Principle of high accuracy for the nonlinear theory of the acceleration ofelectrons in a vacuum by lasers at relativistic intensities

Acceleration of electrons by lasers in a vacuum was considered impossible b ased on the fact that plane-wave and phase symmetric wave packets cannot tr ansfer energy to electrons apart from Thomson or Compton scattering or the Kapitza-Dirac effect. The nonlinear nature of the electrodynamic forces of the fields to the electrons, expressed as nonlinear forces including ponder omotion or the Lorentz force, permits an energy transfer if the conditions of plane waves in favor of the beams and/or the phase symmetry are broken. The resulting electron acceleration by lasers in a vacuum is now well under stood as "free wave acceleration", as "ponderomotive scattering", as "viole nt acceleration", or as "vacuum beat wave acceleration". The basic understa nding of these phenomena relates to an accuracy principle of nonlinearity f or explaining numerous discrepancies on the way to the mentioned achievemen t of "vacuum laser acceleration", which goes beyond the well-known experien ce of necessary accuracy in both modeling and experimental work experiences among theorists and experimentalists in the field of nonlinearity. From ma thematically designed beam conditions, an absolute maximum of electron ener gy per laser interaction has been established. It is shown here how numeric al results strongly (both essentially and gradually) depend on the accuracy of the used laser fields for which examples are presented and finally test ed by the criterion of the absolute maximum.