X. Garbet

Screening of resonant magnetic perturbations by flows in tokamaks

The non-linear reduced four-field RMHD model in cylindrical geometry was extended to include plasma rotation, neoclassical poloidal viscosity and two fluid diamagnetic effects. Interaction of the static resonant magnetic perturbations (RMPs) with the rotating plasmas in tokamaks was studied. The self-consistent evolution of equilibrium electric field due to RMP penetration is taken into account in the model. It is demonstrated that in the pedestal region with steep pressure gradients, mean flows perpendicular to the magnetic field, which includes and electron diamagnetic components plays an essential role in RMP screening by plasma. Generally, the screening effect increases for lower resistivity, stronger rotation and smaller RMP amplitude. Strong screening of central islands was observed limiting RMP penetration to the narrow region near the separatrix. However, at certain plasma parameters and due to the non-linear evolution of the radial electric field produced by RMPs, the rotation can be compensated by electron diamagnetic rotation locally. In this case, RMPs can penetrate and form magnetic islands. Typical plasma parameters and RMPs spectra on DIII-D, JET and ITER were used in modelling examples presented in the paper.

Residual parallel Reynolds stress due to turbulence intensity gradient in tokamak plasmas

A novel mechanism for driving residual stress in tokamak plasmas based on k∥ symmetry breaking by the turbulence intensity gradient is proposed. The physics of this mechanism is explained and its connection to the wave kinetic equation and the wave-momentum flux is described. Applications to the H-mode pedestal in particular to internal transport barriers, are discussed. Also, the effect of heat transport on the momentum flux is discussed.

Fully kinetic description of the linear excitation and nonlinear saturation of fast-ion-driven geodesic acoustic mode instability

We show in this paper that geodesic acoustic modes (GAMs) can be efficiently excited by a population of fast ions even when Landau damping on thermal ions is accounted for. We report in particular fully kinetic calculations of the GAM dispersion relation and its complete solution. Written under a variational form, the quasi-neutrality condition, together with the kinetic Vlasov equation, leads to the density of exchanged energy between particles and the mode. In particular, a linear threshold for the GAMs excitation is derived. Two examples of fast ion distribution have been discussed analytically. It turns out that particles with high perpendicular energy compared to the parallel resonance energy are most responsible for the excitation of the mode. Subsequent numerical simulations of circular plasmas using gysela code have been carried out. In particular, the linear kinetic threshold has been reproduced during the excitation phase, and a nonlinear saturation has been observed. Analysis in the phase space...

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...

Validating a quasi-linear transport model versus nonlinear simulations

In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.

Electromagnetic effects on geodesic acoustic and beta-induced Alfvén eigenmodes

The local kinetic theory of geodesic acoustic modes and beta-induced Alfven eigenmodes is developed. The local dispersion relations are derived in two opposite limits: and , where k0 = (m − nq)/qR, m and n are poloidal and toroidal mode numbers, and is the electron thermal velocity. It is shown that the nature of the (m ± 1, n) sideband oscillations depends on the radial modes width. The localized modes are mostly electrostatic, while the meso-scale modes of the radial width larger than c/(ωpiq) have a strong electromagnetic component. It is shown that the dispersion relations are remarkably similar provided the radial mode width of the principal (m, n) harmonic is sufficiently small.

Neoclassical equilibrium in gyrokinetic simulations

This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.

Fully nonlinear features of the energetic beam-driven instability

The so-called Berk–Breizman model is applied to a cold bulk, weak warm beam, one-dimensional plasma, to investigate the kinetic instability arising from the resonance of a single electrostatic wave with an energetic particle beam. A Vlasov code is developed to solve the initial value problem for the full-f distribution, and the nonlinear evolution is categorized in the whole parameter space as damped, steady-state, periodic, chaotic, or chirping. The saturation level of steady-state solutions and the bifurcation between steady-state and periodic solutions near marginal stability match analytic predictions. The limit of a perturbative numerical approach when the resonant region extends into the bulk is shown. Frequency sweeping is observed, with time-evolution approaching theoretical results. A new method to extract the dissipation rate from frequency diagnostics is proposed. For small collision rates, instabilities are observed in the linearly barely stable region.

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.

On plasma rotation with toroidal magnetic field ripple and no external momentum input

Ripple-induced thermal loss effect on plasma rotation is investigated in a set of Ohmic L-mode plasmas performed in Tore Supra, and comparisons with neoclassical predictions including ripple are performed. Adjusting the size of the plasma, the ripple amplitude has been varied from 0.5% to 5.5% at the plasma boundary, keeping the edge safety factor constant. The toroidal flow dynamics is understood as being likely dominated by turbulence transport driven processes at low ripple amplitude, while the ripple-induced toroidal friction becomes dominant at high ripple. In the latter case, the velocity tends remarkably towards the neoclassical prediction (counter-current rotation). The radial electric field is not affected by the ripple variation and remains well described by its neoclassical prediction. Finally, the poloidal velocity is of the order of the neoclassical prediction at high ripple amplitude, but significantly departs from it at low ripple.