1 Introduction
The idea of a fixed field alternating gradient (FFAG) accelerator is not new. It was invented in the
1950s right after the alternating gradient (AG) synchrotron came out [1, 2]. Instead of using pulsed
magnets as in a synchrotron, FFAG accelerators use constant field magnets like cyclotrons. Unlike
cyclotrons, however, FFAGs rely on AG focusing so that the beam size can be much smaller. In the
literature [1], there are accelerators described as FFAG betatrons, FFAG cyclotrons and FFAG
synchrotrons. This is a little confusing and in these cases, FFAG refers merely to the focusing scheme
based on so-called cardinal conditions, which we discuss later. Here we use the terms “FFAG
accelerator” or “FFAG” to mean accelerators using the FFAG focusing scheme.