Radiation Reaction in Relativistic Motion of a Particle in a Wave Field

Abstract

An approximate solution of the equations of motion of Dirac's classical theory f pointlike particles is obtained for a particle in the field of a plane wave, under the assumption that the radiation reaction terms in these equations can be considered as small. The appearance of runaway terms in this solution is avoided by letting the interaction set in gradually. Considerable simplification is achieved by restriction to the domain of high relativistic energies where the transfer of energy and momentum from the wave to the particle appears to be mainly due to radiation reaction. A quantitative discussion of the conditions of applicability of the formulas obtained is made possible by the assumption that there is correspondence between a photon and a classical wave train of finite length. This assumption leads to the conclusion that the classical formulas can be valid for arbitrarily high energies. An estimate of a lower limit for the duration of the interaction between particle and wave train yields an expression which resembles formulas for lifetimes of unstable particles both in its dependence upon fundamental constants and in its increase with the energy involved in the process.