The interaction of short, relativistic laser pulses with a cold overdense plasma is investigated using computer simulations based on a fluid code. Depending on the background plasma density, two qualitatively different scenarios were observed for the penetration of the laser pulse, which is normally incident onto an overdense plasma. The first scenario is realized at moderate values of the background density (N{sub}0<1.5N{sub}cr, where N{sub}cr is the critical plasma density) and implies a dynamic regime with moving soliton-like structures, which penetrate deeply into the plasma. The second one takes place at higher densities (N{sub}0>1.5N{sub}cr) and the laser radiation penetrates over a finite length only. As long as we can neglect the ion motion, in this regime the plasma-field structures consist of alternating electron layers separated by cavities of about half a wavelength with strong charge separation. When the effects of ion motion become significant, the electron slabs are squeezed by ions with formation of a plasma shock wave.
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