On the correct averaging of the equations of ion motion in high-frequency electric fields
T15N4
A.S. Berdnikov, A.N. Verenchikov, A.G. Kuzmin
Pseudo potential approach is a useful tool to describe qualitatively the motion of ions in inhomogeneous radio frequency electric fields often used in mass spectrometric devices. However, in the theoretical analysis of ion motion in radio-frequency electric fields with close frequencies, a mathematical ambiguity arises, caused by the lack of equivalence of different mathematical approaches. The paper considers and compares the time-dependent pseudopotential model and the model of solenoidal (vortex) pseudo forces. It is shown that the vortex drift model in radio-frequency electric fields with close frequencies can be replaced by the model of ion motion in a pseudopotential that varies in time. The theory of almost periodic time signals with two characteristic time scales, fast and slow, makes it possible to eliminate ambiguity when choosing the correct mathematical method for describing the motion of ions in radio-frequency electric fields.