Divergence of fast ions generated by interaction of intense ultra-high contrast laser pulses with thin foils

We propose an analytical model that analyzes the divergence of fast ion beams accelerated at the rear of thin foils irradiated with ultra-short intense laser pulses. We demonstrate the critical role played by the non-stationary character of the side components of the electric field, which is responsible for ion acceleration from the back of the foil. The model predictions are in very good agreement with 2D PIC simulations and with the experiments performed in the ultra-high-contrast regime as well.