Dynamics of a relativistic charged particle in a constant homogeneous magnetic field and a transverse homogeneous rotating electric field

The relativistic motion of a charged particle in a homogeneous time-independent magnetic field and a transverse circularly polarized homogeneous electric field is reduced to an integrable form. Using canonical transformations, it is shown that the equations of motion can be derived from a one degree of freedom time-dependent Hamiltonian that has a first integral. The trajectories and the dynamics of the particle are studied. Tractable approximate expressions for the maximum kinetic energy are derived in two situations of experimental interest. © 1996 The American Physical Society.