  We study proton acceleration from a foil target with a transversely varying
density using multi-dimensional Particle-in-Cell (PIC) simulations. In order to
reduce electron heating and deformation of the target, circularly polarized
Gaussian laser pulses at intensities of the order of 1022Wcm-2 are used. It is
shown that when the target density distribution fits that of the laser
intensity profile, protons accelerated from the center part of the target have
quasi-monoenergetic spectra and are well collimated. In our two-dimensional PIC
simulations, the final peak energy can be up to 1.4 GeV with the full-width of
half maximum divergence cone of less than 4o. We observe highly efficient
energy conversion from the laser to the protons in the simulations.
