A Markov chain approach to modelling charge exchange processes of an ion beam in monotonically increasing or decreasing potentials

Abstract

A Markov chain method is presented as an alternative approach to Monte Carlo simulations of charge exchange collisions by an energetic hydrogen ion beam with a cold background hydrogen gas. This method was used to determine the average energy of the resulting energetic neutrals along the path of the beam. A comparison with Monte Carlo modelling showed a good agreement but with the advantage that it required much less computing time and produced no numerical noise. In particular, the Markov chain method works well for monotonically increasing or decreasing electrostatic potentials. Finally, a good agreement is obtained with experimental results from Doppler shift spectroscopy on energetic beams from a hollow cathode discharge. In particular, the average energy of ions that undergo charge exchange reaches a plateau that can be well below the full energy that might be expected from the applied voltage bias, depending on the background gas pressure. For example, pressures of ≈20 mTorr limit the ion energy to ≈20% of the applied voltage.