Accurate description of Gaussian laser beams and electron dynamics

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/ kw 0 , where k is the laser wave number and w 0 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 kw 0 ≳50, the paraxial approximation field is good enough to reproduce all the electron dynamic characteristics. In the range of 40≲ kw 0 kw 0 ≲30, one has to utilize seventh-order or higher order corrections to describe more accurately the field of a Gaussian beam.