Regular Article

Analytical and numerical studies of positive ion beam expansion for surface treatment applications

¹ Laboratoire Electronique Quantique, Faculté de Physique, USTHB, BP 32 El Alia, 16111 Bab Ezzouar, Algiers, Algeria
² Laboratoire des Plasmas de Décharges, Centre de Développement des Technologies Avancées (CDTA), Cité du 20 Aout BP 17 Baba Hassen, 16081 Algiers, Algeria

^* e-mail: mbendib@hotmail.com

Received: 15 August 2017
Received in final form: 21 October 2017
Accepted: 22 November 2017
Published online: 30 January 2018

Abstract

The aim of this work is to study the expansion in vacuum, of a positive ion beam with the use of one dimensional (1D) analytic model and a two dimensional Particle-In-Cell (2D-PIC) simulation. The ion beam is extracted and accelerated from preformed plasma by an extraction system composed of two polarized parallel perforated grids. The results obtained with both approaches reveal the presence of a potential barrier downstream the extraction system which tends to reflect the ion flux. The dependence of the critical distance for which all extracted ions are reflected, is investigated as a function of the extracted ion beam current density. In particular, it is shown that the 1D model recovers the well-known Child-Langmuir law and that the 2D simulation presents a significant discrepancy with respect to the 1D prediction. Indeed, for a given value of current density, the transverse effects lead to a greater critical distance.