Spontaneous and stimulated radiation of particles in crystalline and nanotube undulators

In this paper, we are investigating the influence of the medium polarization on the radiation produced by the channeled positive particles in crystalline undulators (CU) and nanotube undulators (NU) without taking into account the multiple scattering and dechanneling of particles. The intensity of this crystalline undulator radiation (CUR) and nanotube undulator radiation (NUR) may exceed the intensity of usual undulator and channeling radiation, because the oscillation amplitudes of the particles in CU and NU are much larger than the amplitudes of channeling motion, while the oscillation periods are much shorter than in case of usual undulators. It is shown that, taking into account the polarization of the medium the spontaneous CUR and NUR have an energy threshold in the X-ray region, they can have quasimonochromatic spectrum and are emitted in narrow angular cones. When the density and energy of the beam of relativistic particles channeled in CU or NU exceed certain values one obtains stimulated CUR (SCUR) or NUR (SNUR). The gain of SCUR as well as its dependence upon the CU or NU parameters and especially upon positron beam energy spread are studied. We give the results of numerical calculations for CUR for existing positron beams as well as for SCUR for positron beams expected at the future linear colliders. We discuss the possibility of obtaining stimulated amplification of spontaneous emission (SASE) in CU or NU. (C) 2001 Elsevier Science B.V. All rights reserved.