Recently, strong effort has been done in exploring shock acceleration for the generation of highly energetic ion beams, with applications e.g. for medical purposes. The heating of a near-critical density plasma target with a laser, increases the electron temperature and excites ion acoustic waves, which can lead to electrostatic shock formation due to non-linear wave breaking. The higher inertia background ions are reflected and accelerated at the shock potential, showing a quasi-monoenergetic profile. For the first time, its feasibility has been demonstrated experimentally, gaining 20 MeV protons with a very narrow energy spread1 and a predicted scaling up to 200 MeV for lasers with a0 = 10.2 In the quest for high proton energies, optimal conditions for shock formation have to be found. We developed a relativistic model that connects the initial parameters with the steady state shock Mach number, which is based on the Sagdeev approach,3, 4 showing an increase of the ion energy for high upstream electron temperatures and low downstream to upstream density ratios5 and high temperature ratios, which has been confirmed by particle-in-cell simulations. In the context of producing a quasi-monoenergetic beam profile, we studied the enhancement of the Weibel instability in an electrostatic shock setup. Governing parameter regimes for the transition to an electromagnetic shock, which is associated with a broadening of the ion spectrum, were determined analytically and confirmed with simulations.