  When a finite contrast petawatt laser pulse irradiates a micron-thick foil, a
prepulse (including amplified spontaneous emission) creates a preplasma, where
an ultrashort relativistically strong portion of the laser pulse (the main
pulse) acquires higher intensity due to relativistic self-focusing and
undergoes fast depletion transferring energy to fast electrons. If the
preplasma thickness is optimal, the main pulse can reach the target generating
fast ions more efficiently than an ideal, infinite contrast, laser pulse. A
simple analytical model of a target with preplasma formation is developed and
the radiation pressure dominant acceleration of ions in this target is
predicted. The preplasma formation by a nanosecond prepulse is analyzed with
dissipative hydrodynamic simulations. The main pulse interaction with the
preplasma is studied with multi-parametric particle-in-cell simulations. The
optimal conditions for hundreds of MeV ion acceleration are found with
accompanying effects important for diagnostics, including high-order harmonics
generation.
