Electron bunch acceleration by a laser pulse having Gaussian radial and temporal profiles of intensity has been studied numerically in a static helical magnetic wiggler in vacuum. The main electron bunch parameters for simulations are 10 MeV initial energy with 0.1% longitudinal energy spread, 1 mm mrad rms transverse emittance, and 31012 cm−3 density. It is shown that the radial Gaussian profile can decrease the acceleration gradient compared with that of the plane-wave approximation due to the reduction of electron-pulse interaction area. In order to collimate electron bunch and overcome the decreasing of the acceleration gradient, an external axial magnetic field is used. The importance of the electron initial phase with respect to laser pulse is considered, and some appropriate values are found. Finally, acceleration of a femtosecond fs microbunch with an optimum appropriate initial phase is considered, which leads to a nearly monoenergetic microbunch and an acceleration gradient of about 0.2 GeV/m
