Constant-Tune Cyclotrons

TL;DR

This paper demonstrates that cyclotrons can be designed to maintain constant betatron tunes across wide energy ranges, challenging traditional assumptions about tune variation with energy.

Contribution

The paper introduces a novel technique for calculating betatron tunes from realistic orbit geometries and presents two specific cyclotron designs with constant tunes.

Findings

Horizontal tune can be kept constant independently of gamma.

A compact cyclotron design is validated with 3D finite element calculations.

The method allows for precise tune control over wide energy ranges.

Abstract

In this paper we demonstrate that cyclotrons can be made to have precisely constant betatron tunes over wide energy ranges. In particular, we show that the horizontal tune can be made constant and does not have to follow the Lorentz factor gamma, while still perfectly satisfying the isochronous condition. To make this demonstration we developed a technique based on the calculation of the betatron tunes entirely from the geometry of realistic non-hard-edge closed orbits. We present two particular cyclotron designs, one compact cyclotron and one ring cyclotron. The compact cyclotron design is backed up by a 3-dimensional finite element magnet calculation, that we also present here.