Crystalline undulator with a small amplitude and a short period

The crystalline undulator is a single crystal with periodically bent crystallographic planes. If ultrarelativistic charged particles channel through such a crystal, they emit hard radiation of undulator type. A crystalline undulator with a bending amplitude smaller than the distance between the bent planes and a bending period shorter than the period of channeling oscillations is proposed. Heretofore, it was believed that such a range of bending parameters was unsuitable for a crystalline undulator. This point of view is refuted. In fact, the undulator with a small amplitude and a short period is far superior to what was proposed previously. It requires much lower beam energy for production of photons of the same frequency. Such an undulator allows for a larger effective number of undulator periods. It is predicted to emit intense undulator radiation in the forward direction with a narrow spectral distribution and a lower and softer background. The undulator effect is seen for both positron and electron beams. Using positrons is, however, preferable because they enable one to obtain higher intensity of the undulator radiation with lower background.