  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.
