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  • In recent series of experiments at Mainzer Microtron with an

    2018-10-26

    In recent series of experiments at Mainzer Microtron [5] with 600 and 855 MeV electrons the effect of a small-amplitude short-period undulator was observed. Another set of experiments with diamond crystalline undulators is planned within the E-212 collaboration at the SLAC facility (Stanford Linear Accelerator Center, USA) with 10–20 GeV angiotensin 2 receptor blocker beam. The current experiments with small-amplitude short-period undulators are based on thin silicon (or diamond) crystals doped with small amount of germanium atoms. These crystals are produced using the Molecular Beam Epitaxy (MBE) technology. The cases of LALP and SASP undulators can be distinguished by the value of the parameter C = ε ∕ (RU′max). In the case of an LALP undulator, the value of this parameter is considered small, C ≪ 1, because the projectile has to follow bends of crystalline planes or axes to produce appropriate radiation. In this case an increase in the bending amplitude leads to an increase in the radiation intensity, but also causes an increase in C being a limiting factor. In SASP undulators the C parameter can also be formally calculated and its value is more than 1. In this case projectiles are unable to follow bends of the crystalline medium. What produces the undulator radiation here is the periodic force acting on the projectile due to the rapid change of the interplanar potential. Then the growth of the bending amplitude also boosts the intensity of radiation but reduces the number of channeling projectiles. The amplitude in this instance is limited to a half of the interplanar distance. In previous papers [10–12] the methodology of simulation of channeling with MBN Explorer was presented and applied for straight and bent crystals for sub-GeV energies. The simulations for multi-GeV energies were also described for bent [13] and periodically bent [6] crystals. MBN Explorer implements a full-atom model of the three-dimensional motion of projectiles in the crystalline medium. In this work, the crystal parameters were taken from experiment [5] as a starting point for the simulations. With these parameters the simulation of propagation of projectiles through the crystals was performed. Using a quasi-classical approach to the calculation of a radiation spectrum the radiation of projectiles was calculated and compared for different crystals. It is shown that for crystals with a thickness less than channeling oscillations period the channeling radiation effect can be suppressed, while undulator radiation can still be generated. The parameters of this radiation are studied numerically.
    Physical model The simulation of propagation of a relativistic projectile in a crystalline medium was performed by solving the classical relativistic equations of motion. The force acting on a projectile was calculated as a sum of its interactions with neighboring atoms of the medium. Each atom of the medium was considered as fixed in space as its velocity is much lower than the speed of projectile. Interaction of the projectile with atoms was modeled using the classical Molière [14] interaction potential for screened charges. The atom positions are conditioned by the crystal grid and random displacement due to thermal vibrations. We took the crystalline grid parameters and thermal vibrations from literature [15]. An accelerated motion of charged projectiles in crystal channels produces radiation which can be characterized by a radiation spectrum differential with respect to the photon energy ℏω and integrated over the given angular aperture θd. The simulated trajectories were used to compute the spectral distribution of the emitted radiation. For each set of simulated trajectories of the total number N0 the spectral distribution emitted within the cone θ < θd with respect to the incident beam was calculated as follows:
    here d3/ℏdωdΩ is the spectral–angular distribution emitted by a particle moving along the jth trajectory.