Numerical simulation of magnetic fusion plasmas

Abstract

The review specializes to the modelling of plasmas in a particular type of fusion experiment. namely the tokamak. Simulation is taken to imply the use of a model which involves variation in at least two coordinate directions and is nonlinear, the nonlinearity invariably being of the advective type. Developments in the period 1976-1992 are covered under five main beadings, with particle methods constituting the first. The remaining four concern the solution via mesh-based methods of (1) the Fokker-Planck equation, (2) drift-wave problems, (3) edge models and (4) time-dependent magnetohydrodynamic problems. Care is taken to outline the capabilities of the currently available software. Progress in the design of numerical algorithms for the mesh-based simulations is found to have been incremental rather than revolutionary. In particle simulation, gyrokinetic schemes and the 'Sf' method have been found to give dramatic gains in some circumstances. Many of the newer results obtained withstand comparison with experimental observation, although it has not dways proved possible to reach the extreme conditions found in tokamaks, especially when threedimensional effects are important.

Direct Numerical Simulations of Two-Fluid Plasma Turbulence

“…At this time, the challenge offered by this problem is truly formidable and the present attempt at its solution is one of many approaches [3] reported in the literature. The finer scales ('subgrid turbulence') are modelled phenomenologically.…”

Application of the particle-in-cell method for numerical simulation of sheath plasma

“…As noted in the survey [12], the details of the computational (particle-in-cell) algorithm are not given in [33]. To an even greater degree this applies to the papers [30,31].…”

“…A brief characterization of the "fluid)" codes used for numerical simulation of a sheath tokamak plasma is given in the survey [12]. In Section 6 (fluid models of the edge) of this paper the application of the basic software packages developed since the early 1980's is discussed.…”

Accurate discretization of advection-diffusion equations

“…A small subset of examples are magnetic fusion plasmas [1], cosmic ray streaming [2,3], electrons in weakly ionized gases [4], microemulsions under shear flow [5], chemical kinetics in driven systems [6,7], hydrodynamics and chemotaxis of bacterial colonies [8,9], phase field dynamics in directional solidification [10], and a wide array of tracer diffusion problems (for example [11]). …”