The interaction of ultra-intense lasers with solid foils can be used to accelerate ions to high energies well exceeding 60 MeV. The non-linear relativistic motion of electrons in the intense laser radiation leads to their acceleration and later to the acceleration of ions. Ions can be accelerated from the front surface, the foil interior region, and the foil rear surface (TNSA, most widely used), or the foil may be accelerated as a whole if sufficiently thin (RPA). Here, we focus on the most widely used mechanism for laser ion-acceleration of TNSA. Starting from perfectly flat foils we show by simulations how electron filamentation at or inside the solid leads to a spatial modulations in the ions. The exact dynamics depend very sensitively on the chosen initial parameters which has a tremendous effect on electron dynamics. In the case of step-like density gradients we find evidence that suggests a two-surface-plasmon decay of plasma oscillations triggering a Raileigh-Taylor-like instability.
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