  We present the results of numerical studies of laser pulse propagating in a
3.5 cm Rb vapor cell in the linear dispersion regime by using a 1D model and a
2D code that has been modified for our special case. The 2D simulation finally
aimed at finding laser beam parameters suitable to make the Rb vapor fully
ionized to obtain a uniform, 10 m-long, at least 1 mm in radius plasma in the
next step for the AWAKE experiment.
