Abstract
Abstract In this paper, the higher order corrections to the description of a Gaussian laser field are derived and expressed as power functions of the parameter s=1/kw0, where k is the laser wave number and w0 the beam width at the focus center. Using the test particle simulation programs, the electron dynamics obtained using the paraxial approximation, the fifth-order correction, and the seventh-order correction are compared. Special attention is given to electron acceleration in vacuum by intense laser beams. The results reveal that, when kw0≳50, the paraxial approximation field is good enough to reproduce all the electron dynamic characteristics. In the range of 40≲kw0
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