We determine conditions allowing to simplify the description of the impact of an arbitrarily intense laser pulse onto a cold plasma at rest. If both the plasma and the pulse have plane simmetry and the pulse propagates in the orthogonal direction z, we determine matched upper bounds on the duration of the pulse and the density of the plasma ensuring a strictly hydrodynamic evolution of the electron fluid (without wave-breakings or vacuum-heating) during their whole interaction with the pulse, while ions can be regarded as immobile. We use a recently developed fully relativistic plane model whereby we reduce the system of the (Lorentz-Maxwell and continuity) PDEs into a family of highly nonlinear but decoupled systems of non-autonomous Hamilton equations with one degree of freedom, with the light-like coordinate ξ = ct−z instead of time t as an independent variable, and new apriori estimates (eased by use of Liapunov functions) of the solutions in terms of the input data (initial density and pulse profile). If the laser spot radius R is finite but not too small the same conclusions hold for the part of the plasma close to the axis z of cylindrical symmetry. These results may drastically simplify the study of extreme acceleration mechanisms of charged particles.
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