On the electrodynamic model of ultra-relativistic laser-plasma interactions caused by radiation reaction effects

{A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notations such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc interactions are also calculated. Based on these solutions we show that about 50% of laser energy can be converted into gamma-rays in the optimal conditions of laser-foil interaction.