Phase locked multiple rings in the radiation pressure ion acceleration process

Laser contrast plays a crucial role for obtaining high quality ion beams in the radiation pressure ion acceleration (RPA) process. Through one- and two-dimensional particle-in-cell (PIC) simulations, we show that a plasma with a bi-peak density profile can be produced from a thin foil on the effects of a picosecond prepulse, and it can then lead to distinctive modulations in the ion phase space (phase locked double rings) when the main pulse interacts with the target. These fascinating ion dynamics are mainly due to the trapping effect from the ponderomotive potential well of a formed moving standing wave (i.e. the interference between the incoming pulse and the pulse reflected by a slowly moving surface) at nodes, quite different from the standard RPA process. A theoretical model is derived to explain the underlying mechanism, and good agreements have been achieved with PIC simulations.