A review of our theoretical studies and computer simulations with PIC codes of the interaction of ultrashort, high-intensity laser pulses with plasmas is presented. The mutual attraction of the currents inside the self-focused channels, arising from the pulse filamentation, makes them interact magnetically and coalesce into a single channel with strongly enhanced electromagnetic energy density. Pulses of finite length and width propagate in the shape of a `bullet' and produce a wake consisting of magnetic dipoles correlated with an electron vortex row behind the pulse. The vortices evolve into an antisymmetric configuration which is shown to be stable when the distance between its vortices is greater than the electron skin depth.
Study of channel formation and relativistic ultra-short laser pulse propagation in helium plasma