Comparison of scaling laws with PIC simulations for proton acceleration with long wavelength pulses

We have performed a survey of proton acceleration induced by long wavelength pulses to explore their peak energy dependence on the pulse intensity, target thickness and density. The simulations carried out with the PIC code ALADYN for a circularly polarized pulse have been compared with the scaling laws for radiation pressure acceleration (RPA) in the thick target and thin target regimes known as hole boring (HB) and relativistic mirror (RM) respectively. Since the critical density scales as λ-2, longer wavelength pulses allow to work with low density targets several microns thick and with moderate laser power. Under these conditions is possible to enter the RM region, where the key parameter is the ratio α between twice laser energy and the mirror rest energy; the corresponding acceleration efficiency is given by α/(1+α). For a fixed intensity the minimum thickness of the target, and consequently the highest acceleration, is determined by the threshold of self induced transparency. In this case the number of accelerated particles scales with λ whereas the total energy does not depend on it. The agreement of PIC simulations with RPA and RM scalings, including the transition regions, suggests that these scalings can safely be used as the first step in the parametric scans also for large wavelength pulses such as CO2 lasers, to explore possible alternatives to short wavelength very high power Ti:Sa lasers for proton acceleration.