Relativistic Quasilinear Diffusion in Axisymmetric Magnetic Geometry for Arbitrary-Frequency Electromagnetic Fluctuations

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the elements of a relativistic quasilinear diffusion tensor are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of gyro-drift-bounce wave-particle resonances. The resonances can destroy any one of the three invariants of the unperturbed guiding-center Hamiltonian dynamics.Comment: 22 pages, Latex, to appear in Physics of Plasma

Mini-Conference on Hamiltonian and Lagrangian Methods in Fluid and Plasma Physics

A mini-conference on Hamiltonian and Lagrangian methods in fluid and plasma physics was held on November 14, 2002, as part of the 44th meeting of the Division of Plasma Physics of the American Physical Society. This paper summarizes the material presented during the talks scheduled during the Mini-Conference, which was held to honor Allan Kaufman on the occasion of his 75th birthday.Comment: 14 pages, conference summar

Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method

The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation ("lift") of the Vlasov-Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to derive explicit Hamiltonian formulations for the guiding-center and gyrokinetic Vlasov-Maxwell equations that have important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov-Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.Comment: 39 page

Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles

A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space (which includes energy and time as independent coordinates) for all three adiabatic invariants. First, the guiding-center equations of motion for a relativistic particle are derived from the particle Lagrangian. Covariant aspects of the resulting relativistic guiding-center equations of motion are discussed and contrasted with previous works. Next, the second and third invariants for the bounce motion and drift motion, respectively, are obtained by successively removing the bounce phase and the drift phase from the guiding-center Lagrangian. First-order corrections to the second and third adiabatic invariants for a relativistic particle are derived. These results simplify and generalize previous works to all three adiabatic motions of relativistic magnetically-trapped particles.Comment: 20 pages, LaTeX, to appear in Physics of Plasmas (Aug, 2007

Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry

The perturbation analysis of the bounce action-angle coordinates $(J,\zeta)$ for charged particles trapped in an axisymmetric dipole magnetic field is presented. First, the lowest-order bounce action-angle coordinates are derived for deeply-trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates $s(J,\zeta)$ and $p_{\|}(J,\zeta)$ are presented, which satisfy the canonical identity $\{s,\; p_{\|}\}(J,\zeta) \equiv 1$. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.Comment: 16 pages, 3 figure