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

Abstract

We describe the operation of an electrodynamic ion trap in which the electric quadrupole field oscillates at two frequencies. This mode of operation allows simultaneous tight confinement of ions with extremely different charge-to-mass ratios, e.g., singly ionised atomic ions together with multiply charged nanoparticles. We derive the stability conditions for two-frequency operation from asymptotic properties of the solutions of the Mathieu equation and give a general treatment of the effect of damping on parametric resonances. Two-frequency operation is effective when the two species' mass ratios and charge ratios are sufficiently large, and further when the frequencies required to optimally trap each species are widely separated. This system resembles two coincident Paul traps, each operating close to a frequency optimized for one of the species, such that both species are tightly confined. This method of operation provides an advantage over single-frequency Paul traps, in which the more weakly confined species forms a sheath around a central core of tightly confined ions. We verify these ideas using numerical simulations and by measuring the parametric heating induced in experiments by the additional driving frequency.

Analytical Approximate Solution of a Coupled Two Frequency Hill's Equation

“…To obtain single frequency solutions one can simply substitute q r = 0 and keep η away from 1. In most of the practical settings [7,15], the value of η is substantially higher than 1, a regime wherein the analytical solutions are a good match to the numerical solutions.…”

“…Such a coupled system has recently gained importance to study the electrodynamics of charge particles relevant to particle confinement using two radio frequencies [7,15] in a combinational trap utilizing features of both Paul and Penning trap. In context to such a trapping, coefficients a, q 1 , q 2 are proportional to the applied electrostatic DC and RF (radio frequency) and p is the proportional to the applied magnetic field.…”

Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

“…Ref. [43] describes an electrodynamic ion trap in which the electric quadrupole field oscillates at two different frequencies. The authors report simultaneous tight confinement of ions with extremely different charge-to-mass ratios, e.g., singly ionized atomic ions together with multiply charged nanoparticles.…”

Cold ion chemistry within Coulomb crystals

“…Ions as small as H + 2 [63] and as large as protonated glycyrrhetinic acid (C 30 H 47 O + 4 ) [9] have been incorporated into Coulomb crystals with laser-cooled Be + and Ba + ions (respectively). The simultaneous tight confinement of ions with 'extremely' different mass-to-charge ratios has recently been proposed using a two-frequency Paul ion trap [64]. In the two-frequency mode of operation, the electric quadrupole field oscillates between the optimal trapping frequencies required for each of the species, thereby confining both ions tightly and lifting the upper limit on the mass-to-charge ratio of the sympathetically cooled species.…”