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Acceleration of electrons in a vacuum by lasers and the accuracy principle of nonlinearity

The new principle of nonlinearity requesting a much higher degree of accuracy of all physical presumptions for the treatment, can be demonstrated ideally by the field of acceleration of electrons by lasers in vacuum. Initially the net energy conversion from electromagnetic radiation to electrons, e.g. by lasers in vacuum, was considered to be impossible based on the fact that plane-wave and phase symmetric wave packets can never transfer 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 ponderomotion or the Lorentz force, however, does permit an energy transfer if the conditions of plane waves in favor of beams and/or the phase symmetry are broken. The result in electron acceleration is now well understood as 'free wave acceleration', as 'ponderomotive scattering', as 'violent acceleration' or as 'vacuum beat wave acceleration'. The basic understanding of these phenomenon, however, relates to an accuracy principle of nonlinearity for explaining numerous discrepancies on the way to the mentioned achievement of 'vacuum laser acceleration'. From mathematically designed beam conditions, an absolute maximum of electron energy per laser interaction has been established. Numerical results strongly depend on the accuracy of the used laser fields for which examples are presented and finally tested by a criterion of the absolute maximum.