We investigate the influence of the initial size of the proton layer on proton acceleration in the interaction of high intensity laser pulses with double-layer targets by using two-dimensional particle-in-cell code. We discuss the influence of proton layer initial sizes on the cut-off energy, energy spread, and divergence angle of proton beam. It is found that Coulomb explosion plays an important role on the proton cut-off energy. This causes the cut-off energy to increase for increasing proton layer thickness, at the expense of energy spread. The proton divergence angle reaches a peak value and then falls again with increasing the width. Proton divergence angle grows with target thickness. It is found that there is an optimal thickness to obtain the narrowest energy spread, which may provide an effective method (change the size of proton layer) to obtain high quality proton beams. This work may serve to improve the understanding of sheath field proton acceleration.
