Intensity Limit in Compact H$^-$ and H$_2^+$ Cyclotrons

TL;DR

This paper analyzes the intensity limits of compact H$^-$ and H$_2^+$ cyclotrons by examining beam dynamics, scaling laws, and mechanical effects, with reference to existing machines to inform future high-current designs.

Contribution

It provides a detailed review of beam dynamics and scaling laws affecting current limits in compact cyclotrons, including experimental insights from specific models.

Findings

Phase acceptance scales with RF gap voltage and harmonic number

Mechanical erosion impacts electrode longevity and beam stability

Scaling laws differ for H$^-$ and H$_2^+$ ions

Abstract

Compact H$^-$ cyclotrons are used all across the globe to produce medical isotopes. Machines with external ion sources have demonstrated average extracted currents on the order of a few mA, although reported operational numbers are typically around 1\,mA or below. To explore the possibility of extracting even more current from such cyclotrons, it is important to understand the mechanisms that drive intensity limits and how they scale. In this paper we review some of the key aspects of the beam dynamics in the central region of compact cyclotrons, including rf electric focusing and space charge effects. We derive the scaling of the phase acceptance with the rf gap voltage, harmonic number, etc. We also explore the scaling with different types of ions such as H$^-$, H$_2^+$ and H$_3^+$. We discuss the impact of mechanical erosion of the central region electrodes. Thoughout the paper, we use examples and experimental data from two compact H$^-$ cyclotrons for reference: the TR-30 series and the TRIUMF 500\,MeV machine.