A simple model for the velocity modulation detection technique of molecular ions

We present a simple model to describe the line-profile of velocity modulated ions. This model is based on Langevin's theory of the mobility and on the independence of the electric field strength on the discharge current in the ideal positive column. A comparison of time constants responsible for the drift of the ions, the concentration, and the ignition and extinction of the discharge itself is essential for a rough understanding of the velocity modulation. The behaviour of H₃O⁺ ions in an ac glow discharge was examined. Under our experimental conditions the line-profile can be explained by a temporal dependence of the velocity which is close to a square-wave. Due to this particular temporal dependence the amplitude of the signal only depends on the concentration modulation, while the line-shape is a simple difference line-profile.