Laser-driven particle mechanics

Ulrich H. Gerlach

Abstract:

The dynamics of laser-driven charged particles is developed telegraphically from four different perspectives, all of them relativistic: Lagrangian, Hamiltonian, Hamilton-Jacobi, and action-angle. Their unifying idea is the principle of constructive interference. Its physical and mathematical appeal arises from its conceptual unit economy and simplicity.

Being driven by a travelling plane wave, the dynamics of a charged particle is that of an integrable exactly soluble dynamical system having four degrees of freedom. Each one is a uniform rotation whose frequency depends on the action of the that degree, and whose motion is related to the physical motion by the principle of constructive degree of freedom.