Photon Emission by an Ultra-Relativistic Particle Channeling in a Periodically Bent Crystal

Abstract

This paper is devoted to a detailed analysis of the new type of undulator radiation generated by an ultra-relativistic charged particle channeling along a crystal plane, which is periodically bent by a transverse acoustic wave, as well as to the conditions limiting the observation of this phenomenon. This mechanism makes feasible the generation of electromagnetic radiation, both spontaneous and stimulated, emitted in a wide range of the photon energies, from X-up to 7-rays. II Int. J. Mod. Phys. E 1999.08:49-100. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 03/16/15. For personal use only. Int. J. Mod. Phys. E 1999.08:49-100. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 03/16/15. For personal use only.

An electron-based crystalline undulator

“…This quantity can be estimated as L d (0) = (256/9π 2 )(a TF dγ/r 0 Λ c ) [3,19], where r 0 and a TF are the classical radius of the electron and the Thomas-Fermi radius of the crystal atom, and Λ c = ln( √ 2γ mc 2 /I) − 23/24 (I stands for an average ionization potential of the atom). The factor (1 − C) 2 takes into account the decrease of the interplanar potential well due to periodic bendings.…”

“…This quantity is tabulated for a number of elements and over wide ranges of photon frequencies [17]. It is worth noting that for sufficiently high photon energies ( ω ≥ 10 2 keV) the restriction on the length of undulator due to the photon attenuation effect becomes much less severe than to the dechanneling process [2,3,8].…”

“…Since for an ultra-relativistic particle L d ∝ ε [18][19][20], it seems natural that to increase N d one can consider higher energies. However, at higher energies another limitation appears [2,3,6]. The coherence of undulator radiation is only possible when the energy loss ∆ε of the particle during its passage through the undulator is small, ∆ε ≪ ε.…”

“…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.…”

Experimental Study for the Feasibility of a Crystalline Undulator

“…The crystalline undulators (CU) with periodically deformed crystallographic planes offer huge electromagnetic fields and could provide a quite short period L of an undulator in sub-millimeter range. This way one can also arrange for substantial amplitudes A of oscillation for the particles channeled through the undulator and thus increase the intensity of the radiation.Currently, bent crystals are largely used for channeling extraction of 70-GeV protons at IHEP (Protvino) with efficiency reaching 85% at intensity well over 10 12 particle With a strong world-wide attention to novel sources of radiation, there has been broad theoretical interest to compact crystalline undulators, with some approaches covering also nanotechnology to make use of nanotubes to guide radiating particles [4][5][6][7][8][9][10][11][12] In bent crystal channeling experiments at IHEP Protvino with 70-GeV protons, it was found that accidental micro-scratches on a crystal surface caused a deformation of the crystallographic planes to substantial depths, down to a few hundred microns as depicted in Fig. 1(a).…”