Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Notation
- Part I Introduction
- Part II Synchrotron radiation
- Part III Undulator radiation
- Part IV Applications
- 12 Optics of SR – imaging
- 13 Electron-storage rings
- 14 Effects of radiation on the electron beam
- 15 Radiation emitted by many particles
- A Airy functions
- B Bessel functions
- C Developments of strong-undulator radiation
- References
- Index
15 - Radiation emitted by many particles
Published online by Cambridge University Press: 09 October 2009
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Notation
- Part I Introduction
- Part II Synchrotron radiation
- Part III Undulator radiation
- Part IV Applications
- 12 Optics of SR – imaging
- 13 Electron-storage rings
- 14 Effects of radiation on the electron beam
- 15 Radiation emitted by many particles
- A Airy functions
- B Bessel functions
- C Developments of strong-undulator radiation
- References
- Index
Summary
Effects of the electron distribution on the radiation
Introduction
We calculated the synchrotron radiation emitted by a single particle on the nominal orbit. In other words, the position and angular direction of the moving electron were identical to the origin and axis we used to describe the synchrotron radiation. For an electron beam of finite emittance there is a spread in position and angle, with RMS values σx, σ′x and σy, σ′y around the nominal values. As a result, we observe radiation emitted at different angles and positions. As a first consequence, the emitted photon beam has an increased emittance, at least equal to the sum of the electron emittance and the natural photon emittance. Furthermore, since the frequency emitted by an electron depends on the angle of observation, the angular spread of the electrons tends to broaden the spectrum observed on the axis. This effect is negligible for standard synchrotron radiation but can be pronounced in the case of undulators with many periods.
Apart from a spread in angle and position, the electrons have also a spread in energy. The synchrotron-radiation frequency depends strongly on the electron energy. The spread of the latter leads again to a broadening of the synchrotron-radiation spectrum.
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- The Physics of Synchrotron Radiation , pp. 286 - 299Publisher: Cambridge University PressPrint publication year: 2004