Analytical approach for description of ion motion in quadrupole mass spectrometer

Implementation of the analytical method of the solution of the Mathieu equation in conjunction with the algebraic presentation of Mathieu functions is discussed in this work. This approach is used for the analytical expression of fundamental properties of the quadrupole field such as ion trajectory stability and transmission. Extensive comparison with the matrix method is presented with demonstration of the fundamental advantages of the analytical method. However, contrary to the matrix method, the analytical method is limited to the cos trapping waveforms.