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Ions can be effectively accelerated during the interaction of an ultra‐intense ultra‐short laser pulse irradiating a thin solid target via the so‐called Target Normal Sheath Acceleration (TNSA) mechanism. One of the crucial issues at this stage of the research is how to predict the properties of the accelerated ions, both from a fundamental point of view and in the light of foreseen applications. Thus, it is desirable to have a simple but reliable description, to be used to extrapolate current results to regimes likely to be reached in the near future, thanks to developments in laser technology. In this work we theoretically investigated the maximum ion energy achieved in TNSA as a function of laser properties, with special focus to the ranges IL (pulse intensity) 1020–1022 W/cm2 and EL (pulse energy) 1–30 J, which appear to be the most interesting for future facilities. Particular attention will be devoted to elucidate the effective dependence of the maximum ion energy on the laser intensity for differen...

Low frequency, relativistic sub‐cycle localised (soliton‐like) concentrations of the electromagnetic (em) energy are found in two‐dimensional (2D) and in three‐dimensional (3D) Particle in Cell simulations of the interaction of ultra‐short, high‐intensity laser pulses with homogeneous and inhomogeneous plasmas. These solitons consist of electron and ion density depressions and intense em field concentrations with a frequency definitely lower than that of the laser pulse. The downshift of the pulse frequency, due to the depletion of the pulse energy, causes a significant portion of the pulse em energy to become trapped as solitons, slowly propagating inside the plasma. In an earlier phase solitons are formed due to the trapping of the em radiation inside an electron cavity, while ions can be assumed to remain at rest. Later on, after (mi/me)1/2 times the laser period, ions start to move and the ion depletion occurs producing a slowly growing hole in the plasma density. In inhomogeneous plasmas the solitons are accelerated toward the plasma vacuum interface where they radiate away their energy in the form of bursts of low frequency em radiation. In the frame of a 1D cold hydrodynamic model for an electron‐ion plasma, the existence of multipeaked em solitons has been investigated both analytically and numerically. The analytical expression for a sub‐cycle relativistic soliton has been derived for circularly polarized pulses in a cold isotropic plasma, and in the presence of an externally applied magnetic field. Recently, em relativistic solitons in a hot multi‐component plasma have been investigated in the frame of an hydrodynamic (adiabatic) model and of a kinetic (isothermal) model. An overview of the most recent analytical and numerical results on the soliton dynamics is given.Low frequency, relativistic sub‐cycle localised (soliton‐like) concentrations of the electromagnetic (em) energy are found in two‐dimensional (2D) and in three‐dimensional (3D) Particle in Cell simulations of the interaction of ultra‐short, high‐intensity laser pulses with homogeneous and inhomogeneous plasmas. These solitons consist of electron and ion density depressions and intense em field concentrations with a frequency definitely lower than that of the laser pulse. The downshift of the pulse frequency, due to the depletion of the pulse energy, causes a significant portion of the pulse em energy to become trapped as solitons, slowly propagating inside the plasma. In an earlier phase solitons are formed due to the trapping of the em radiation inside an electron cavity, while ions can be assumed to remain at rest. Later on, after (mi/me)1/2 times the laser period, ions start to move and the ion depletion occurs producing a slowly growing hole in the plasma density. In inhomogeneous plasmas the solitons...