  The radiation reaction effects on electron dynamics in counter-propagating
circularly polarized laser beams are investigated through the linearization
theorem and the results are in great agreement with numeric solutions. For the
first time, the properties of fixed points in electron phase-space were
analyzed with linear stability theory, showing that center nodes will become
attractors if the classical radiation reaction is considered. Electron dynamics
are significantly affected by the properties of the fixed points and the
electron phase-space densities are found to be increasing exponentially near
the attractors. The density growth rates are derived theoretically and further
verified by particle-in-cell simulations, which can be detected in experiments
to explore the effects of radiation reaction qualitatively. The attractor can
also facilitate to realize a series of nanometer-scaled flying electron slices
via adjusting the colliding laser frequencies.
