Theoretical Study on the Stability Characteristics of a Quadrupole Cell

Abstract

The stability characteristics of a quadrupole cell were investigated by means of the stability maps for particle motions in both vertical and horizontal directions by two computational methods: the numerical solution of the Mathieu equation for vertical and horizontal motions and the direct numerical simulation of two-dimensional particle trajectory within the cell. The stability map for the vertical motion generally coincided with the results of previous workers. The validity of a new stability map for two-dimensional motion was confirmed by the simulation of particle trajectory. Numerical results of the trajectory method also suggested the importance of a restriction of particle motion by a geometrical dimension of a quadrupole cell.