Traveling Wave Undulators for FELs and Synchrotron Radiation Sources

We study the use of a traveling wave waveguide as an undulator for short wavelength free-electron lasers (FELs) and synchrotron radiation sources. This type of undulator -which we will call TWUcan be useful when a short electron oscillation period and a large aperture for the propagation of the beam are needed. The availability of high power X-band microwave sources, developed for the electron-positron linear collider, make it possible today to build TWUs of practical interest to produce short wavelength radiation from a beam of reduced energy respect to the case of more conventional undulators. In this paper we will discuss the characteristic of the TWU, the systems that can be used to control the effects of RF power losses in the waveguide walls, and how to optimize a TWU and the associated electron transport system for use in a synchrotron radiation source or FEL. Microwave undulators have been considered before in a standing wave configuration [1], [2]. Measurements of the spontaneous undulator radiation when propagating a beam with energy of 143 or 220 MeV through the undulator have also been reported in reference[1]. A discussion of the parameters of radio frequency undulator in various configurations has also been made recently in reference [3 ]. The use of a radio frequency wiggler operating at 30 GHz, as a damping device in a damping ring for a linear collider has been considered in reference [4]. In this paper we discuss a traveling wave, radio frequency undulator operating at 12 Ghz. The reason for the choice of this frequency is that high power RF sources operating near this frequency, and pulse compression techniques have been developed as part of the international linear collider R&D [5]. Using these sources and pulse compression, power level as high as 450MW are now available, with pulse duration of hundreds of nanoseconds. This power level makes possible to consider a traveling wave, radio frequency undulator (TWU) as a a practical and interesting part of linac based synchrotron radiation sources and free-electron lasers. As we will discuss in the following undulator parameter values of the order of 0.4 for an undulator period of 1.45 cm are possible. The corresponding waveguide transverse size is about 1.8 cm. Some of the advantages of a TWU are: short undulator period; the possibility of