Tailored laser pulse chirp to maintain optimum radiation pressure acceleration of ions

Ion beams generated with ultra-intense lasers-plasma accelerators hold promises to provide compact and affordable beams of relativistic ions. One of the most efficient acceleration setups was demonstrated to be direct acceleration by the laser's radiation pressure. Due to plasma instabilities developing in the ultra-thin foils required for radiation pressure acceleration, however, it is challenging to maintain stable acceleration over long distances. Recent studies demonstrated, on the other hand, that specially tailored laser pulses can shorten the required acceleration distance suppressing the onset of plasma instabilities. Here we extend the concept of specific laser pulse shapes to the experimentally accessible parameter of a frequency chirp. We present a novel analysis of how a laser pulse chirp may be used to drive a foil target constantly maintaining optimal radiation pressure acceleration conditions for in dependence on the target's areal density and the laser's local field strength. Our results indicate that an appropriately frequency chirped laser pulse yields a significantly enhanced acceleration to higher energies and over longer distances suppressing the onset of plasma instabilities.