An analysis of ion beam trajectories by using boundary element method

A two-dimensional ion extraction system is studied using the boundary-element method. Ion beam trajectories with their space charge are calculated by solving the equations of motion and the Poisson equation under the assumption of stationary charge flow, and the shape of the plasma boundary is modified until the Child-Langmuir relationship on the boundary surface is satisfied. An ion extraction system with a three-electrodes structure is also investigated. It is shown that the shape of the plasma boundary depends on the variation of extraction voltage, and that it strongly depends on the shape of the first aperture, the extraction voltage, and the plasma density. It is concluded that the proposed algorithm can accurately determine the shape of the plasma boundary