Other parameters listed in the

Other parameters, listed in the table, describe the so-called dechanneling length [1], i.e. the average distance traveled by a positron in channeling mode. The parameter is defined as the average distance traveled by a trapped particle from entering the crystal until exiting the channel. In other words, the averaging is over the distance traveled by the trapped particle in the first segment of channeling. From the results it is clear that for a straight crystal this distance is only slightly less than the length of the crystal. This means that the positron trapped in the channel upon entering travels through nearly the entire crystal while staying in a single channel. The value of practically does not change with an increase in crystal bending up to C = 0.1, and decreases with a further increase of C. The listed statistical error caused by the finite value of N0 simulated tracks matches the confidence probability of 0.999. The particle exiting the channel due to collisions either loses its channeling properties or may be trapped into another channel and continue to propagate along it. This is also called rechanneling. This is why it is often necessary to introduce one more channeling length that is obtained by averaging all the channeling segments [1]. However, as the length of the crystal is small, the contribution of rechanneling is insignificant and has virtually no influence on the distance traveled by a particle in the channel. is a more general parameter determining the channeling length of a positron averaged for all incident particle tracks. This parameter decreases rather rapidly with the increase of C, owing to two factors: a decrease in particles trapped in the channel and a decrease in the channeling length . The obtained particle tracks allow to calculate their emission spectra using Eqs. (7) and (8). The resulting emission spectra, obtained by averaging over all simulated tracks, can be seen in Figs. 1 and 2. Curve maxima in the vicinity of 3–4 MeV are associated with the channeling ccr2 antagonist of the positrons experiencing transverse oscillations when propagating along the channel. Segments of particles traveling in a single channel make the largest contribution to the spectrum in this region of frequencies, and the radiation intensity is proportional to the segment length. For a straight crystal (curve 1) the maximum has the highest value, but as the bending of the crystal increases, the value decreases. The decrease in dechanneling length and trapping parameter as the bending of the crystal increases are the main cause of the decrease in radiation intensity in this region of the spectrum [34]. While the bending is low and the mean distance traveled in the channel is approximately equal to the length of the crystal (see Table 1 and Fig. 1), the height of the maximum decreases insignificantly. However, for a radius R = 0.4 cm (С = 0.3, curve 5 in Fig. 1), the height decreases by 5 times, and for С = 0.8 the maximum for 3–4 MeV practically vanishes. Another feature of the emission spectrum is the maximum appearing in the low-frequency region in bent crystal channeling. Its occurrence is associated with the synchotron radiation of a channeling particle that not only experiences transverse oscillation but also moves along the axis of a bent channel. The radiation in this region of the spectrum is naturally absent for a straight crystal but first occurs and then grows in intensity with the increase of the bending parameter C (see Fig. 1). In Fig. 2 the region of synchrotron radiation is shown for high values of C on a larger scale. As C increases in value, the synchrotron maximum also increases, and for C = 0.3 dominates the full radiation spectrum. However, with the further increase of the bending parameter the maximum starts to decrease in height, thus shifting towards higher energies (curves 4 and 5 in Fig. 2). A decline in intensity is associated with a decrease in the number of particles trapped into the channel. An increase of the bending parameter C or a decrease in the bending radius R leads to the spectral maximum shifting to the high-frequency region.