The present paper aims at reconsidering the Kapitsa method in the case of rf traps or multipole ion mass filters. Based on this method a couple of invariants of the corresponding motion are derived in some particular cases. The method and the invariants presented here are useful in numerical analyses which investigate of stability of motion that a charged particle develops in nonlinear rf fields

The stability of hexapole rf trap under DC electric field is theoretically investigated. Analytical arguments based on the 3D slow-fast Kapitsa method are developed to find the locus of the minimum in the effective potential. We investigate the motions with both vanishing and not vanishing angular momentum with respect to the z-axis. The numerical analysis confirms the theoretical results.

An accurate numerical method for calculating the potential distribution useful for 2D problems is proposed. Numerical results for quadrupole mass filter, hexapole, and octupole ion guide are presented and discussed.

Constant-phase Poincar´e sections were used to assess the stability of rectilinear motions in a sextupole rf trap. A simple method for exploring the main domain of stability is proposed. Using numerical algorithms, the nonlinear and nonautonomous motion is analyzed in some interesting regions of the phase space.