<title>Number of photons and brilliance of the radiation from a crystalline undulator</title>

Abstract

The scheme for accurate quantitative treatment of the radiation from a crystalline undulator in presence of the dechanneling and the photon attenuation is presented. The number of emitted photons and the brilliance of electromagnetic radiation generated by ultra-relativistic positrons channeling in a crystalline undulator are calculated for various crystals, positron energies and different bending parameters. It is demonstrated that with the use of high-energy positron beams available at present in modern colliders it is possible to generate the crystalline undulator radiation with energies from hundreds of keV up to tens of MeV region. The brilliance of the undulator radiation within this energy range is comparable to that of conventional light sources of the third generation but for much lower photon energies.

Channeling and Radiation in Periodically Bent Crystals

“…The results of calculations [162,164] carried out for the (111) planes in diamond, silicon and germanium, and for (110) plane in tungsten, are presented in Fig. 5.…”

“…Initially, the influence of the dechanneling and attenuation was analyzed in detail for a positron-based CU [114,153,156,158,161,162,166,186] as well as for CUs based on channeling of heavier positively-charged ultra-relativistic projectiles (μ + -mesons, protons, heavy ions) [156,160,161,167]. For a negatively-charged projectile, e.g., an electron, it was pointed out in [156,161] and has become commonly accepted, that the concept of CU can not be realized due to a severe limitation of L due to the strong dechanneling of electrons.…”

“…Below in this section we describe a model [162] which allows one to carry out a qualitative analysis of this influence. In a CU the particles can dechannel and, thus, be lost for further motion through the undulator.…”

“…15 The energy ω 1 of first harmonic of UR emitted in the forward direction versus undulator period λ u for the crystalline undulators described by Fig. The frequency ω ch of the ChR is estimated as ω ch ≈ 2γ 2 Ω ch with the frequency of the channeling oscillations found using the harmonic approximation to the interplanar potential: Most of the important conditions (4.60) were realized and carefully investigated in [114,153,156,157,158,161,162,164,166,171,183,187] where realistic numerical calculations of the characteristics of CUR were performed as well (these are discussed below in Chaps. The horizontal lines mark the values of the channeling radiation energy.…”

“…It is seen that for all energies the dechanneling length for a positron exceeds that for an electron by more than an order of magnitude: L e + d /L e − d ∝ 10 1 −10 2 [193]. In this case it is possible to achieve large number of of undulator periods within the dechanneling length N d ∝ 10 1 −10 2 [161,162], which results in λ u lying within the range λ u = 10 1 −10 2 µm. 4.5 and 4.6, a positron-based CU can be considered for ε ≤ 5−10 GeV, where the radiation length greatly exceeds L d .…”