Radiation reaction dynamics in an electromagnetic wave and constant electric field

Abstract

The relativistic motion of a charged particle is studied when it is acted on simultaneously by a constant electric field and a plane electromagnetic wave, propagating in the direction of the electric field (x axis). The dynamics includes the radiation reaction (self-force) on the particle through a standard approximation of the Lorentz–Dirac equation. The interest is to determine the result of the competition between the average acceleration due to the electromagnetic wave (‘‘radiation pressure’’) and the acceleration due to the constant force of the static field. Each of these actions alone of course produce an unbounded particle energy asymptotically in time. However, it is proved first that, when the ‘‘forces’’ are in opposite directions, the particle can never accelerate (on the average) indefinitely in the x direction, regardless how weak the electric field (E0) is compared to the amplitude of the wave (A). It is then proved that all solutions converge to a region of zero area in a suitable velocity phase space and, if there exists a periodic solution [in the phase ξ=ω (t−x/c)] in a specified region of this phase space, then all solutions must converge to this solution asymptotically (ξ→+∞). In the case when (E0A2/ω2) has a specified bound (ω: wave frequency), an iterative method is developed which explicitly yields such a periodic solution, showing that the energy remains bounded. The direction of the average drift is determined in terms of (A,E0,ω). When the parameter (E0A2/ω2) is above this bound, a combination of numerical and analytic results are obtained which indicate that this periodic solution persists. These results indicate that all motions tend to states with bounded energy, regardless of the field strengths.