MERCREDI 11 MARS 2009
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Alain Brizard
St-Michael College, Colchester, Vermont, USA

Title: Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles

Abstract: 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.