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Title: Quantum theory for 1D X-ray free electron laser

Abstract

Classical 1D X-ray Free Electron Laser (X-ray FEL) theory has stood the test of time by guiding FEL design and development prior to any full-scale analysis. Future X-ray FELs and inverse-Compton sources, where photon recoil approaches an electron energy spread value, push the classical theory to its limits of applicability. After substantial efforts by the community to find what those limits are, there is no universally agreed upon quantum approach to design and development of future X-ray sources. We offer a new approach to formulate the quantum theory for 1D X-ray FELs that has an obvious connection to the classical theory, which allows for immediate transfer of knowledge between the two regimes. In conclusion, we exploit this connection in order to draw quantum mechanical conclusions about the quantum nature of electrons and generated radiation in terms of FEL variables.

Authors:
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1414149
Report Number(s):
LA-UR-17-22821
Journal ID: ISSN 0950-0340
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Modern Optics
Additional Journal Information:
Journal Volume: 65; Journal Issue: 1; Journal ID: ISSN 0950-0340
Publisher:
Taylor and Francis
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; accelerator design; technology and operations; free-electron laser; quantum theory; quantum X-ray FEL; photon statistics at startup; quantum state of an electron

Citation Formats

Anisimov, Petr Mikhaylovich. Quantum theory for 1D X-ray free electron laser. United States: N. p., 2017. Web. doi:10.1080/09500340.2017.1375567.
Anisimov, Petr Mikhaylovich. Quantum theory for 1D X-ray free electron laser. United States. doi:10.1080/09500340.2017.1375567.
Anisimov, Petr Mikhaylovich. 2017. "Quantum theory for 1D X-ray free electron laser". United States. doi:10.1080/09500340.2017.1375567.
@article{osti_1414149,
title = {Quantum theory for 1D X-ray free electron laser},
author = {Anisimov, Petr Mikhaylovich},
abstractNote = {Classical 1D X-ray Free Electron Laser (X-ray FEL) theory has stood the test of time by guiding FEL design and development prior to any full-scale analysis. Future X-ray FELs and inverse-Compton sources, where photon recoil approaches an electron energy spread value, push the classical theory to its limits of applicability. After substantial efforts by the community to find what those limits are, there is no universally agreed upon quantum approach to design and development of future X-ray sources. We offer a new approach to formulate the quantum theory for 1D X-ray FELs that has an obvious connection to the classical theory, which allows for immediate transfer of knowledge between the two regimes. In conclusion, we exploit this connection in order to draw quantum mechanical conclusions about the quantum nature of electrons and generated radiation in terms of FEL variables.},
doi = {10.1080/09500340.2017.1375567},
journal = {Journal of Modern Optics},
number = 1,
volume = 65,
place = {United States},
year = 2017,
month = 9
}

Journal Article:
Free Publicly Available Full Text
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  • Starting from the general QED Hamiltonian for the free-electron laser (FEL), a quantum-mechanical, many-particle theory of the FEL in the laboratory frame is presented. When suitable variables are introduced, the Hamiltonian is seen to a good approximation to be formally identical to the nonrelativistic Hamiltonian in the resonant (Bambini-Renieri) frame used in other treatments. The derivation is given for a general multimode laser field, although only the simpler case of single-mode operation is discussed in detail. It is shown how the large-gain evolution equations for the field, in the small-signal regime, may be obtained from the quantum theory. Then, frommore » fourth-order perturbation theory, the change in the first two moments of the photon-number distribution in a single pass through the FEL is computed. Large-gain and saturation terms are obtained, for arbitrary values of the quantum recoil (i.e., both the classical and quantum-mechanical regimes are included). The evolution of the photon statistics over many cavity round trips is discussed. In the small-signal regime, the variance of the photon-number distribution is shown to correspond, to a good approximation, to that of thermal, or ''chaotic,'' radiation. At saturation, a significant reduction of the fluctuations is expected, but no conclusions can be drawn from the perturbation-theory approach. A numerical calculation of the buildup of the field from vacuum (through spontaneous emission) is presented. For simplicity, a uniform, circularly polarized, static wiggler is assumed in the text; however, the theory may be generalized (along lines shown) to deal with nonuniform, linearly polarized and/or traveling electromagnetic-wave wigglers.« less
  • A simple N-electron free-electron-laser (FEL) Hamiltonian is seen to define a (1+1)-dimensional quantum field theory. For large N, the FEL dynamics is shown to be solved by a single-electron Schroedinger equation in a self-consistent field. The fluctuations around such a Schroedinger wave function are shown to be O(1/ ..sqrt..N ) and computable by a perturbative strategy. A number of observations are also reported on the best strategy to solve the Schroedinger equation.
  • We consider the question whether quantum effects associated with the electron recoil on the field quantization have an significant effect on the FEL operation in the x-ray regime. We consider the gain formulae, spontaneous emission and electron multirecoil effect due to spontaneous multiphoton emission. It is concluded that quantum effects are usually negligible in the x-ray regime above 1A wavelength. They only may be detectable in a stimulated Compton FEL if high enough gain could ever be realized.
  • The problem of fundamental laser line broadening due to random spontaneous emission of radiation and amplification of thermal radiation noise is analyzed in terms of a classical fluctuating field phasor model. We derive a general expression for the intrinsic linewidth, given in terms of the spectral power of the radiation noise source, which can be classical or quantum mechanical in nature. In the case of a two-level atomic laser, we recover by the use of Einstein relations, the traditional linewidth formula of the Schalow-Townes form. In the case of the free-electron laser (FEL), using the explicit expression for the spontaneousmore » emission, we present calculation of the laser linewidth by purely classical methods. The result agrees with the one obtained in the framework of a quantum-mechanical model. By using ''extended Einstein relations'' which are applicable to classical radiators, we show that a Schalow-Townes-type formula can also be obtained for the FEL. The theory predicts extremely narrow intrinsic linewidth (10/sup -7/ Hz) for cw FEL's with parameters similar to those of the FEL experiment of Elias et al.« less
  • A free-electron laser (FEL) with a dielectric-loaded waveguide operating in an undulator (multiple mirror) field is analyzed. The stability properties are investigated self-consistently on the basis of the linearized Vlasov--Maxwell equations for an electron distribution function, in which all electrons have a Lorentzian distribution in the axial canonical momentum. Using appropriate boundary conditions, a dispersion relation is derived in the low density approximation; ..nu../sub b//..gamma../sub b/<<1, and the growth rates of several types of mode couplings are computed. Even for a mildly relativistic electron beam (..gamma../sub b/less than or equal to1.5), the typical maximum growth rate of instability is amore » few percent of c/R/sub w/. As the axial momentum spread increases, the growth rate decreases substantially while the instability bandwidth increases. For the long-wiggler wavelength (LWW) mode, which only occurs in the dielectric-loaded waveguide, Cerenkov interaction plays an important role in the free-electron laser instability. In the case of the short-wiggler wavelength (SWW) mode, the frequency of the free-electron laser is greatly enhanced in mildly relativistic electron beams with appropriate choices of physical parameter values. Therefore, intense submillimeter microwaves might be produced by making use of a mildly relativistic electron beam with ..gamma..approx. =1.1. A wide band free-electron laser amplifier is also possible with a proper choice of external parameters, such as wiggler wavenumber k/sub 0/, dielectric constant, and beam energy ..gamma../sub b/.« less