Detailed study of the quadrupole mass analyzer operating within the first, second, and third (intermediate) stability regions. II. Transmission and resolution

Abstract

Theoretical aspects of ion separation in imperfect fields of the quadrupole mass analyzer operating within the first, second, and third stability regions are applied to simulate transmission and resolution by using an analytical approach. A mathematical simulation based on statistical mechanics reveals in analytical form that the region of beam capture, i.e., the transmission, is inversely proportional to the relative values of the mass analyzer distortions to the 1.18th power in log scale. Otherwise, taking into account tails of peaks from unstable ion trajectories shows that the maximum attainable resolution is directly proportional to the number of cycles the ions spend in the field to the 1.33rd power. Because the ion current is amplitude modulated by the frequency of the alternating component of the field, transmission losses because of a parasitic modulation increase more than tenfold as the resolution and distortion increase. These losses are reduced to a minimum by applying a heterogeneous standing wave voltage to the mass analyzer with a linear distribution of amplitude along the ion transit axis. This additional standing wave increases the transmission tenfold. This procedure has the additional advantage of ion injection at zero phase in each cycle of the radiofrequency (rf) field. Experimental verification of the techniques used to avoid transmission losses caused by field distortions indicates the validity of the simulation results. The coarse approximation by means of the operating surface of electrodes in the form of rings instead of a solenoid to create a heterogeneous standing wave voltage applied to the mass analyzer with a linear distribution of amplitude along the drift axis increases the transmission by a factor of 5 compared with a traditional coupling mass filter with pre- and post-filters. Such a comparison proves the advantages of ion injection into the mass analyzer at zero phase in each cycle of an rf field. This reduces the mechanical tolerances of the mass analyzer by an order of magnitude and creates prospects for an increase in attainable resolution by using electrodes of circular profile.