A magnetic fusion plasma is a hot gas of ionized ions and electrons confined by a closed magnetic field that winds around toroidal surfaces. Just like all laboratory plasmas, it is ultimately intertwined with its solid boundaries, or walls. A thin region of plasma right next to the wall develops a large electric field that reduces the overall electron outflow to preserve plasma quasineutrality. Far from the wall, we strive to achieve good enough energy confinement in the plasma core to make fusion reactions there self-sustaining (a burning plasma). One of the main obstacles to reaching such a state is the turbulent transport associated to microturbulence. This is successfully described and simulated within the framework of a kinetic theory, called gyrokinetics, which is averaged over the Larmor orbits of charged particles. Turbulence in the edge region has emerged as crucial in determining the overall confinement in the device, and it is ultimately the wall that sets the boundary conditions to gyrokinetic codes simulating the edge. Yet, the fundamental underlying approximation of gyrokinetics, that the ion motion is quasi-periodic and circular, fails in a region near the wall, known as the magnetic presheath, whose width is several ion Larmor radii. Here, the electric field directed towards the target is so large and inhomogeneous that it distorts ion gyro-orbits to non-circular and causes strong sheared ExB flows tangential to the target. Closer to the target, the electric field increases sharply over another smaller length scale, the Debye length, over which the plasma becomes non-neutral in a thinner region called the Debye sheath. I will present a theoretical framework and a numerical scheme that allow to iteratively obtain fast numerical solutions of the steady state of both these regions for shallow magnetic field incidence at the wall, relevant to fusion devices. Examples of outputs of the code that can provide refined boundary conditions to gyrokinetic codes used to simulate fusion devices are shown, such as the ion and electron distribution functions reaching the target, current-potential relations and electron heat flux. I will also present a new promising steady-state PIC-like scheme, currently under development at EPFL, that will simulate the region near the wall for general magnetic field angle, thus allowing the simulation of a much wider range of systems.
Laboratory for Simulation and Modeling