Recent progress in the theory of the crystalline undulator

If an ultrarelativistic charged particle channels inside a single crystal with periodically bent crystallographic planes, it emits hard electromagnetic radiation of the undulator type. Due to similarity of its physical principles to the ordinary (magnetic) undulator, such a device is termed as the crystalline undulator. Recent development of a new Monte Carlo code ChaS made possible a detailed simulation of particle channeling and radiation emission in periodically bent crystals. According to recent findings, energy of the electron beam below 1 GeV is sufficient to observe the undulator effect in a periodically bent crystal. Even more exciting results were obtained for a crystalline undulator whose bending period is shorter than the period of the channeling oscillations and the bending amplitude is smaller than the width of the planar channel. Such a crystalline undulator is far superior to what was proposed previously. It allows for a large effective number of undulator periods. Therefore, it is predicted to emit intense undulator radiation in the forward direction. A narrow undulator peak is seen for both positron and electron beams. Using positrons is, however, more desirable because in this case the intensity of the undulator radiation is higher while the background is lower.