Misphasing of ion motion in quadratic potential induced by space-periodic disturbance

An ideally quadratic potential used in different types of ion mass analyzer such as Paul trap, Kingdon trap and quadratic field reflectron may be space-periodically disturbed due to inaccuracy of fabrication and design features. If ion motion in such devices is computer-simulated, disturbances of potential may be caused by the peculiarity of the computation method. The problem investigated in this work is the effect that weak space-periodic disturbance of a quadratic potential takes on the ion motion in such a potential. The effect of the disturbance we considered is the misphasing of an ion cloud oscillating in a disturbed quadratic potential. A method to evaluate the characteristic misphasing time is presented. For the case of disturbance amplitude being constant along ion trajectories, the designated problem may be considered analytically. If the disturbance amplitude depends on oscillation co-ordinate, the result can be obtained by use of numerical integration. An example of numerical calculation is presented.