Abstract
In a previous paper we proposed a new method based on resummations for studying radiation reaction of an electron in a plane-wave electromagnetic field. In this paper we use this method to study the electron momentum expectation value for a circularly polarized monochromatic field with ${a}_{0}=1$, for which standard locally constant-field methods cannot be used. We also find that radiation reaction has a significant effect on the induced polarization, as compared to the results without radiation reaction, i.e., the Sokolov-Ternov formula for a constant field, or the zero result for a circularly monochromatic field. We also study the Abraham-Lorentz-Dirac equation using Borel-Pad\'e resummations.
Highlights
Radiation reaction (RR) [1,2], i.e., the difference between the actual trajectory of a charge and the one predicted by the Lorentz force equation, is becoming an important effect in high-intensity laser experiments [3,4]
In [14] we focused for simplicity on a constant field, but this method is not restricted to locally constant-field (LCF) or a0 ≫ 1
IV we show the details of how to use the general methods in [14] for a circularly polarized monochromatic field with a0 1⁄4 1, and we apply these methods to both the momentum expectation value and the induced polarization
Summary
Radiation reaction (RR) [1,2], i.e., the difference between the actual trajectory of a charge and the one predicted by the Lorentz force equation (with only the background field, no self-field), is becoming an important effect in high-intensity laser experiments [3,4] (see [5]). In [14] we developed a new method for calculating the momentum expectation value of an electron in a plane-wave background field It is fully quantum, includes both real photon emissions and loops and can be used for arbitrary spin (see e.g., [15,16,17] for other studies of spin-dependent RR). If one just lets an electron stay in the laser field RR will eventually lead to a considerable change in the momentum This is not included in the Sokolov-Ternov result. V we compare its leading classical limit, which we in [14] showed is equal to solution of the Landau-Lifshitz (LL) equation [29,30], with a resummation of the AbrahamLorentz-Dirac (LAD) equation
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