PPPL-4040 is available in pdf format (6.8 MB).

Introduction to Gyrokinetic Theory with Applications in Magnetic Confinement Research in Plasma Physics

Author: W.M. Tang

Date of PPPL Report: January 2005

To be published in: Fields Institute Communications

The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics — the research arena from which this formalism was originally developed. It was presented as a component of the "Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations" held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources.

Excellent progress has been made in developing codes for which computer run-time and problem size scale well with the number of processors on massively parallel processors (MPP's). Examples include the effective usage of the full power of multi-teraflop (multi-trillion floating point computations per second) supercomputers to produce three-dimensional, general geometry, nonlinear particle simulations which have accelerated advances in understanding the nature of turbulence self-regulation by zonal flows. These calculations, which typically utilized billions of particles for thousands of time-steps, would not have been possible without access to powerful present-generation MPP computers and the associated diagnostic and visualization capabilities.

In looking towards the future, the current results from advanced simulations provide great encouragement for being able to include increasingly realistic dynamics to enable deeper physics insights into plasmas in both natural and laboratory environments. However, it should be kept in mind that even with access to greatly improved computational hardware and software advances, there will remain limitations to what can be practically achieved. For example, some of the most complex plasma phenomena involving highly transient nonlinear behavior may defy mathematical formulation and be beyond the reach of computational physics.