Gauss–Schell Sources as Models for Synchrotron Radiation

Coı̈sson, R.; Marchesini, S.

doi:10.1107/s0909049597008169

Cited by 46 publications

(24 citation statements)

References 9 publications

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“…The Wigner distribution, or Wigner distribution function (WDF), was recognized to be a general framework to represent quantum [1] and therefore wave phenomena in phase space [2] and specifically synchrotron radiation [3][4][5]. The approach allows light characterization of arbitrary degree of coherence [6] and polarization [7] in phase space, though its application by the accelerator community has so far been mostly limited to the simplest cases of Gaussian or Gauss-Schell beams [8,9], despite the fact that the non-Gaussian nature of undulator radiation in phase space has been long recognized [4,5,8,10]. The Gaussian approximation provides a set of useful analytical expressions for quick estimates of performance of x-ray sources even though incorrect values for rms phase-space dimensions are often used (for example, the undulator radiation in the central cone is incorrectly assumed to have a diffraction limited rms emittance of !=4%).…”

Section: Introductionmentioning

confidence: 99%

Synchrotron radiation representation in phase space

Bazarov

2012

Phys. Rev. ST Accel. Beams

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The notion of brightness is efficiently conveyed in geometric optics as density of rays in phase space. Wigner has introduced his famous distribution in quantum mechanics as a quasiprobability density of a quantum system in phase space. Naturally, the same formalism can be used to represent light including all the wave phenomena as originally done by Walther and for synchrotron radiation by Kim. It provides a natural framework for radiation propagation and optics matching by transferring the familiar ''baggage'' of accelerator physics ( function, emittance, phase-space transforms, etc.) to synchrotron radiation. More specifically, the use of Wigner distribution formalism allows a rigorous description of partially coherent non-Gaussian sources, which is generally the case for synchrotron radiation from an undulator with a high degree of transverse coherence. This paper reviews many of the properties of the Wigner distribution starting from quantum mechanics and provides examples of how its use enables physically insightful description of partially coherent synchrotron radiation in phase space. The concepts of diffraction limit and coherence are given an exact correspondence to their quantum mechanical counterparts. In particular, it is shown that the undulator radiation on resonance by a single electron is not diffraction limited though fully coherent. An extension of how to account for practically important cases of electron beams with nearly diffraction limited emittances is presented along with a discussion of appropriate figures of merit suitable for comparing future light sources.

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Section: Introductionmentioning

confidence: 99%

Synchrotron radiation representation in phase space

Bazarov

2012

Phys. Rev. ST Accel. Beams

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“…(21). Hence, some of our analysis will be applicable to the full coherent mode eigenproblem, as solving (29) requires first determining W ν from either (21) or (31).…”

Section: A Coherent Mode Representation For Arbitrary Electron Beamentioning

confidence: 99%

“…The Gaussian-Schell model of undulator radiation has been discussed in many previous papers (see, e.g., [17,31]), while its coherent mode decomposition (36) and (37) was applied to study the propagation of x rays for both synchrotron light sources and FEL applications in Ref. [32].…”

Section: Representing the Cross-spectral Density With Coherent Mmentioning

confidence: 99%

Compact representations of partially coherent undulator radiation suitable for wave propagation

Lindberg

Kim

2015

Phys. Rev. ST Accel. Beams

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Undulator radiation is partially coherent in the transverse plane, with the degree of coherence depending on the ratio of the electron beam phase space area (emittance) to the characteristic radiation wavelength λ. On the other hand, numerical codes used to predict x-ray beam line performance can typically only propagate coherent fields from the source to the image plane. We investigate methods for representing partially coherent undulator radiation using a suitably chosen set of coherent fields that can be used in standard wave propagation codes, and discuss such "coherent mode expansions" for arbitrary degrees of coherence. In the limit when the electron beam emittance along at least one direction is much larger than λ the coherent modes are orthogonal and therefore compact; when the emittance approaches λ in both planes we discuss an economical method of defining the relevant coherent fields that samples the electron beam phase space using low-discrepancy sequences.

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“…The qualitative agreement with the experimentally observed data was found, although the quantitative discussion needs taking into account of the diffraction effects. The synchrotron radiation treatment as a laser-like Gaussian beam with a small opening angle was performed in (Coisson & Marchesini, 1997;Kim, 1986;Ogata, 1991;Takayama et al, 1998Takayama et al, , 1999. The important benefit to the use of this approximation is that the Gaussian beams have been much studied.…”

Section: Introductionmentioning

confidence: 99%

Wave Optics of Synchrotron Radiation

Smolyakov¹

2012

Infrared Radiation

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Gauss–Schell Sources as Models for Synchrotron Radiation

Cited by 46 publications

References 9 publications

Synchrotron radiation representation in phase space

Synchrotron radiation representation in phase space

Compact representations of partially coherent undulator radiation suitable for wave propagation

Wave Optics of Synchrotron Radiation

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