Confining rigid balls by mimicking quadrupole ion trapping

TL;DR

This paper explores the stability of a rigid ball in a rotating saddle trap, drawing analogies to quadrupole ion traps, and highlights the importance of considering the ball's rigidity and spin in the trapping mechanism.

Contribution

It introduces a rigid-body dynamics approach to analyze ball trapping, providing theoretical stability conditions and experimental verification, differing from traditional mass-point models.

Findings

Rigid-body dynamics reveal larger discrepancies with mass-point models.

The spin of the ball affects stability similarly to ion cyclotron frequency.

Experimental results confirm theoretical stability conditions.

Abstract

The rotating saddle not only is an interesting system that is able to trap a ball near its saddle point, but can also intuitively illustrate the operating principles of quadrupole ion traps in modern physics. Unlike the conventional models based on the mass-point approximation, we study the stability of a ball in a rotating-saddle trap using rigid-body dynamics. The stabilization condition of the system is theoretically derived and subsequently verified by experiments. The results are compared with the previous mass-point model, giving large discrepancy as the curvature of the ball is comparable to that of the saddle. We also point out that the spin angular velocity of the ball is analogous to the cyclotron frequency of ions in an external magnetic field utilized in many prevailing ion-trapping schemes.