Speaker
Prof.
Hartmut Backe
(Institute for Nuclear Physics)
Description
The formula of Baier et al. for the de-channeling length of electrons in single crystals
Lee = 2U_0 pvX_0/E_s^2 [1] was frequently used for a comparison with various calculations, including simulation calculations. It will be pointed out in this contribution, that the fundamental parameter E_s^2 = (2π/α) (m_ec^2)^2 = (15 MeV)^2 must be replaced by E_s = 10.6 MeV if thin crystals are used. The same parameter Lde appears also as a scaling length in the Fokker-Planck equation if written in a dimensionless form. This fact has the consequence that both, the formula of Baier et al. as well as the solution of the Fokker-Planck equation, overestimate the de-channeling length by more than a factor of two in comparison with recent simulation calculations, e.g. [2].
It is well known that in the photon spectra of diamond at electron beam energies below 110.2 MeV pronounced line structures appear. Such structures were recently also observed at a beam energy of 195 MeV at the Mainz Microtron MAMI [3]. Since it is an open question whether quantum state phenomena may enhance the de-channeling length even at such high beam energies, we performed de-channeling length measurements for plane diamond single crystals. The analysis requires model assumptions. We rely on the solution of the Fokker-Planck equation for plane crystals. In addition, results obtained for silicon [4] have been reanalysed.
The Fokker-Planck equation has been modified also for bent crystals [5]. Measurements at the National Accelerator Laboratory SLAC, USA, at electron beam energies in the multi-GeV range for a bent (111) silicon single crystal (bending radius 0.15 m) [6] can be reproduced. This result provides confidence to apply solutions also for a typical bending radius of 6.6 mm for our Si_1-xGe_x undulator crystal in (110) orientation (four periods with 9.9 µm each) resulting in small de-channeling lengths at MAMI beam energies in accord with observations [7].
References
1. V.N. Baier, V.M. Katkov and V.M. Strakhovenko, Electromagnetic Processes at High Energies in Oriented Single Crystals, World Scientific Publishing, Singapore (1998), p. 250
2. A.V. Korol, V.G. Bezchastnov, and A.V. Solov’yov, Eur. Phys. J. D 71 (2017) 174
3. H. Backe, W. Lauth, and Thu Nhi TRAN THI, JINST 13 (2018) C04022
4. H. Backe and W. Lauth, Channeling experiments with sub-GeV electrons in flat silicon single crystals, Nucl. Instrum. Meth. B 355 (2015) 24
5. H. Backe, JINST 13 (2018) C02046
6. T.N. Wistisen, U.I. Uggerhøj, U. Wienands, T.W. Markiewicz, R.J. Noble, B.C. Benson et al.,
Phys. Rev. Accel. Beams 19 (2016) 071001
7. H. Backe et al., Nucl. Inst. Meth. Phys. Res. B 309 (2013) 37,
and Journal of Physics: Conference Series 438 (2013) 012017
Primary author
Prof.
Hartmut Backe
(Institute for Nuclear Physics)
