  We show that monoenergetic ion beams can be accelerated by moderate Mach
number collisionless, electrostatic shocks propagating in a long scale-length
exponentially decaying plasma profile. Strong plasma heating and density
steepening produced by an intense laser pulse near the critical density can
launch such shocks that propagate in the extended plasma at high velocities.
The generation of a monoenergetic ion beam is possible due to the small and
constant sheath electric field associated with the slowly decreasing density
profile. The conditions for the acceleration of high-quality, energetic ion
beams are identified through theory and multidimensional particle-in-cell
simulations. The scaling of the ion energy with laser intensity shows that it
is possible to generate $\sim 200$ MeV proton beams with state-of-the-art 100
TW class laser systems.
