The interaction of free electrons with intense laser beams in vacuum is studied using a 3D test particle simulation model that solves the relativistic Newton-Lorentz equations of motion in analytically specified laser fields. Recently, a group of solutions was found for very intense laser fields that show interesting and unusual characteristics. In particular, it was found that an electron can be captured within the high-intensity laser region, rather than expelled from it, and the captured electron can be accelerated to GeV energies with acceleration gradients on the order of tens of GeV/cm. This phenomenon is termed the capture and acceleration scenario (CAS) and is studied in detail in this paper. The maximum net energy exchange by the CAS mechanism is found to be approximately proportional to
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