The propagation of the circularly polarized ( CP ) and the linearly polarized ( LP ) intense lasers in overdense relativistic plasma is studied and compared using analysis and 3D and 2D PIC simulation. It is found that for the CP laser the axial magnetic field up to 100 MG generated by the circular current plays an essential role in channel stability and hot electron beam collimating. The ratio of the number of thermal electrons to total electrons is an important parameters in these processes.
The simulations also reveal the toroidal magnetic field generated by the ponderomotive current can affect nonlinear electron dynamics in responsible of high harmonic generation.