  We derive a modified non-perturbative Lorentz-Abraham-Dirac equation. It
satisfies the proper conservation laws, particularly, it conserves the
generalized momentum, the latter property eliminates the symmetry-breaking
runaway solution. The equation allows a consistent calculation of the electron
current, the radiation effect on the electron momentum, and the radiation
itself, for a single electron or plasma electrons in strong electromagnetic
fields. The equation is applied to a simulation of a strong laser pulse
interaction with a plasma target. Some analytical solutions are also provided.
