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The pullback transformation of the distribution function is a key component of 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 noncanonical and nonfibered. For the phase space (cotangent bundle T[sup *]M) associated with a configuration space M, a nonfibered coordinate system (X, V) is a coordinate system where X is not necessarily the coordinates for the configuration space M, and V is not necessarily the coordinates for the cotangent fiber T[sub x][sup *]M at each x. On the other hand, Maxwell’s equations, which are needed to complete a kinetic system, are initially only defined in the fibered 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 six-dimensional symplectic manifold. The resultant systematic treatment of the moment integrals enabled by the pullback transformation is shown to be an important step in the proper formulation of gyrokinetic theory. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfvén wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Focuses on a fully kinetic assessment of the stability properties of toroidal drift modes obtained for nonaxisymmetric (stellarator) geometry in the electrostatic limit. Solution of the linearized gyrokinetic equation; Toroidal drift waves destabilized by temperature gradients and/or trapped particle dynamics; Design effort for a quasiaxisymmetric stellarator.

Develops a linear gyrokinetic system for arbitrary wavelength electromagnetic modes. Inclusion of internal kink and drift modes in the system; Investigation of the kinetic magnetohydrodynamics phenomena from the kinetic side; Development on a two-dimensional finite element code in tokamak geometries.

Investigates neoclassical transport in the presence of large ion orbits. Relaxation of the basic neoclassical assumption that the ions orbital excursions are much smaller than the local toroidal minor radius and the equilibrium scale lengths of the system; Development of a general formalism for neoclassical transport theory.

Derives a simplified two-field nonlinear model for collisionless trapped-ion-mode turbulence from nonlinear bounce-averaged drift kinetic equations. Renormalized thermal diffusivity; Bohm-like scaling; Nonlinearity associated with the neoclassical polarization density; Isotope-dependent modification to the Bohm-like diffusivity.

Investigates the influence of radially sheared toroidal flows on the Trapped Ion Mode (TIM), using a two-dimensional eigenmode code. Influence of the radially extended toroidal microinstabilities on the interpretation of confinement scaling trends and associated fluctuation properties; Average trapped ion banana width.

Discusses the application of a time varying weighting scheme for gyrokinetic particle simulation to a steady-state, multispecies simulation of neoclassical transport. Development of accurate collision operators conserving momentum and energy; Neoclassical theory in steep gradient profile relevant to the edge regime.

Presents the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Influence of sheared equilibrium flows on the confinement properties of tokamak plasmas; Subsonic rotation velocity in the direction of symmetry; Symmetry properties of the magnetic geometry and toroidal flow.

Develops HINST, a high-n stability code for stabilization analysis of toroidicity induced Alfven eigenmodes (TAE) in large tokamaks. Spectrum of unstable TAE modes; Reduction of two-dimensional eigenmode problem based on the Fourier-ballooning formalism; Growth rate of the unstable modes.

Investigates the role of ExB flow shear on confinement enhancement in DIII-D high internal inductance discharges. Discharges with stronger ExB flow shear at similar internal inductance; Importance of the ExB flow shear.

Analyzes the kinetic stability properties in a number of high performance discharges from the DIII-D tokamak, using a comprehensive kinetic eigenvalue code. Toroidal drift mode; Computation of magnetohydrodynamic equilibria; Presence of a wide region of instability.

Analyzes the influence of the large-scale radial electric field on the frequency of shear-Alfven-type instability. Use of a frozen-in-flux constraint and the moderate-beta ion gyrokinetic equation; Possible identification of the edge-localized-mode-associated magnetic activity observed in PBX-M tokamak experiment.