Laser diffraction effects on the Rayleigh-Taylor instability of radiation pressure accelerated thin foils

We present a theoretical model for the Rayleigh-Taylor (RT)-like instability for a thin foil accelerated by an intense laser, taking into account diffraction effects due to the finite wavelength of the laser wave. The diffraction effects become important when the laser light is scattered off the periodic structures arising from the instability of the foil, and significantly modify the growth rate of the RT-like instability when the perturbations on the foil have wavenumbers comparable to or larger than the laser wavenumber. In particular, the growth rate has a maximum at the resonance arising when the perturbation wavenumber approximately equals the laser wavenumber. The standard RT instability due to a pressure difference between the two sides of a foil, is approximately recovered for perturbation wavenumbers smaller than the laser wavenumber, while in the opposite case, when the perturbation wavenumbers are larger than the laser wavenumber, the reflected laser light is evanescent and the growth rate is smaller than that of the Rayleigh- Taylor instability. Differences in the results for different polarizations and angles of incidence of the laser light are discussed. Preliminary comparisons with particle-in-cell simulation results show good agreement with the theoretical model, with a maximum growth rate for perturbation wavelengths near the laser wavelength. The presented model has significance to radiation pressure acceleration of thin foils, where RT-like instabilities are significant obstacles for the realization of mono-energetic ion beams needed for medical applications.