4. Radiation, diffraction and channeling of charged particles
This activity had begun in our laboratory in the early 1970s. The channeling is the phenomenon very close by nature to dynamical diffraction of charged particles. At first, a new kind of electromagnetic radiation (the pendulum radiation) of diffracted in a single crystal electrons was predicted (V.V.Fedorov, 1972) and theoretically investigated (V.V.Fedorov, K.E.Kiryanov, A.I.Smirnov [66-68]). The advanced researches of the pendulum radiation have shown that it may be completely similar (for electrons with energies up to a few MeVs) to the radiation of oscillating multipoles, moving through the refractive medium with the "circaluminal" and "superluminal" velocities (the magnetic and electric dipole as well as the electric quadrupole radiation takes place simultaniously, for example, in the case of 4-wave electron diffraction) [68-70]. It has also been shown  that the dependence on the radiation direction of frequency is determined by either normal, or anomalous Doppler effect for photons emitted by the "superluminal" particles. This was the first case giving a real possibility to study this phenomenon predicted by I.M.Frank as early as 1942.
The first results [66-68] stimulated an appearance in 1975 of the work devoted to analogous radiation of the channelling particles (A.A.Vorobiev, V.V.Kaplin, S.A.Vorobiev (Tomsk group), NIM, 1975, 127, 265). Later in 1976 two more works on channeling radiation were published practically simultaneously (V.G.Baryshevskii, I.Ya.Dubovskaya (Minsk), DAN SSSR, 1976, 231, 1335; M.A.Kumakhov (Moscow), Phys. Lett., 1976, 57A, 17). These works in turn gave rise to numerous further theoretical and experimental investigations of such a kind of radiation as well as to very active polemics and controversy (including the priority one) between different scientific groups (sometimes the polemics was not purely scientific).
In 1979 O.I. Sumbaev (see [71-74]) had paid attention that for curved crystal the phenomenon of vol-ume capture into the channeling mode for the proton beam could take place like as the X-rays in the bent crystal can find in the volume the point, where the Bragg condition is satisfied. It should increase essentially the capture angle into the channeling regime just in the same way as the quasimosaicity does for diffraction angles in the case of the X-ray diffraction in the elastically deformed crystals.
This phenomenon was confirmed experimentally at the PNPI accelerator . That opened new possibility to increase the intensity of channeling particles by use of the beams with the angular divergence exceeding the Lindhard angle more than two orders of magnitude and allowed to carry out a number of experiments with the channeling particles, in which new interesting results were received. For registration of the channeling particles the unique installation  was created, combining the working bent crystal with a few semiconductor detectors realized at the same crystal. The fact of a particle channeling was detected by a small value of signal from ionization losses in all detectors (see Figs. 16, 17).
Fig. 16. Three semiconductor detectors SD1, SD2, SD3are realized on the bent crystal of silicon, through which the particles are channeling ("alive target" )
Fig. 17. Effect of volume capture. Dependences of number of particles with a small signal amplitude in SD1, SD2, SD3 on the angle of a crystal turn. These distributions are much wider then the Lindhard angle (» 0.12 mrad), that testifies the presence of capture of protons into a channelling mode on the whole length of the bent crystal
Using the effect of the volume capture and the mentioned installation, new phenomena of different kinds of focusing a beam of the high-energy particles was experimentally observed [75,76]. Recently, using the new crystal installation created in our institute, it turned out to be possible to carry out the experiment at FNAL accelerator (Batavia, USA)  on the determination of the magnetic moment of the S+-hyperon, by measuring its spin rotation angle after channeling in the bent single crystal (such a spin rotation was predicted earlier by V.G.Baryshevskii). The results of this experiment (directed by V.M.Samsonov) are as fol-lows: 1) the existence of the effect of spin rotation in channeling was first demonstrated, 2) the new method of measuring the anomalous magnetic moments of relativistic particles was developed, and 3) the magnetic moment of the S+-hyperon was first measured by this a method.
The study of channeling phenomena was further developed in the works carried out under direction of A.I.Smirnov. The phenomenon of focusing a proton beam is predicted and experimentally observed for 70 GeV protons channeling in the bent crystal with a special cut of the face side of the crystal plate . In works [78,79], this phenomenon is experimentally confirmed. The linear sizes of the beam in the focus have been 15x0.05 mm2. Installation of the second crystal, the focus of which is combined with the focus of the first one, has allowed to transform a linearly-focused (divergent) beam into the parallel one (in a horizontal plane) at the exit from the second crystal. The technology of manufacturing the deflecting and focusing crystal devices for needs of the crystal optics of the charged particle beams (see Fig. 18) is developed.
The works on channeling were awarded by the State Prize of the Russian Federation in the field of a science and engineering.
Fig. 18. The possible scheme of application of focusing crystal for outgoing of beam of secondary particles from the accelerator
The X-ray tomograph of detectors for the high energy physics [80,81] are created and tested. The narrow diffraction beam of X-rays formed by a crystal with a given coordinates and detected by some detectors allows to measure the position of wire of this detector with the accuracy better than 1 mm. The setup is used now in designing detectors for LHC (CERN).