Nonlinear Integrable Ion Traps

TL;DR

This paper demonstrates how to transform quadrupole ion traps into nonlinear, integrable systems with adjustable potentials, enabling stable, regular particle motion in complex trap configurations.

Contribution

It introduces methods to create nonlinear, integrable ion traps with adjustable electrostatic potentials, expanding the design possibilities beyond traditional quadrupole traps.

Findings

Particle motion remains regular and stable across various parameters.

Transformations enable double-well and toroidal-well trap configurations.

Examples include modifications of Penning and Paul traps.

Abstract

Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.