Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
Total yield of channeling radiation from relativistic electrons in thin Si and W crystals
Introduction
Since its discovery channeling radiation (CR) has been considered as a powerful and brilliant x- and gamma-ray source which, for instance, provides one of the promising techniques to be used for production of low-emittance positron beams (see, in the review [1]). Due to the direct dependence of emitted radiation on crystal thickness, known theories, calculations and most of experiments were mainly performed for thick crystals in order to obtain the maximal total yield CR (YCR) (integrated over emission angles and photon energies) [2], [3], [4], [5], [6], [7].
Besides, other applications of CR are possible and should be investigated. For example, YCR is sensitive to the crystal alignment and initial angular spread of electron beam. Earlier work on this subject was devoted to the calculations of CR intensity of electrons with energy below 1 GeV by semiclassical Baier–Katkov method [2]. Also YCR was studied for 1 GeV electrons in the framework of classical electrodynamics using the multistring model (axial channeling) [8]. The main goal of the work analyzed in [8] was investigation of local ionization and radiation energy loss as a function of penetration depth aiming at the “flux peaking effect” studies.
In our investigations we focus on YCR orientation dependence, namely, in dependence of YCR on the angle of incidence with respect to the crystal axes or planes. We have performed YCR calculation for different moderate relativistic energies corresponding to the following electron facilities: 155 MeV SPARC LNF (Italy), 255 MeV linear accelerator of SAGA Light Source synchrotron (Japan), 855 MeV Mainz Microtron MAMI (Germany). Our studies were also justified by new experimental programs on interaction of electrons with crystals. Using the computer code BCM-1 [9], we carried out computer simulations of trajectories and YCR for both 〈1 0 0〉 axial and (1 0 0) planar channeling in Si and W crystals taking into account the angular divergence of initial electron beam. The possibility to align thin crystals using the orientation dependence of YCR is confirmed by detailed quantitative calculations.
Section snippets
Simulation of electrons trajectories and total yield of CR
The electrons trajectories at both axial and planar channeling are determined by the periodic crystal potential U(r⊥), where r⊥ (x,y) is the transverse radius-vector of electron (in the case of planar channeling a vector r⊥ has only one component x). We consider (1 0 0) and 〈1 0 0〉 channeling in Si and W crystals. The potential energy of 〈1 0 0〉 channeled electron in W is calculated using the Doyle-Turner approximation [10] and presented in Fig. 1a. In order to find the trajectories of electrons,
Energy and orientation dependence of total CR yield (YCR)
To investigate the dependence of YCR on the incident angle of electrons with respect to the channeling axis or plane (orientation dependence) we have calculated YCR for every trajectory (for different entry points, see in Fig. 3), and averaged over all N trajectories:
Fig. 4a shows normalized to the maxima averaged YCR from electrons at (1 0 0) planar channeling in Si crystal: curve 1 – result of our simulation, curve 2 represents result of calculation using Baier–Katkov method [2]
Conclusions
We developed the model and computer code which allows us to get the quantitative results for orientation dependence of channeling radiation. The obtained results can be applied for crystal alignment in channeling experiments and/or for diagnostics of initial angular divergence of electron beam. The analysis was performed for 155–855 MeV relativistic electrons channeled in the thin Si and W crystals. As a result we have shown that calculated orientation dependence of CR total yield in a thin
Acknowledgements
The authors are grateful to H. Backe for helpful discussions. This work was supported by the Russian Fund for Basic Research within the Grant No. 10–02–08607 and Grant of the President of RF No. МК–237.2013.2.
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2015, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsCitation Excerpt :Thus, for the correct calculation of the yield of positrons in the range of energy up to 2 MeV one need to take into account the contributions of both types of radiation. For the comparison of the axial CR intensity (Fig. 2b) and the BS intensity (Fig. 2c) we involve total yield of radiation [18]. The total yield of BS is twice larger than the total yield of axial CR, but the axial CR spectrum is almost 20 times narrower than BS spectrum, so the maximum of axial CR spectrum is expected to be 10 times larger than the maximum for BS spectrum.
Angular distributions of relativistic electrons under channeling in half-wavelength crystal and corresponding radiation
2015, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsCitation Excerpt :At the same time, the electrons under such conditions are influenced less by the crystal planes (moving in a weak electric field) and have minimal acceleration, it explains the difference between the spectra in the absolute value. This behavior of the emission spectra depends on the type of trajectory and looks similar to channeling radiation spectrum [11–14], except the low number of oscillations N in the case of HWC channeling. Calculated spectral distributions of the radiation intensity in a forward direction (θ = 0°) from electrons channeled in Si HWC, averaged over the points of entry into the crystal, are presented in Fig. 5.
Simulation code for modeling of coherent effects of radiation generation in oriented crystals
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