Phase focusing for finite emittance beams

An accelerator is a prime example of a physical system in which a beam of particles absorbs energy continuously from externally imposed electromagnetic fields only by remaining in, or very close to synchronism with the fields. Traveling-wave amplifiers are another example. When the injected beam has finite emittance, deviations from exact synchronism can arise, usually limiting the ultimate energy exchange with the fields, and the ultimate emittance of an accelerated beam. A general theory is provided in this paper for a means of limiting deviations from exact synchronism. This can be achieved by providing a small space-varying detuning from synchronism for a particle near the center of the distribution, thus allowing otherwise nonsynchronous particles brief opportunities to enjoy synchronism, and thus to limit their excursions in phase. To illustrate, an example is given of two-stage cyclotron autoresonance acceleration of a finite emittance beam, with and without detuning in the first stage. Space-varying detuning is shown to provide phase focusing in the first stage, lower phase spread at the entrance of the second stage, and thus higher ultimate energy. copyright 1999 American Institute of Physics