A linearized multi-species collision operator valid for arbitrary masses and charges has been developed and implemented in the gyrokinetic code GYSELA (Grandgirard et al., 2016) [1]. This operator has all the required properties: it conserves particles, total momentum and energy, fulfills the Boltzmann H theorem and recovers neoclassical results. This operator takes into account both pitch angle scattering and energy diffusion while operating in the (nu(parallel to), mu) phase space. Derivatives with respect to the magnetic moment are treated using a projection on a set of orthogonal polynomials. The numerical aspects of the implementation are detailed and a set of physical benchmarks allows a verification of the properties of the operator. (C) 2018 Elsevier B.V. All rights reserved.

We quantify the contribution of kinetic electrons to GAM damping. This contribution is not negligible due to a resonance between barely trapped/passing electrons bounce/transit frequency and the mode pulsation.

Trace impurity transport is studied with the flux-driven gyrokinetic GYSELA code (Grandgirard et al 2016 Comput. Phys. Commun. 207 35). A reduced and linearized multi-species collision operator has been recently implemented, so that both neoclassical and turbulent transport channels can be treated self-consistently on an equal footing. In the Pfirsch–Schlüter regime that is probably relevant for tungsten, the standard expression for the neoclassical impurity flux is shown to be recovered from gyrokinetics with the employed collision operator. Purely neoclassical simulations of deuterium plasma with trace impurities of helium, carbon and tungsten lead to impurity diffusion coefficients, inward pinch velocities due to density peaking, and thermo-diffusion terms which quantitatively agree with neoclassical predictions and NEO simulations (Belli et al 2012 Plasma Phys. Control. Fusion 54 015015). The thermal screening factor appears to be less than predicted analytically in the Pfirsch–Schlüter regime, which can be detrimental to fusion performance. Finally, self-consistent nonlinear simulations have revealed that the tungsten impurity flux is not the sum of turbulent and neoclassical fluxes computed separately, as is usually assumed. The synergy partly results from the turbulence-driven in–out poloidal asymmetry of tungsten density. This result suggests the need for self-consistent simulations of impurity transport, i.e. including both turbulence and neoclassical physics, in view of quantitative predictions for ITER.

When a steady-state cylindrical plasma discharge is centrally fuelled, the collisionless radial electron flux is canonically coupled to an axial current. The identification and analysis of this transport driven current, previously reported in collisionless simulations [W. J. Nunan and J. M. Dawson, Phys. Rev. Lett. $\mathbf{73}$, 1628 (1994)], is addressed analytically and extended to the collisional regime by means of first-principles kinetic models. Collisionless radial transport is described with the standard quasilinear model and collisional velocity anisotropy relaxation with the Landau kinetic equation. When trapped particles corrections are taken into account, the solution of this kinetic model provides the analytical expression for the transport driven current in a centrally fuelled steady-state tokamak as a function of the thermonuclear power and discharge parameters. For ITER type discharges, with central fuelling, a current of about one mega-ampere is predicted by this first-principles analytical kinetic model.

Core fusion plasmas are almost collisionless as the plasma density and temperature in the core of fusion devices are extremely small and high, respectively. Nevertheless, accounting for collisions remains essential for three main reasons. First, to a large extent, collisions govern the level of large scale flows – both the mean ion poloidal flow and turbulence-driven zonal flows – via the friction on trapped particles. Second, neoclassical transport can reveal dominant (or at least competitive) with respect to turbulent transport in certain regimes such as transport barriers, or for certain classes of particles such as heavy impurities like tungsten. Third, and more fundamentally, collisions ensure the relaxation of the distribution function towards a Maxwellian. In turn, they are critical for gyrokinetic simulations since they smooth out small scale structures in velocity space, contributing to numerical stability.

Two full-F global gyrokinetic codes are benchmarked to compute flux-driven ion temperature gradient (ITG) turbulence in tokamak plasmas. For this purpose, the Semi-Lagrangian code GYrokinetic SEmi-LAgrangian and the Eulerian code GT5D are employed, which solve the full-F gyrokinetic equation with a realistic fixed flux condition. The equilibrium poloidal flow profile formation processes are benchmarked and compared against the local neoclassical theory. The simulations above are carried out without turbulence, which agree well with each other and with the theoretical estimates. Here, a lot of attention has been paid to the boundary conditions, which have huge impacts on the global shape of radial electric field. The behaviors of micro-instabilities are benchmarked for linear and nonlinear cases without a heat source, where we found good agreements in the linear growth rates and nonlinear critical gradient level. In the nonlinear case, initial conditions are chosen to be identical since they dominate the transient turbulence behavior. Using the appropriate settings for the boundary and initial conditions obtained in the benchmarks above, a flux-driven ITG turbulence simulation is carried out. The avalanche-like transport is assessed with a focus on spatio-temporal properties. A statistical analysis is performed to discuss this self-organized criticality (SOC) like behaviors, where we found a 1/f spectra and a transition to 1/f3 spectra at high-frequency side in both codes. Based on these benchmarks, it is verified that the SOC-like behavior is robust and not dependent on numerics.

Radial fluxes of parallel momentum due to E x B and magnetic drifts are shown to be correlated in tokamak plasmas. This correlation comes from the onset of poloidal convective cells generated by turbulence. The entire process requires a symmetry breaking mechanism, e.g. a mean shear flow. An analytical calculation shows that anti-correlation between the poloidal and parallel components of the turbulent Reynolds stress results in anti-correlation of the fluxes of parallel momentum generated by E x B and curvature drifts.

The linear properties of the geodesic acoustic modes (GAMs) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, and safety factor), electro-magnetic effects, collisions, and the presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the Lagrangian (particlein-cell) code ORB5, the Eulerian code GENE, and semi-Lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.

A connection is established between two classical problems: the non linear saturation of a bump-on tail instability in collisionless regime, and the decay of a zonal flow towards a finite amplitude residual. Reasons for this connection are given and commented.

In tokamak plasmas, the radial transport of matter and energy, governed by collisions and turbulence, is intrinsically multi scales. While neoclassical transport results from stationary large scale structures, namely static (m,n) = (1,0) modes (m,n = poloidal, toroidal Fourier wave numbers), turbulence develops fluctuating small scale modes m,n 1. On the basis of this scale separation, it is usually assumed that both contributions are additive. In turn, these two transport channels are modeled with different dedicated codes. One of the key questions is whether this assumption is valid, or whether neoclassical and turbulent transports exhibit synergistic effects. We address this fundamental issue through the study of the transport of impurities, acting as passive scalars. Predicting impurity concentration is important for ITER, where tungsten particles coming from the divertor could lead to prohibitive radiative losses [1] and impact dramatically plasma performance and stability. Actually, on-axis accumulation of tungsten has been widely observed in tokamaks. While the very core impurity peaking is generally attributed to neoclassical effects [2], turbulent transport could well dominate in the gradient region [3]. We report here for the first time on self-consistent simulations of both transports by means of full-f and flux-driven gyrokinetic simulations, and present clear evidences of a neoclassical-turbulence synergy for impurity transport. It likely originates from the turbulence driven poloidal asymmetries, which depart from neoclassical expectations.

Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation.