradient. External momentum input is shown to effectively cancel the intrinsic rotation profile, thus confirming the existence of a local residual stress and intrinsic torque. Fluctuation intensity, intrinsic torque and mean flow are demonstrated to develop inwards from the boundary. The measured correlations between residual stress and two fluctuation spectrum symmetry breakers, namely E × B shear and intensity gradient, are similar. Avalanches of (positive) heat flux, which propagate either outwards or inwards, are correlated with avalanches of (negative) parallel momentum flux, so that outward transport of heat and inward transport of parallel momentum are correlated and mediated by avalanches. The probability distribution functions of the outward heat flux and the inward momentum flux show strong structural similarity.

A 5D gyrokinetic full-f global semi-lagrangian code for flux-driven ion turbulence simulations

This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic Gysela code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the Gysela code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.

Neoclassical physics in full distribution function gyrokinetics

Treatment of binary Coulomb collisions when the full gyrokinetic distribution function is evolved is discussed here. A spectrum of different collision operators is presented, differing through both the physics that can be addressed and the numerics they are based on. Eulerian-like (semi-Lagrangian) and particle in cell (PIC) (Monte-Carlo) schemes are successfully cross-compared, and a detailed confrontation to neoclassical theory is shown.

Turbulent acceleration and heating in toroidal magnetized plasmas

It is shown that turbulence is responsible for a source of momentum, which cannot be recast as a divergence of a momentum flux. This process is similar to turbulent heating, with similar properties. The sum over all species vanishes up to polarization contributions. Hence, toroidal momentum is transferred from species to species, mediated by turbulence. As for momentum flux, symmetry breaking is needed. Flow shear is investigated as a source of symmetry breaking, leading to a source of momentum proportional to the shear rate. Turbulent acceleration is significant for ion species. It is found that it is proportional to the charge number Z, while turbulent heating scales as Z2/A, where A is the mass number. It is maximum in the edge, where the E × B flow shear rate and turbulence intensity are maximum. When both are large enough, the turbulent torque may overcome the collisional friction between impurities and main ions, thus leading to different toroidal velocities.

Turbulent momentum transport in core tokamak plasmas and penetration of scrape-off layer flows

The turbulent transport of toroidal angular momentum in the core of a tokamak plasma is investigated in global, full-f gyrokinetic simulations, performed with the GYSELA code in the flux-driven regime. During the initial turbulent phase, a front of positive Reynolds stress propagates radially, generating intrinsic toroidal rotation from a vanishing initial profile. This is also accompanied by a propagating front of turbulent heat flux. In the statistical steady-state regime, turbulent transport exhibits large-scale avalanche-like events which are found to transport both heat and momentum, and similar statistical properties are obtained for both fluxes. The impact of scrape-off layer flows is also investigated by modifying the boundary conditions in the simulations. The observed impact is radially localized for L-mode like poloidal profiles of parallel velocity at the edge, while a constant velocity at the edge can modify the core toroidal rotation profile in a large fraction of the radial domain.

Thermodynamics of neoclassical and turbulent transport

A variational principle based on the calculation of the entropy production rate is derived, which covers particle, momentum and heat transport. This principle is used to define proper thermodynamical forces and fluxes. When turbulent parallel wavenumbers are small, and fluctuations are ballooned, it is found that the forces are the gradients of density, velocity and temperature normalized to canonical profiles, which are power laws of the magnetic field. The transport matrix is symmetrical for a given background of fluctuations, i.e. if the dependence of the turbulence intensity on gradients is ignored. Minimization of the entropy production rate implies that the profiles tend to relax towards their canonical values, though these values are never reached simultaneously since they are linearly stable. Also it turns out that parallel and perpendicular canonical temperatures are not the same, so that the equilibrium distribution function relaxes towards a two-temperature Maxwellian. When finite turbulence parallel wavenumbers are accounted for, residual fluxes appear. Forces can be redefined to preserve Onsager symmetry but residual heat and momentum sources remain, which correspond to turbulent heating and momentum transfer.

Interplay between fast ions and turbulence in magnetic fusion plasmas

Evidence for the impact of energetic particles (EPs) on turbulence is given in this paper. Firstly, the excitation of electrostatic instabilities in linear gyrokinetic simulations performed with the global GYSELA code by introducing distribution functions typical of fast ions in tokamak plasmas is presented. The obtained mode is unambiguously characterized as an EGAM, i.e. a geodesic acoustic mode (GAM) excited by EPs. The influence of EGAMs on turbulence and associated transport is then analyzed by implementing a source adapted to the inclusion of fast particle populations in non-linear simulations. This source successfully excites EGAMs in the presence of turbulence, which leads to a drastic reduction of the turbulent transport. However, this reduction is only transient; it is followed by an increase of the turbulent activity, characterized by a complex interaction between the EGAMs and the turbulence. In the subsequent steady-state regime, turbulent transport appears to be modulated at the EGAM frequency.