The mechanisms of the laser acceleration of ions in under-dense or near-critical plasmas (gas, foams) are at their early stage of development [1, 2, 3]. They offer a better laser/electron coupling than in solid targets resulting in a more efficient ion acceleration. They also enable a high repetition rate operation and reduce the formation of debris which could damage the interaction chamber.
Our work deals with this interaction regime and focuses on understanding how electrons and ions absorb energy from the laser pulse in low density plasmas. This interaction regime involves various non linear processes that strongly modify the particle distribution functions and induce strong non-local effects. The numerical simulations were performed with the Particle-In-Cell (PIC) code OCEAN .
By one dimensional PIC simulations, we have shown  that the interaction of a 1 ps long relativistic laser pulse with a under-critical homogeneous (0.5 n_c) plasma leads to a very high plasma absorption reaching 68 % of the laser pulse energy. By a very detailed analysis of the electrostatic and electromagnetic wave spectra in the plasma and a confrontation with the theory , we have demonstrated that this energy transfer originates from the process of stimulated Raman scattering in the relativistic regime. Due to the increase of the effective mass of the electrons oscillating in the relativistic laser wave, this instability occurs in plasmas with a density significantly larger than the quarter of critical density and permits a homogeneous electron heating all along the plasma followed by an efficient ion acceleration at the plasma edges. We also have observed the formation of cavities , which lead to the formation of quasi-monoenergetic bunches of ions inside the plasma.
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