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

Ion acceleration using a laser pulse irradiating a thin disk target is examined using 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 time of $27$ fs is irradiated on a double-layer target. Simulations are performed by varying the ion density, i.e., electron density, of the first layer. It is shown that the obtained proton energy jumps at a certain density of the first layer, which is made of a "light" material such as carbon; that is, Coulomb explosion of the target and radiation pressure acceleration act effectively above a certain density. Moreover, even at the same electron density, the reflection of the laser pulse from the first layer is small for a "light" material.