Pullback Transformations in Gyrokinetic Theory

Qin, H. ; Tang, W.M.

Princeton University. Plasma Physics Laboratory.

关键词: Fibers;    70 Plasma Physics And Fusion Technology;    Kinetics;    Distribution Functions;    Mathematical Physics;   

DOI  :  10.2172/811954
RP-ID  :  PPPL-3772
RP-ID  :  AC02-76CH03073
RP-ID  :  811954

美国|英语

来源: UNT Digital Library

【 摘 要 】

The Pullback transformation of the distribution function is a key component of the gyrokinetic theory. In this paper, a systematic treatment of this subject is presented, and results from applications of the uniform framework developed are reviewed. The focus is on providing a clear exposition of the basic formalism which arises from the existence of three distinct coordinate systems in gyrokinetic theory. The familiar gyrocenter coordinate system, where the gyromotion is decoupled from the rest of particle's dynamics, is non-canonical and non-fabric. On the other hand, Maxwell's equations, which are needed to complete a kinetic system, are initially only defined in the fabric laboratory phase space coordinate system. The pullback transformations provide a rigorous connection between the distribution functions in gyrocenter coordinates and Maxwell's equations in laboratory phase space coordinates. This involves the generalization of the usual moment integrals originally defined on the cotangent fiber of the phase space to the moment integrals on a general 6D symplectic manifold, is shown to be an important step in the proper formulation of gyrokinetic theory. The resultant systematic treatment of the moment integrals enabled by the pullback transformation. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfven wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered.