Target normal sheath acceleration for arbitrary proton layer thickness

• The TNSA mechanism is studied using analytical and simulation models.
• The effect of the proton layer thickness on the acceleration efficiency is analyzed.
• Depending on the layer thickness, three acceleration regimes are identified.
• Scaling laws for the energy conversion from the hot electrons to protons are derived.
• We infer the optimal laser pulse length in dependence on the layer thickness.

The Target Normal Sheath Acceleration (TNSA) of a rear-side hydrogen-rich layer from a heavy-ion target is studied using Particle-In-Cell (PIC) simulations together with analytical models. The TNSA mechanism depends on the hydrogen layer thickness. Analytical models describe the two asymptotic cases: a thin layer (the quasi-static acceleration) and a thick layer (plasma expansion into vacuum). We investigate the phase–space structure of the accelerated protons, especially for layers of intermediate thickness, and study the applicability of the analytical models. It is demonstrated that the relevant regime depends on the thickness of the hydrogen layer relative to the characteristic penetration depth of the electric field into the target. We describe the modifications of the accelerating electric field by the protons for different layer thicknesses. The consequences for the resulting proton energy spectrum are discussed.