# Keplerian motion of particles with permanent electric dipole within cylindrical coaxial electrodes

## TL;DR

This paper investigates trapping particles with permanent electric dipoles in cylindrical electrostatic fields, revealing Keplerian orbits and establishing criteria for stable trapping using dimensionless parameters and numerical methods.

## Contribution

It introduces the first detailed analysis of Keplerian orbits for electric dipoles in cylindrical electrodes and develops a numerical interpolation method for complex cases.

## Key findings

- Keplerian orbits exist for certain dipole particles within cylindrical electrodes.
- A dimensionless criterion for successful trapping on closed orbits is derived.
- A numerical interpolation method for local electric field maps is proposed.

## Abstract

A research on a possibility of trapping a particle with permanent electric dipole in an electrostatic field has been conducted. For cylindrical coaxial electrodes, Keplerian orbits for some particles were revealed. The exact criterion of successful trapping on a closed orbit within the electrodes is expressed in dimensionless parameters. For more complicated cases where the exact solution is unknown, a useful tool for numerical solution -- local field map interpolation with continuous first derivatives -- is constructed.