# Dynamics of an unbalanced two-ion crystal in a Penning trap for application in optical mass spectrometry

## TL;DR

This paper investigates the dynamics of an unbalanced two-ion crystal in a Penning trap, proposing a measurement scheme for optical mass spectrometry by analyzing mode frequencies and discussing potential systematic effects.

## Contribution

It introduces a detailed analysis of unbalanced two-ion crystal dynamics in a Penning trap and proposes a method to determine ion frequencies optically.

## Key findings

- Mode frequencies can be used to determine the target ion's cyclotron frequency.
- Harmonic approximation is valid in the low amplitude regime.
- Non-harmonic Coulomb effects may cause systematic errors.

## Abstract

In this article, the dynamics of an unbalanced two-ion crystal comprising the 'target' and the 'sensor' ions confined in a Penning trap has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron and reduced-cyclotron modes split up into the so-called 'stretch' and 'common' modes, that are generalizations of the well-known 'breathing' and 'center-of-mass' motions of a balanced crystal made of two ions. By measuring the frequency modes of the crystal and the sensor ion eigenfrequencies using optical detection, it will be possible to determine the target ion's free-cyclotron frequency. The measurement scheme is described and the non-harmonicity of the Coulomb interaction is discussed since this might cause large systematic effects.