Eur. Phys. J. D 41, 641-654 (2007)
https://doi.org/10.1140/epjd/e2006-00262-4

Test ion acceleration in a dynamic planar electron sheath

Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218 Moscow, Russian Federation

Corresponding author: ^a basko@itep.ru

Received: 21 August 2006
Revised: 13 October 2006
Published online: 8 December 2006

Abstract

New exact results are obtained for relativistic acceleration of test positive ions in the laminar zone of a planar electron sheath evolving from an initially mono-energetic electron distribution. The electron dynamics is calculated against the background of motionless foil ions. The limiting gamma-factor γ_p∞ of accelerated ions is shown to be determined primarily by the values of the ion-electron charge-over-mass ratio μ=m_eZ_p/m_p and the initial gamma-factor γ₀ of the accelerated electrons. For μ> 1/8 a test ion always overtakes the electron front and attains γ_p∞> γ₀. For μ< 1/8 a test ion can catch up with the electron front only when γ₀ is above a certain critical value γ_cr, which for μ≪1 can most often be evaluated as . In this model the protons and heavier test ions, for which γ_cr> 10³⁹⁸ is enormous, always lag behind the front edge of the electron sheath and have γ_p∞< γ₀; for their maximum energy an appropriate intermediate asymptotic formula is derived. The domain of applicability of the laminar-zone results is analyzed in detail.