We present 3D particle-in-cell simulations for laser pulses with relativistic intensity propagating in slightly underdense plasma. We observe strong flows of relativistic electrons, axially comoving with the pulse. They generate magnetic fields up to 100 MG and strongly influence light propagation. After a phase of filamentation, a single light channel with a width of 1--2 wavelengths is formed by magnetic interaction. A representative case is discussed in which the intensity on axis increases from initially 1. 210^19 to 2. 010^20 W/cm^2. Ion acceleration and plasma cavitation are also discussed.
Pukhov et al. (1996) studied this question.