Transition free-electron laser (amplifier) driven by an electron bunch

Abstract

A theory of transition free-electron laser ͑FEL͒ driven by an electron bunch of finite longitudinal length is presented. It is shown that one can introduce concepts of a long, a short, and a very short bunch depending on the degree of correlation between the bunch effective length and the transition radiation formation length. It is obtained that a long Gaussian bunch produces an electromagnetic pulse with a double-exponent-type envelope exp͓exp(Ϫ 2 )͔, whereas in the short bunch case the latter has an oscillating nature. Both analytic and numerical studies show that the long bunch compression into the short one improves the bunch-field coupling and results in the enhancement of the logarithm of a gain at the pulse center by nearly one order. The further bunch compression leads to the gain vanishing. It is noted that a similar picture is probably possible for an undulator FEL. The results are generalized for a bunch train. ͓S1063-651X͑99͒06103-6͔ PACS number͑s͒: 41.60.Cr Electromagnetic waves produced by the passage of a charged particle through the interface between two media with different dielectric constants are known as transition radiation ͑TR͒ ͓1͔. In contrast to the Cherenkov effect ͓when the radiated frequencies are limited by n()Ͼ1 condition͔ and to the Compton ͑or undulator͒ effect ͑where the frequencies are bounded both by the wavelength of a pump wave and by the energy E of an electron beam͒, in the device there are no restrictions on frequency values ͑of course, except for an obvious condition បϽEϪmc 2 ͒. Hence the transition radiation seems to be a very suitable source for a tunable free-electron laser ͑FEL͒. An analysis of single-particle spontaneous TR has been done in a great number of both theoretical and experimental works and generalized in monographs ͓2-4͔. Coherent TR, produced by an electron bunch ͑e bunch͒ with a length l, which is of the order of or smaller than the emission wavelength , was studied in ͓5͔. Reference ͓6͔ marked the beginning of studies of the stimulated transition effect. A number of both linear and nonlinear effects considered in our papers ͑including a charged particle acceleration, an e beam modulation and polarization, and an electromagnetic wave amplification, for such configurations as a single interface, a dielectric plate, a resonant medium͒ were summarized in Ref. ͓7͔, Sec. III. Here one can find a number of references in the field as well. Our analysis showed ͓7͔ that a notable gain in a transition laser ͑TL͒ driven by an ordinary e beam could be achieved in a lowfrequency range. Interesting ways of the FEL gain increasing in a high-frequency range have been discussed in ͓8,9͔. Note that there is a well-known approach for the transition effect increasing based on a resonant medium ͓2,3͔. The possibilities for such a device application for the ultraviolet and x-ray FEL were considered in ͓10-12͔.As was shown in ͓7͔, in a space-heterogeneous medium one may consider a monochromatic amplified signal as a superposition of plane waves which have the same frequency, b...