Particle dynamics in damped nonlinear quadrupole ion traps

Abstract

Articles you may be interested in Erratum: "Averaging peak-to-peak voltage detector for absolute mass determination of single particles with quadrupole ion traps" [Rev. Sci. Instrum.76, 023108 (2005) We examine the motions of particles in quadrupole ion traps as a function of damping and trapping forces, including cases where nonlinear damping or nonlinearities in the electric field geometry play significant roles. In the absence of nonlinearities, particles are either damped to the trap center or ejected, while their addition brings about a rich spectrum of stable closed particle trajectories. In three-dimensional (3D) quadrupole traps, the extended orbits are typically confined to the trap axis, and for this case we present a 1D analysis of the relevant equation of motion. We follow this with an analysis of 2D quadrupole traps that frequently show diamond-shaped closed orbits. For both the 1D and 2D cases, we present experimental observations of the calculated trajectories in microparticle ion traps. We also report the discovery of a new collective behavior in damped 2D microparticle ion traps, where particles spontaneously assemble into a remarkable knot of overlapping, corotating diamond orbits, self-stabilized by air currents arising from the particle motion.

Outside localization around a toroidal electrode of a Paul trap

“…Since the depth of the effective potential is inversely proportional to the frequency, Φ n[1] ∝1/Ω 2 from (16), this configuration is suitable to localize even particles of more than 10 −5 m size [20,33,34]. Localization dynamics of such particles is in agreement with the model of nonlinear damping [20], which allows to estimate the quasi-equilibrium points taking into account cubic nonlinearities (discussed in section 2.2). Figure 4(a) illustrates the experimental realization of a particle localization inside and outside of the Paul trap, which is indicated by areas A and B, correspondingly.…”

“…In sufficiently dense medium, the motion of a charged particle is damped. For instance, it was reported that particles of the size bigger than 10 μm undergo a strong nonlinear friction upon the localization in air, which results in unusual expanded orbits [20].…”

“…To generalize our model, let us consider the effective potential in the presence of a strong friction. In a simplified one-dimensional model case [20], the particle motion is described bÿ…”

“…There are works on the tuning of the trap voltages, for instance, AC voltage parametrizations [18,19]. Trapping can be considered not only in vacuum, but also in viscous gases [20].…”

Multipole electrodynamic ion trap geometries for microparticle confinement under standard ambient temperature and pressure conditions

“…Other relevant quantities are the gas viscosity coefficient µ, the particle diameter d p , the particle mass m, while b represents the geometrical constant of the electrodynamic balance. harmonically confines ions in a region where the field exhibits a minimum, under conditions of dynamic stability 6, 16,22,28,59,75 . As it is almost impossible to achieve quadratic a.c. and d.c. endcap potentials for the whole trap volume, it can be assumed that the potential in the vicinity of the trap axis region can be regarded as harmonic, which is a sufficiently accurate approximation.…”