Acceptance and transmission of a quadrupole mass filter with a prefilter

We have proposed an analytical model of a quadrupole mass filter with an additional rf quadrupole (prefilter) at its entry, which is based on the model of a transient field in the region between the edges of the mass filter electrodes and the prefilter electrodes. The characteristics of the complex mass filter have been investigated by the methods of phase space dynamics. In the presence of the entrance prefilter, instead of the entrance diaphragm, the $y$ acceptance increases by 1.5 times relative to the $x$ acceptance. Upon an increase in the ion residence time in the fringing field, the $y$ acceptance contour exhibits the tendency to rotation on the phase plane, while the $x$ acceptance contour is broadened in the $x$ coordinate. The transmission function increases and oscillates upon an increase in the ion residence time in the fringing field. The result of numerical experiment using the SIMION 8 software differs from the result of analytical calculation by 14% for the $x$ acceptance and by 35% for the $y$ acceptance.