In-target electron thermalization by the Weibel instability during intense irradiation of a thin aluminum foil

Proton-radiography of the electromagnetic fields developing after irradiation of a 3$\mu$m-thick Al foil by a high-intensity laser($5 \times 10^{19}$W.cm$^{-2}$, 700fs, 8$\mu$m focal spot) was performed at the Titan facility. The obtained radiographs evidence filamentary structures which develop inside the dense target, $300\mu$m away from the focal spot, a few picoseconds after the laser drive. We will demonstrate that the radiographs' structures are due to magnetic fields triggered by the so-called Weibel instability, inside the dense target. For this purpose, large scale particle-in-cell simulations of hot electrons thermalization in a dense, cold and collisional target have been performed. They demonstrate the ability of the laser-heated electrons to sustain a strong temperature anisotropy during their relaxation in the thin foil. This hot electron anisotropy results in a Weibel instability, thus triggering magnetic fluctuations of spectrum consistent with the experiment over 10 picoseconds.