  We investigate the propagation of ultra-short laser pulses in atomic rubidium
vapor. The pulses are intensive enough to ionize the atoms and are directly
resonant with the 780 nm $D_2$ line. We derive a relatively simple theory for
computing the nonlinear optical response of atoms and investigate the competing
effects of strong resonant nonlinearity and ionization in the medium using
computer simulations. A nonlinear self-channeling of pulse energy is found to
produce a continuous plasma channel with complete ionization. We evaluate the
length, width and homogeneity of the resulting plasma channel for various
values of pulse energy and initial focusing to identify regimes optimal for
applications in plasma-wave accelerator devices such as that being built by the
AWAKE collaboration at CERN. Similarities and differences with laser pulse
filamentation in atmospheric gases are discussed.
