Pullback Transformations in Gyrokinetic Theory Page: 4 of 36
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Most of the interesting plasmas in laboratory and space are magnetized. The particle's
motion in a magnetized equilibrium plasma consists of fast gyromotion and slow guiding
center motion. It is the fast gyromotion which restricts the allowable time step in particle
simulations of the associated dynamics in the laboratory phase space coordinate frame. In
the past twenty years, gyrokinetic theory has been developed to remove the fast gyromotion
from the kinetic system for low frequency and long parallel wavelength phenomena [1-13].
Gyrokinetic particle simulations, which use a much larger time step than the time scale of
gyromotion [4, 14-20], have been successfully applied in studies of the transport problems
of fusion plasmas. In particular, gyrokinetic theory offers a simplified version of the Vlasov-
Maxwell system by utilizing the fact that in strongly magnetized plasmas the particle's
gyroradius is much smaller than the scale length of the magnetic field: EB P/LB 1,
where LB - B/VB . More fundamentally, gyrokinetic theory requires the construction of
a gyrocenter coordinate system in which the particle's gyromotion is decoupled from the
rest of the particle dynamics. The Vlasov-Maxwell equation system can then be derived in
this special coordinate system [21-26]. Guiding center coordinates are employed in the mag-
netostatic case, while gyrocenter coordinates are employed when there are electromagnetic
perturbations in the system. Modern gyrokinetic theory [9-13, 21-26] utilizing non-canonical
Hamiltonian and phase space Lie perturbation method [1-3] has been carefully established
over a number of years. It not only sets up a rigorous and systematic foundation for the
gyrokinetic framework, but also clarifies numerous confusing concepts and introduces much
more physics content into the theory. For example, gyrokinetic theory has been extended to
arbitrary frequency, arbitrary wavelength, electromagnetic perturbations in general geome-
One of the key components of modern gyrokinetic theory is the pullback transformation
of the distribution function. This is responsible for many important physics properties in
gyrokinetic theory. Famous examples include the polarization drift density in the gyrokinetic
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Qin, H. & Tang, W.M. Pullback Transformations in Gyrokinetic Theory, report, January 21, 2003; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc740903/m1/4/: accessed April 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.