Multi-scale analytical description of an expanding plasma slab

We present a new analytical model for the expansion of a thin slab of plasma into vacuum. By considering the rising plasma scale length during the initial heating phase, we were able to give the plasma a smooth quadratic behavior at the origin while describing its exponentially falling density at a large distance. We show this functional form to be a solution to the plasma equations and validate its predictions against numerical simulations and experimental measurements. We demonstrate the applicability of the model to experimental scenarios in which solid foils are turned into tens of micrometer-scale plasmas, to serve as targets for direct laser acceleration of electrons.