Based on the drift-reduced Braginskii equations, the Global Braginskii Solver, GBS, is able to model the scrape-off layer (SOL) plasma turbulence in terms of the interplay between the plasma outflow from the tokamak core, the turbulent transport, and the losses at the vessel. Model equations, the GBS numerical algorithm, and GBS simulation results are described. GBS has been first developed to model turbulence in basic plasma physics devices, such as linear and simple magnetized toroidal devices, which contain some of the main elements of SOL turbulence in a simplified setting. In this paper we summarize the findings obtained from the simulation carried out in these configurations and we report the first simulations of SOL turbulence. We also discuss the validation project that has been carried out together with the GBS development.

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), δf 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-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. Anoter 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 10 9 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.

Turbulent transport of toroidal momentum is investigated in global linear gyrokinetic simulations. The poloidal tilt of the global mode structure arising from the radial variation of the equilibrium (profile shearing) is shown to induce non-diagonal non-pinch momentum transport (residual stress). Local simulations performed at finite radial wave vector show that the effect is mainly due to the antisymmetric radial component of the magnetic drift. The residual stress resulting from profile shearing enhances co-current rotation for ion temperature gradient turbulence and counter-current rotation for trapped electron mode turbulence.

The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with Ti≪Te and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v||i, v||e, n, ϕ, Te, and for the vorticity ω=∇⊥2ϕ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.

In the context of gyrokinetic flux-tube simulations of microturbulence in magnetized toroidal plasmas, different treatments of the magnetic equilibrium are examined. Considering the Cyclone DIII-D base case parameter set ͓Dimits et al., Phys. Plasmas 7, 969 ͑2000͔͒, significant differences in the linear growth rates, the linear and nonlinear critical temperature gradients, and the nonlinear ion heat diffusivities are observed between results obtained using either an s-␣ or a magnetohydrodynamic ͑MHD͒ equilibrium. Similar disagreements have been reported previously ͓Redd et al., Phys. Plasmas 6, 1162 ͑1999͔͒. In this paper it is shown that these differences result primarily from the approximation made in the standard implementation of the s-␣ model, in which the straight field line angle is identified to the poloidal angle, leading to inconsistencies of order ͑ = a / R is the inverse aspect ratio, a the minor radius and R the major radius͒. An equilibrium model with concentric, circular flux surfaces and a correct treatment of the straight field line angle gives results very close to those using a finite , low ␤ MHD equilibrium. Such detailed investigation of the equilibrium implementation is of particular interest when comparing flux tube and global codes. It is indeed shown here that previously reported agreements between local and global simulations in fact result from the order inconsistencies in the s-␣ model, coincidentally compensating finite ‫ء‬ effects in the global calculations, where ‫ء‬ = s / a with s the ion sound Larmor radius. True convergence between local and global simulations is finally obtained by correct treatment of the geometry in both cases, and considering the appropriate ‫ء‬ → 0 limit in the latter case.