Proton energy behavior by variation of the target density in laser acceleration

Ion acceleration using a laser pulse irradiating a thin disk target is examinedusing three-dimensional and two-dimensional particle-in-cell simulations.A laser pulse of $620$ TW, with an intensity of $5\times 10^{21}$ W/cm$^{2}$and a duration of $27$ fs is irradiated on to a double-layer target.Simulations are performed by varying the ion density, i.e., electron density,of the first layer with a fixed areal mass density.It is shown that the obtained proton energy increases dramatically fora certain density of the first layer,which is made of a material having a small mass over charge ratio, ``light\u27\u27 material, such as carbon; that is, the Coulomb explosion of the target and radiation pressure acceleration act effectively above a certain density. Moreover, even for the same electron density, the reflection of the laser pulsefrom the first layer is small for a ``light\u27\u27 material