Mathematical simulation of the influence of ion-compensation, self-magnetic field and scattering on an electron beam during welding

The determination of the position of minimal electron beam cross-section wa s carried out using two methods, one known as the Arata-Beam test and the o ther by measuring the beam diameter with the DIABEAM system. The comparison reveals differences in the position of minimal cross-section detected by t hese two methods. The scattering of the electron beam and its focusing by p ositive space charge of generated ions are possible reasons responsible for the change of the position of its minimal cross-section during welding. A mathematical model based on the solution of a modified trajectory equation for edge electrons taking into account the vapour expanding from the capill ary into the vacuum and possible beam-vapour interaction mechanisms was dev eloped in order to estimate quantitatively the influence of these effects o n the beam focusing. The developed model reproduces the experimental result s for low- and high-beam power and can be applied as a part of a general mo del of simulation of electron beam welding, which predicts the beam geometr y close to a workpiece. (C) 2001 Elsevier Science Ltd. All rights reserved.