Analytical study of electrostatic ion beam traps

TL;DR

This paper introduces an analytical method using conformal mapping to accurately calculate electrostatic potentials in axisymmetric ion traps, enabling optimized trapping conditions at higher energies.

Contribution

It presents a general analytical approach for electrostatic potential calculation in axisymmetric traps, improving tuning efficiency and trapping performance.

Findings

Developed an analytical formula for potential inside ion traps.

Achieved stable trapping of oxygen 4+ ions at higher energies.

Provided stability maps for optimal electrode potentials.

Abstract

The use of electrostatic ion beam traps require to set many potentials on the electrodes (ten in our case), making the tuning much more difficult than with quadrupole traps. In order to obtain the best trapping conditions, an analytical formula giving the electrostatic potential inside the trap is required. In this paper, we present a general method to calculate the analytical expression of the electrostatic potential in any axisymmetric set of electrodes. We use conformal mapping to simplify the geometry of the boundary. The calculation is then performed in a space of simple geometry. We show that this method, providing excellent accuracy, allows to obtain the potential on the axis as an analytic function of the potentials applied to the electrodes, thus leading to fast, accurate and efficient calculations. We conclude by presenting stability maps depending on the potentials that enabled us to find the good trapping conditions for oxygen 4+ at much higher energies than what has been achieved until now.