Test Ion Acceleration in the Field of Expanding Planar Electron Cloud
  New exact results are obtained for relativistic acceleration of test positive ions in the non-Boltzmann laminar zone of a planar electron sheath evolving from an initially mono-energetic electron distribution. The electron dynamics is analyzed against the background of motionless foil ions. The limiting gamma-factor of accelerated ions is shown to be determined primarily by the values of the ion-electron charge-over-mass ratio and the initial gamma-factor of the accelerated electrons: there exists a critical relationship between these two quantities, which determines whether the ion can overtake the electron front moving with initial electron velocity. It is proven that in reality protons and heavier test ions can never catch up with the electron front; for their maximum energy an appropriate intermediate asymptotic formula is derived. The domain of applicability of the laminar-zone results is analyzed in detail. 
M.M. Basko