Abstract
Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.
Highlights
Recent progress of accelerator theories and technologies has made it possible to generate an electron beam whose emittance is comparable to that of diffraction limited light even in the angstrom x-ray region, both in the storagering and energy-recovery-linac schemes
Note that the optimum betatron function at this optimum photon energy is shifted from 1 m to 0.7 m. This means that the optimum betatron function at the photon energy of ħωopt, which is determined by the Wigner function method, is close to βopt;G, i.e., the optimum value roughly determined by the Gaussian approximation without taking into account the energy detuning
We have described the numerical methods to compute the phase-space density based on the Wigner function method
Summary
Recent progress of accelerator theories and technologies has made it possible to generate an electron beam whose emittance is comparable to that of diffraction limited light even in the angstrom x-ray region, both in the storagering and energy-recovery-linac schemes. Another way of accurately characterizing SR is based on the so-called Wigner function [3], which is directly related to dðr; θÞ and has been introduced by several authors [4,5,6,7,8,9] In these papers, analytical and numerical methods have been discussed to calculate the phase-space density of UR emitted from a single electron, which makes clear the difference between the exact and Gauss-approximated profiles of dðr; θÞ. Analytical and numerical methods have been discussed to calculate the phase-space density of UR emitted from a single electron, which makes clear the difference between the exact and Gauss-approximated profiles of dðr; θÞ It should be noted, that the effects due to the finite emittance and energy spread of the electron beam have not been taken into account except for a few examples. Note that the bending magnet radiation (BMR) and wiggler radiation (WR), in addition to UR, are within the scope of this paper, whose Wigner functions have not been seriously considered in the previous papers
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