Fixed-Field Alternating-Gradient Particle Accelerators

TLDR

Alternating‑gradient focusing enables circular accelerators with constant magnetic guide fields that support stable orbits across all energies, offering simpler construction, higher output currents, and design formulas from a linear‑approximation orbit theory. These principles are applied to design fixed‑field synchrotrons, betatrons, and high‑energy cyclotrons. Two magnetic field patterns are described: the radial‑sector pattern, which is easier to understand and construct, and the spiral‑sector pattern, which yields a much smaller accelerator for a given energy.

Abstract

It is possible, by using alternating-gradient focusing, to design circular accelerators with magnetic guide fields which are constant in time, and which can accommodate stable orbits at all energies from injection to output energy. Such accelerators are in some respects simpler to construct and operate, and moreover, they show promise of greater output currents than conventional synchrotrons and synchrocyclotrons. Two important types of magnetic field patterns are described, the radial-sector and spiral-sector patterns, the former being easier to understand and simpler to construct, the latter resulting in a much smaller accelerator for a given energy. A theory of orbits in fixed-field alternating-gradient accelerators has been worked out in linear approximation, which yields approximate general relationships between machine parameters, as well as more accurate formulas which can be used for design purposes. There are promising applications of these principles to the design of fixed-field synchrotrons, betatrons, and high-energy cyclotrons.