New ion-optical devices utilizing oscillatory electric fields. II. Stability of ion motion in a two-dimensional hexapole field

Abstract

Trajectories and stability diagrams have been calculated for oscillatory motions of charged particles in a two-dimensional hexapole electric field by numerical integration of the appropriate equations of motion. A charged particle in its dynamically stable state can execute a wide variety of non-linear periodic and non-periodic forced oscillations. Numerical computations of trajectories for charged particle motion were applied to determine a whole series of stability diagrams associated with different sets of initial conditions. The trajectories remain stable for an unexpectedly wide range of vlaues for the parameters, a 3 and q 3, which are equivalent to the parameters a and q, respectively, for the quadrupole geometry. However, the shape and size of the stability diagram depend on the initial conditions. The boundary of the stable and unstable regions in the ( a 3, q 3) plane is diffuse. Possible explanations for this anomalous effect are also given. This phenomenon is likely to occur in multipoles of any order, except for the quadrupole geometry. Hexapoles are suitable for confining and transporting low-energy ion beams for the purpose of ion spectroscopy and ion chemistry experiments. However, their mass resolution is probably too low for purpose of mass analysis.