Nonlinear field effects in quadrupole mass filters

The performance of a quadrupole mass filter (QMF) generally degrades when using electrodes of circular cross section in place of mathematical ideal hyperbolic electrodes. The circular cross section of electrodes produces nonlinear resonances resulting in distortion and peak splitting in mass spectra. In addition, resonances reduce the actual working cross section, resulting in limited ion yield. In this article we study nonlinear resonances and intensities of resonance lines passing through the tip of the stability diagram of the QMF. We have found that balancing of multipole terms, rather than eliminating individual multipole terms, improves the sensitivity of the QMF considerably. The theory for assessing intensities of nonlinear resonances is presented in detail along with rescaling laws to adjust current QMF parameter settings. A general formula is presented from which the location and intensity of nonlinear can be derived, which then may be used for the design of special purpose QMFs.