  Proton acceleration by using a 620-TW, 18-J laser pulse of peak intensity of
$5\times 10^{21}$ W/cm$^{2}$ irradiating a disk target is examined using
three-dimensional particle-in-cell simulations. It is shown that protons are
accelerated efficiently to high energy for a "light" material in the first
layer of a double-layer target, because a strongly inhomogeneous expansion of
the first layer occurs by a Coulomb explosion within such a material. Moreover,
a large movement of the first layer for the accelerated protons is produced by
radiation-pressure-dominant acceleration. A time-varying electric potential
produced by this expanding and moving ion cloud accelerates protons
effectively. In addition, using the best material for the target, one can
generate a proton beam with an energy of 200 MeV and an energy spread of 2$%$.
