Computer simulation of the quadrupole mass filter

A computer program, called MMFCODE, has been developed to analyze numerically the dynamics of ion beams in a Quadrupole Mass Filter (QMF). The motion of the ions can be known by solving the three-dimensional equation of motion. A harmonic expansion of the electric field is introduced to get a reasonable computing time. For the incident beam, more than 104 ions are generated by a Monte Carlo method. After the mass scan line was determined with the condition that ΔM = const. at two different mass numbers (M), the mass spectrum and the acceptance can be simulated. By using MMFCODE, the simulation of a real dimension can be done without neglecting the fringing field or using the model field. In this paper, a model of a QMF with an RF-only pre-filter, called the delayed DC ramp [W. Brubaker, U.S. patent 3,371,204 (1968)], was analyzed by using MMFCODE. By our simulation, the transmittance was oscillated with respect to the pre-filter length in the case of a low mass number as reported by C. Trajber et al. [Rapid Commun. Mass Spectrom. 6 (1992) 459], but was not oscillated in the case of a high mass number. This is probably because the distribution of the axial velocities is narrow in the case of a low mass number but broad in the case of a high mass number. This discrepancy is caused by the influence of the fringing field at the pre-filter entrance.