Classical relativistic electron-field dynamics: Hamiltonian approach to radiation reaction

Abstract

Motivated by the renewed interest due to the presently available extreme light sources, the dynamics of a single classical relativistic (spinless) extended electron interacting with a classical electromagnetic field (an incoming radiation and the field radiated by the electron) is revisited. The field is treated in Lorentz gauge, with the Lorentz condition. By assumption, there is a crucial finite cut-off k _max on the magnitude of any wavevector contributing to the field (preventing a point electron) and, for a simple formulation, the initial conditions for particle and fields are given in the infinitely remote past. In an infinite three-dimensional vacuum and in an inertial system, Hamilton’s dynamical equations for the particle and the complex field amplitudes acting as canonical variables ( a 's) yield an exact Lorentz force equation for the former, that includes the incoming radiation and an exact radiation reaction force F _RR due to the field radiated by the electron. Uniform motion is obtained as a test of consistency. Based upon numerical computations, some approximations on F _RR are given. A covariant formulation is also presented.

Keywords

• ultra intense lasers
• classical relativistic electron-field dynamics
• Hamiltonian approach
• radiation reaction effects