On the use of stroboscopic samples in the analysis of the motion of ions in quadrupole radio-frequency fields. I. Critical analysis of the concept

A new concept of effective potential, proposed by M.Yu. Sudakov and M.V. Apatskaya, is analyzed. The said concept is based on the envelopes of stroboscopic samples of coordinates and ion velocities in a radio-frequency quadrupole field and seems rather interesting. However, it is shown that the proposed formulas are not completely correct and require some elaboration.