  A numerical study on ion acceleration in electrostatic shock waves is
presented, with the aim of determining the best plasma configuration to achieve
quasi-monoenergetic ion beams in laser-driven systems. It was recently shown
that tailored near-critical density plasmas characterized by a long-scale
decreasing rear density profile lead to beams with low energy spread [F.
Fi\'uza et al., Physical Review Letters 109, 215001 (2012)]. In this work, a
detailed parameter scan investigating different plasma scale lengths is carried
out. As result, the optimal plasma spatial scale length that allows for
minimizing the energy spread while ensuring a significant reflection of ions by
the shock is identified. Furthermore, a new configuration where the required
profile has been obtained by coupling micro layers of different densities is
proposed. Results show that this new engineered approach is a valid
alternative, guaranteeing a low energy spread with a higher level of
controllability.
