Theory of coupling axial and radial ion motion in an ion cyclotron resonance cell during off‐resonance excitation

Abstract

AbstractAn analytic theory of nonlinear effects in the Z‐oscillation (axial motion) during off‐resonance excitation is proposed. This theory is fbased on a representation of electric potential in an ion cyclotron resonance cell in the fourth‐order approximation. Z‐oscillation is considered as a parametric oscillation with a defined motion in the plane of the magnetic field. It is shown that a peculiarity of ion motion due tocoupling of axial and radial motions can be understood in terms of the stability of the Mathieu equation common to the dthree‐dimensional quadrupole ion trap (quistor). Analytic expressions relating parameters (A, Q) of the dMathieu equation to the coefficients of electric potential expansion in the cell are obtained. The strongest coupling effects arise when the frequency of excitation differs from the base cyclotron frequency bytwice the value of the effective frequency of Z‐oscillation that correof parametric resonance in Z‐oscillations.