  {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.
