Constant-tune cyclotrons

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 γ, 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.

Cyclotrons: Why/how are their dynamics different?

“…This in general results in tunes that vary with energy; in particular, the radial tune will be nearly equal to 𝛾 since the radial focusing depends mainly on the field gradient and this in turn results to lowest order from the isochronism scaling condition [27]. As Planche shows, to flatten the radial tune requires unconventional magnet designs, but is in principle still possible [31].…”

“…A difficult feature of cyclotrons is that the radial tune usually varies with radius. With the simplest sector focusing, the radial tune is approximately equal to 𝛾. Planche has found a way that in principal can overcome this feature, but no magnets have been designed to check its feasibility [31]. As Kleeven shows [27], the number of sectors of a cyclotron must be chosen to avoid the half-integer intrinsic stopband at top energy.…”

High-power Fixed-Field Accelerators

“…This paper is a concise summary of the more detailed white-paper report of the workshop [25]. Subsequent to the workshop, an issue dedicated to the dynamics of high-power and high-energy cyclotrons was also published in International Committee for Future Accelerators (ICFA) Newsletter series [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”