Phase-space contraction and attractors for ultrarelativistic electrons.

Ultrashort-pulse laser intensities can reach 10(22) W/cm(2). In this case the electron motion becomes ultrarelativistic and significant bremsstrahlung occurs. The radiation causes a dissipative effect, which is called a radiation reaction. It has been shown in the literature that the radiation reaction force causes phase-space contraction when the motion of electrons in a laser field is considered. The effect of the radiation reaction force is smaller for electron propagation in the direction of a propagating plane wave compared to counterpropagation. In the case of two colliding laser beams with sufficiently large amplitudes, stochastic heating is an important process that will be influenced by the radiation reaction. It is shown here that the radiation reaction causes attractors and in certain parameter regimes electron motion converges to regular attractors. This causes a significant reduction of stochastic heating. The forms of the attractors are presented. The results confirm the general prediction of phase-space contraction and provide quantitative results for the speed of contraction as well as the type of attracted motion.