Total yield of channeling radiation from relativistic electrons in thin Si and W crystals

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Abstract

Orientation dependences of channeling radiation total yield from relativistic 155–855 MeV electrons at both 〈1 0 0〉 axial and (1 0 0) planar channeling in thin silicon and tungsten crystals are studied by means of computer simulations. The model as well as computer code developed allows getting the quantitative results for orientation dependence of channeling radiation that can be used for crystal alignment in channeling experiments and/or for diagnostics of initial angular divergence of electron beam.

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:ΔE=1Ni=1NΔEi

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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