Focal spot effects on the generation of proton beams during target normal sheath acceleration

973 Program [2011CB808104]; National Natural Science Foundation of China [11335013, 11125526, 11305236, 11575274]; International S&T Cooperation Program of China [2011DFA11300]; Shanghai Natural Science Foundation [13ZR1463300]Focal spot effects on the generation of proton beams are investigated by a high-intensity high-contrast laser irradiating on solid foil in target normal sheath acceleration experiments. Different spot size, transverse shape, and intensity of the laser are obtained by appropriately using deformable mirrors and parabolic mirrors. Experiments show that the maximum proton energy is mainly determined by the laser intensity if the focal spot size is not seriously changed. Compared with the previous experimental results, the optimum foil thickness d(o) is scaled by the laser intensity I as d(o) similar to I-0.33. The corresponding theoretical estimation is carried out as d(o) similar to I-0.25 for ultra-high intensity laser systems with similar contrast. MULTI and particle-in-cell simulations are used to interpret the experimental results