External field-induced dynamics of a charged particle on a closed helix

TL;DR

This paper studies how external electric fields influence the chaotic dynamics and directed transport of a charged particle constrained on a toroidal helix, revealing mechanisms for controlling particle motion.

Contribution

It introduces new insights into the phase space structure and transport phenomena of a charged particle on a helix under time-dependent electric fields, highlighting mechanisms for directed transport control.

Findings

Chaotic phase space splits prevent velocity inversion at low amplitudes.

Average transport velocity remains constant with increasing driving amplitude.

Large amplitudes enable trajectories to cross chaotic regions via permeable cantori.

Abstract

We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split-up of the chaotic part of the phase space which prevents the particle from inverting its direction of motion. This allows for a non-zero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport. Within our chosen normalized units, the resulting average transport velocity is constant and does not change significantly with the driving amplitude. A very similar effect is found in case of the circularly polarized field and low driving amplitudes. Furthermore, when driving with a circularly polarized field, we unravel a second mechanism of the split-up of the chaotic phase space region for very large driving amplitudes. There exists a wide range of parameter values for which trajectories may travel between the two chaotic regions by crossing a permeable cantorus. The limitations of these phenomena, as well as their implication on manipulating directed transport in helical geometries are discussed.