Brightness, coherence and propagation characteristics of synchrotron radiation

Abstract

A formalism is presented by means of which the propagation and imaging characteristics of synchrotron ragiation can be studied, taking into account the effects of diffraction, electron beam emittance, and the transverse and longitudinal extent of the source. An important quantity in this approach is the Wigner distribution of the electric fields, which can be interpreted as a phase-space distribution of photon fl~x. and thus can be identified with the brightness.When integrated over the angular variahles, the brightness becomes the intensity distribution in the spatial variables and when integrated over the spatial variables, it becomes the intensity distribution in angular variables. The brightness so defined transforms through a general optical medium in exactly the same way as in the case of a collection of geometric rays. Finally, the brightness of different electrons adds in a simple way. Optical characteristics of various synchrotron radiation sources -bending magnets, wigglers and undulators, are analyzed using this formalism.

The Properties of Undulator Radiation

“…The extension to the normal coherence theory based on the use of the frequency·space representation approximation applies has been achieved by Kim, 1986Kim, , 1989. This author has developed an is often encountered.…”

“…brightness function as described in the published accounts (Kim, 1986(Kim, , 1989) before using the obtained from it. It is, therefore, necessary to pay special attention to the meaning of the used by Kim is not a physically measurable quantity, although several such quantities can be enabled by knowledge of the brightness function.…”

On the Importance of Electron Beam Brightness in High Gain Free Electron Lasers

“…At the same time, in order to minimize emittance effects and to ensure optimal transverse overlap of the co-propagating radiation and electron beam, the electron beam trajectory, transverse size and angular divergence must be controlled with steering and quadrupole magnets that are interleaved between the undulator segments (similarly, the individual undulator magnet pole strengths and overall magnetic centerline tilt must also be carefully controlled but we will not discuss those issues here). The most efficient electron-photon beam interaction occurs when the transverse beam phase space area and distribution matches that of the radiation, whereas the transverse electron beam size scales as (u  Considerations of both the maximum allowable effective energy spread and the transverse overlap lead to an rms value of  that must be smaller than, or of the same order as, that of the diffraction-limited photon beam [30]: (4) in order to maximize the FEL gain; this emittance value limit also optimizes the FEL transverse coherence. The aforementioned opposing scaling laws with u, instead, suggest that there is some optimal value of u (for any given and ) that maximizes the FEL gain.…”

Performance of the x-ray free-electron laser oscillator with crystal cavity

“…4(b), we use the paraxial approximation to study the transverse x-ray cavity modes. A convenient way to do this is to introduce a distribution of fictitious rays in the position (x) and angle (x 0 ) phase space [14]. Since the rays transform in the same way as in geometric optics, we can make use of the familiar matrix formalism in particle optics [15,16].…”