The expansion dynamics of a finite size plasma is examined from an analytical perspective. Results regarding the charge distribution as well as the electrostatic potential are presented. The acceleration of the ions and the associated cooling of the electrons that takes place during the plasma expansion is described. An extensive analysis of the transition between the semi infinite and the finite size plasma behaviour is carried out. Finally, a test of the analytical results, performed through numerical simulations, is presented.
PACS numbers:The production of energetic particles through the interaction of an intense laser pulse with a solid target is a topic that has been widely investigated during the last three decades. For sufficiently long pulses, the emitted particles emerge from a coronal plasma formed by the laser on the target foil and the expansion of the plasma in vacuum plays a key role in such a phenomenon. Thus, despite in Refs. [1,2,3,4] the expansion of a semi infinite plasma has been widely investigated, present experiments often involve "thin foils" as targets [5,6,7,8,9,10,11] which are in some cases no thicker than a few tens of a Debye length, and we believe that, in these cases, the experimental results must be analyzed in terms of the expansion of a finite size plasma. The finite-size and the semi-infinite cases are very different from each other, as in the latter case an infinite amount of energy is available. As a consequence, even if the ions are accelerated, the energy of the electron plasma remains constant. On the contrary, in the case of a finite size plasma an exchange of kinetic energy between electrons and ions takes place as long as the two populations have different velocity distributions, i.e., as long as a charge separation is present. The aim of this work is to provide a detailed analytical description of the thermal expansion of a globally neutral, finite size, unidimensional plasma. Analytical predictions will be compared with numerical results obtained with a Particle in Cell (PIC) code. The configuration at the initial time t 0 , which formally can be defined as the hydrostatic equilibrium in the limit of infinitely massive ions, is specified by the ion density n i0 (x) ≡ n i (x, t 0 ) = n 0 θ(a − |x|), and by the Boltzmann-like electron profile n e0 (x) ≡ n e (x, t 0 ) = n exp (eΦ(x, t 0 )/T e0 ), where a is the half-thickness of the plasma, 2an 0 is the total number of positively charged particle, θ(x) = 0 for x < 0 and θ(x) = 1 for x > 0, Φ(x, t 0 ) is the electrostatic potential,n is the density at the position where Φ(x, t 0 ) = 0, T e0 the initial electron plasma temperature and ∞ −∞ n e0 (x)dx = 2an 0 because the system is globally neutral. For the sake of * Electronic address: betti@df.unipi.it notational simplicity we are considering a plasma where the ion charge is equal and opposite of that of the electrons. Measuring space in units of the initial electron Debye length λ d,0 = (T e0 /4πe 2 n 0 ) 1/2 and rescaling the potential Φ(x, t) as Φ(x, t) → φ(x, t) = eΦ...
