Chapter 7. Undulator Radiation

  1. Prof. Richard Talman

Published Online: 16 FEB 2007

DOI: 10.1002/9783527610303.ch7

Accelerator X-Ray Sources

Accelerator X-Ray Sources

How to Cite

Talman, R. (2006) Undulator Radiation, in Accelerator X-Ray Sources, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610303.ch7

Author Information

  1. Cornell University, Laboratory of Elementary Physics, Ithaca, NY, USA

Publication History

  1. Published Online: 16 FEB 2007
  2. Published Print: 22 MAY 2006

ISBN Information

Print ISBN: 9783527405909

Online ISBN: 9783527610303



  • undulator radiation;
  • electron orbit in a wiggler or undulator;
  • energy radiated from one wiggler pole;
  • spectral analysis for arbitrary longitudinal field profile;
  • spectrum of the radiation from a single pole;
  • coherence from multiple deflections;
  • phasor summation for K1;
  • photon energy distributions;
  • undulator radiation for arbitrary K value;
  • post-monochromator profile


This chapter contains sections titled:

  • Preview

  • Introduction

  • Electron Orbit in a Wiggler or Undulator

  • Energy Radiated From one Wiggler Pole

  • Spectral Analysis for Arbitrary Longitudinal Field Profile

  • Spectrum of the Radiation from a Single Pole

    • Orbit Treated as Arc of Circle

    • Radiation from a Single, Short, Isolated, Magnet, K1

  • Coherence from Multiple Deflections

  • Phasor Summation for K1

  • Photon Energy Distributions

    • Energy Distribution from the n = 1 Undulator Fundamental

  • Undulator Radiation for Arbitrary K Value

    • Analytic Formulation

    • Diffraction Grating Analogy

    • Numerical/Graphical Representation of Undulator Radiation

    • Approximation of the Integrals by Special Functions

    • Practical Evaluation of the Series

  • Post-monochromator Profile

    • Monochromatic Annular Rings

    • Numerical Investigation of Undulator Rings

    • Is the Forward Undulator Peak Subject to Angular Narrowing?