Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Abstract

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Lastly, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

11 pages

References in corpus (2)

• Equivalence of two independent calculations of the higher order guiding center Lagrangian
• Equivalent Higher-order Guiding-center Hamiltonian Theories

Cited by in corpus (17)

• Second order Gyrokinetic theory for Particle-In-Cell codes
• Variational principles for the guiding-center Vlasov-Maxwell equations
• Gyrokinetics from variational averaging: existence and error bounds
• Second order nonlinear gyrokinetic theory : From the particle to the gyrocenter
• Hierarchy of second-order gyrokinetic Hamiltonian models for particle-in-cell codes
• On the validity of the guiding-center approximation in the presence of strong magnetic gradients
• Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method
• Exact conservation laws for gauge-free electromagnetic gyrokinetic equations
• Variational principle for the parallel-symplectic representation of electromagnetic gyrokinetic theory
• Faithful guiding-center orbits in an axisymmetric magnetic field
• On the validity of the guiding-center approximation in a magnetic dipole field
• Action-angle coordinates for motion in a straight magnetic field with constant gradient
• Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
• Particle and guiding-center orbits in crossed electric and magnetic fields
• Verification of Gyrokinetic codes: theoretical background and applications
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations
• A Tale of Two Polarization Paradoxes I: the Diamagnetic Polarization Paradox