In Penning trap mass spectrometry ion masses are determined by measuring the free cyclotron frequency via the resonant conversion of the magnetron into the cyclotron motional mode, induced by the interaction with an external radio-frequency field. With octupolar rf-fields of frequency the mass resolution has been improved by more than an order of magnitude as compared to conventional quadrupolar fields of frequency and with the same pulse duration. This result raises the question what one might expect from using 12-polar rf-fields with frequency or even 16-polar rf-fields with frequency .
In this paper the theoretical model for the interconversion of the radial modes by quadrupolar and octupolar rf-fields is generalized to general 4n-polar fields. As in the earlier work the complex amplitudes of the cyclotron and magnetron oscillators are used as dynamical variables and the Hamiltonian equations of motion are reformulated in terms of Bloch vector components. The resulting non-linear differential equations can be solved numerically.
Results are presented on excitation functions (conversion at the exact resonance frequency) and on conversion line shapes (dependence of conversion on the detuning parameter). The most important observation is the decrease of the resonance width by a factor of 2 × 103 as one passes from quadrupolar () to 12-polar () and 16-polar () excitation.