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We describe the operation of an electrodynamic ion trap in which the electricquadrupole field oscillates at two frequencies. This mode of operation allowssimultaneous tight confinement of ions with extremely different charge-to-massratios, e.g., singly ionised atomic ions together with multiply chargednanoparticles. We derive the stability conditions for two-frequency operationfrom asymptotic properties of the solutions of the Mathieu equation and give ageneral treatment of the effect of damping on parametric resonances.Two-frequency operation is effective when the two species' mass ratios andcharge ratios are sufficiently large, and further when the frequencies requiredto optimally trap each species are widely separated. This system resembles twocoincident Paul traps, each operating close to a frequency optimized for one ofthe species, such that both species are tightly confined. This method ofoperation provides an advantage over single-frequency Paul traps, in which themore weakly confined species forms a sheath around a central core of tightlyconfined ions. We verify these ideas using numerical simulations and bymeasuring the parametric heating induced in experiments by the additionaldriving frequency.

Two-frequency operation of a Paul trap to optimise confinement of two species of ions