Ion energy in quadrupole mass spectrometry.

Application of an analytical solution of the Mathieu equation in conjunction with algebraic presentation of the Mathieu functions for description of the ion energy in a radiofrequency quadrupole field is discussed in this work. The analytical approach is used to express the ion energy averaged over the initial ion velocity distribution function, field phase and ion residence time. Comparisons with the approximate solutions for potential ion energy are presented with demonstration of their limits. Application of the method for different stability regions is discussed.