Total spectrum of photon emission by an ultra-relativistic positron channelling in a periodically bent crystal

Abstract

We present the results of numerical calculations of the channelling and undulator radiation generated by an ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due either to the propagation of a transverse acoustic wave through the crystal, or due to the static strain as it occurs in superlattices. The periodically bent crystal serves as an undulator. We investigate the dependence of the intensities of both the ordinary channelling and the undulator radiations on the parameters of the periodically bent channel with simultaneous account for the dechannelling effect of the positrons. We demonstrate that there is a range of parameters in which the undulator radiation dominates over the channelling one and the characteristic frequencies of both types of radiation are well separated. This result is important, because the undulator radiation can be used to create a tunable source of X-ray and γ-radiation.In this Letter we present for the first time the results of calculations of the total spectrum of emitted photons accompanying the channelling process of ultra-relativistic

An electron-based crystalline undulator

“…In [25,26] the dechanneling length for 1.2 GeV electrons, channeled in Si(110) was determined as L d (0) = 25±5 µm. This value, as indicated in [25], is in a good agreement with (5). However, in the experiment [27] the dechanneling length for 350 MeV electrons channeled in Si(110) was found as L d (0) = 31 µm, which is even greater than the value based on (5).…”

“…Wide peak in each graph stands for the spectral distribution of the channeling radiation in the forward direction. To obtain the latter we, at first, calculated the spectra for individual trajectories (using the Pöschl-Teller model [18] for the interplanar potential), corresponding to a stable channeling for given C. Then, the averaging procedure was carried out to calculate the spectra (see [5,6] for the details). Figure 8 clearly demonstrates that by tuning the parameters of bending and varying the electron energy it is possible to separate the frequencies of the undulator radiation from those of the channeling radiation, and to make the intensity of the former comparable or higher than of the latter.…”

“…A thorough analysis of the conditions (1) for the system "periodically bent crystal + ultra-relativistic positrons" was performed for the first time in [2,3] (and analyzed further in [5,6,8,9] ). The ranges of ε, a and λ for a number of crystals were established within which the operation of the crystalline undulator is possible.…”

Spontaneous and stimulated undulator radiation by an ultra-relativistic positron channeling in a periodically bent crystal

“…The quantity L d is called the dechanneling length [5]. To estimate L d one may follow the method described in [6,7]. Thus, to consider the undulator radiation formed in a crystalline undulator, it is meaningful to assume that the crystal length does not exceed L d .…”

“…The trajectories of the particles were calculated numerically and then the spectra were evaluated [7]. The latter include both radiation mechanisms, the undulator and the channeling radiation.…”