On the Correct Averaging of the Equations of Ion Motion in High-Frequency Electric Fields

The pseudopotential approach is a useful tool for the qualitative description of ion motion in inhomogeneous high-frequency electric fields, often used in mass spectrometric devices. However, in the theoretical study of the motion of ions in high-frequency electric fields with close frequencies, mathematical ambiguity arises, caused by the nonequivalence of different mathematical approaches. The paper considers and compares the time-dependent pseudopotential model and the model of solenoidal (vortex) pseudoforces, that is, vortex drift. The vortex drift model in high-frequency electric fields with close frequencies can be replaced by the model of ion motion in a pseudopotential varying in time. The theory of almost periodic time signals with two characteristic time scales, fast and slow, eliminates the ambiguity in selecting the correct mathematical method for describing ion motion in high-frequency electric fields.