BRIGHTNESS AND COHERENCE OF SYNCHROTRON RADIATION AND FELs∗

This paper reviews the brightness and coherence properties of radiation from storage rings and free electron lasers (FELs). Starting from the statistical optics and using mutual coherence function of the radiation field, we define the transverse and temporal coherence and modes. Spectral brightness can be represented in radiation phase-space via the Wigner function which is the Fourier transformation of the transverse correlation function. The brightness convolution theorem can be employed to calculate the total source brightness and the degree of transverse coherence of the radiation emitted by an electron beam. Undulator radiation possesses partial transverse coherence until the beam emittances can be reduced below the diffraction limit. For x-ray FELs the radiation has excellent transverse coherence and at least 9 orders of magnitude enhancement in peak brightness. Seeding can further improve temporal coherence of FELs. Future development includes diffraction limited light sources, higher peak and average power x-ray FELs and compact coherent radiation sources based on laser and plasma accelerators.