Ion acceleration due to expansion of non-quasi-neutral plasmas into vacuum

Ion acceleration is studied both analytically and numerically. In the analytical model, a new self-similar solution, which can be applied to any geometry (planar, cylindrical, and spherical), is employed to describe non-relativistic expansion of a finite plasma mass into vacuum with a full account of charge separation effects. It turns out that the normalized plasma size Λ = R/λD plays the dominant role in determining the whole ion energy spectrum and thus the maximum ion kinetic energy, where R and λD are the plasma scale length and the Debye length, respectively. The analytical model is compared with particle simulations and experiments to show excellent agreement. It is argued that, when properly formulated, the analytical results obtained from the present model can be applied more generally than the self-similar solution itself