Nonlinear Gyrokinetics: A Powerful Tool for the Description of Microturbulence in Magnetized Plasmas
Gyrokinetics is the description of low-frequency dynamics in magnetized plasmas. In magnetic-confinement fusion, it provides the most fundamental basis for numerical simulations of microturbulence; there are astrophysical applications as well. In this tutorial, a sketch of the derivation of the novel dynamical system comprising the nonlinear gyrokinetic (GK) equation (GKE) and the coupled electrostatic GK Poisson equation will be given by using modern Lagrangian and Lie perturbation methods. No background in plasma physics is required in order to appreciate the logical development. The GKE describes the evolution of an ensemble of gyrocenters moving in a weakly inhomogeneous background magnetic field and in the presence of electromagnetic perturbations with wavelength of the order of the ion gyroradius. Gyrocenters move with effective drifts, which may be obtained by an averaging procedure that systematically, order by order, removes gyrophase dependence. To that end, the use of the Lagrangian differential one-form as well as the content and advantages of Lie perturbation theory will be explained. The electromagnetic fields follow via Maxwell's equations from the charge and current density of the particles. Particle and gyrocenter densities differ by an important polarization effect. That is calculated formally by a "pull-back" (a concept from differential geometry) of the gyrocenter distribution to the laboratory coordinate system. A natural truncation then leads to the closed GK dynamical system. Important properties such as GK energy conservation and fluctuation noise will be mentioned briefly, as will the possibility (and diffculties) of deriving nonlinear gyro fluid equations suitable for rapid numerical solution -- although it is probably best to directly simulate the GKE. By the end of the tutorial, students should appreciate the GKE as an extremely powerful tool and will be prepared for later lectures describing its applications to physical problems.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-ACO2-09CH11466
- OSTI ID:
- 989195
- Report Number(s):
- PPPL-4557; TRN: US1007056
- Resource Relation:
- Conference: Turbulent Mixing and Beyond (July 2009)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
CURRENT DENSITY
DIFFERENTIAL GEOMETRY
DISTRIBUTION
ELECTROMAGNETIC FIELDS
ELECTROSTATICS
ENERGY CONSERVATION
FLUCTUATIONS
LAGRANGIAN FUNCTION
MAGNETIC CONFINEMENT
MAGNETIC FIELDS
NUMERICAL SOLUTION
PERTURBATION THEORY
PHYSICS
PLASMA
POISSON EQUATION
POLARIZATION
WAVELENGTHS
Gyrokinetic Equations
Turbulence
Nonlinear Theories