Divergence of laser-driven relativistic electron beams

Electron acceleration by ultrahigh intensity lasers is studied by means of two-dimensional planar particle-in-cell simulations. It is shown that the full divergence of the fast electron beam is defined by two complementary physical effects: the regular radial beam deviation depending on the electron radial position and the angular dispersion. If the scale length of the preplasma surrounding the solid target is sufficiently low, the radial deviation is determined by the transverse component of the laser ponderomotive force. The random angular dispersion is due to the small scale magnetic fields excited near the critical density due to the collisionless Weibel instability. When a preplasma is present, the radial beam deviation increases due to the electron acceleration in larger volumes and can become comparable to the local angular dispersion. This effect has been neglected so far in most of the fast electron transport calculations, overestimating significantly the beam collimation by resistive magnetic fields. Simulations with a two-dimensional cylindrically-symmetric hybrid code accounting for the electron radial velocity demonstrate a substantially reduced strength and a shorter penetration of the azimuthal magnetic field in solid targets.