Fully kinetic simulation of coupled plasma and neutral particles in scrape-off layer plasmas of fusion devices

Abstract

Fluid descriptions of plasmas, which are usually applied to a collisional plasma, can only be justified for very small Coulomb Knudsen numbers. However, the scrape-off layer (SOL) plasmas of experimental magnetic confinement fusion devices tend to have operational regimes characterized by a Coulomb Knudsen number around 0.1. In interesting detached regimes of an SOL plasma in a tokamak, when the plasma detaches from the limiters or divertors, this number may increase along with the local plasma gradients. Plasma gradients are also known to increase (and thus drive non-local effects) in inertial confinement fusion. Neutrals, which are being produced owing to plasma recombination at the plasma–divertor interface, may be in a mixed collisional regime as well. Thus simultaneous kinetic treatments of plasma and neutral particles with self-consistent evaluation of boundary conditions at the material walls are required. We present a physical model and a numerical scheme, and discuss results of purely kinetic simulations of plasmas and neutrals for actual conditions in the Alcator C-Mod and Tokamak-de-Varennes experimental tokamaks. Results for both steady-state and transient regimes of SOL plasma flow are presented. Our approach, unlike particle-in-cell and Monte Carlo methods, is free from statistical noise.

Particle simulation of Coulomb collisions: Comparing the methods of Takizuka & Abe and Nanbu

“…A fluid approximation is not valid since the high energy (superthermal) electrons result in a relatively large ratio of the mean free path to the system's characteristic length. A kinetic approach is essential for satisfactory physical modeling and numerical simulations for such plasmas [1]. One feature which distinguishes a plasma from a fluid is that its particles are charged and have long-range Coulomb interactions.…”

Charge Separation and Electric Field at a Cylindrical Plasma Edge

“…The application of the method of characteristics for the numerical solution of the kinetic equations of plasmas and for the guiding center equations has been recently discussed in several publication (see for instance Shoucri, 2008aShoucri, ,c, 2009a. These methods are Eulerian methods which use a computational mesh to discretize the equations on a fixed grid, and have been successfully applied to different important problems in plasma physics involving kinetic equations, such as laser-plasma interaction (Ghizzo et al, 1990, 1992, Strozzi et al, 2006, Shoucri, 2008d, the calculation of an electric field at a plasma edge (Shoucri, 2002, 2008b, 2009b, Shoucri et al, 2000, 2003, 2004, the applications of gyro-kinetic codes to study edge physics problems in plasmas (Manfredi et al, 1996, Shoucri, 2001, Pohn & Shoucri, 2008 and to collisional plasmas (Batishchev et al, 1999). These methods present the great advantage of having a low noise level, and allow accurate results in the low density regions of the phase-space (Shoucri, 2008c).…”

A hybrid kinetic–fluid model for solving the Vlasov–BGK equation

“…This approach was first developed for diffusion equations in [12], and for hydrodynamic equations in [13] and [14]. It bears some similarities with the so-called δf method ( [1,35,7]). Most hybrid kinetic-fluid approaches used so far are based on a domain-decomposition in position space: a fluid model is used except in specific regions where the flow is supposed to be far from equilibrium, and where a kinetic model is used (see [5,27,28] for the gas dynamics context and [6,20,31] for the plasmas or [17] for the semiconductors).…”