Modeling of ion transient response to dipolar AC excitation in a quadrupole ion trap

A theoretical modeling method was explored for characterizing the ion transient response to a dipolar AC excitation in quadrupole ion trap. The ion motion equation was established by applying the pseudo-potential approximation to Mathieu Equation with an ion-molecule collision term included. A step function was introduced to model the transient state of applying a dipolar excitation The Laplace transformation was performed to solve the ion motion equation. The high-frequency ion motion components, typically ignored by the pseudo-potential approximation, have also been included in the modeling. Characterization of ion motions at the excitation frequency, secular frequency and their corresponding high-order harmonic frequencies was achieved using this method. The capability of this theoretical modeling method was validated by applying it for interesting phenomena previously observed, including ion beat motions, frequency broadening at higher pressures, and ion bunching. Numerical simulations were also performed to confirm the results obtained with the theoretical modeling.