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TY - CONF AU - Anisimov, P.M. ED - Bishofberger, Kip:Carlsten, Bruce (LANL, Los Alamos, NM, USA)[ORCID:0000-0001-5619-907X] ED - Schaa, Volker RW TI - Canonical Formulation of 1D FEL Theory Revisited, Quantized and Applied to Electron Evolution J2 - Proc. of FEL2017, Santa Fe, NM, USA, August 20-25, 2017 C1 - Santa Fe, NM, USA T2 - International Free Electron Laser Conference T3 - 38 LA - english AB - An original FEL theory relied on quantum analysis of photon generation by relativistic electrons in alternating magnetic field.* In most cases, however, the system of pendulum equations for non-canonical variables and the theory of classical electromagnetism proved to be adequate. As XFELs advance to higher energy photons, quantum effects of electron recoil and shot noise has to be considered. This work presents quantization procedure based on the Hamiltonian formulation of an XFEL interaction in 1D case. The procedure relates the conventional variables to canonical coordinates and momenta and does not require the transformation to the Bambini-Renieri frame.** The relation of a field operator to a photon annihilation operator reveals the meaning of the quantum FEL parameter, introduced by Bonifacio, as a number of photons emitted by a single electron before the saturation takes place.*** The quantum description is then applied to study how quantum nature of electrons affects the startup of XFEL and how quantum electrons become indistinguishable from a classical ensemble of electrons due to their interaction with a ponderomotive potential of an XFEL. PB - JACoW CP - Geneva, Switzerland SP - 576 EP - 580 KW - ion KW - electron KW - FEL KW - radiation KW - undulator DA - 2018/02 PY - 2018 SN - 978-3-95450-179-3 DO - 10.18429/JACoW-FEL2017-FRB04 UR - http://jacow.org/fel2017/papers/frb04.pdf ER -