Compact representations of partially coherent undulator radiation suitable for wave propagation

Abstract

Undulator radiation is partially coherent in the transverse plane, with the degree of coherence depending on the ratio of the electron beam phase space area (emittance) to the characteristic radiation wavelength λ. On the other hand, numerical codes used to predict x-ray beam line performance can typically only propagate coherent fields from the source to the image plane. We investigate methods for representing partially coherent undulator radiation using a suitably chosen set of coherent fields that can be used in standard wave propagation codes, and discuss such “coherent mode expansions” for arbitrary degrees of coherence. In the limit when the electron beam emittance along at least one direction is much larger than λ the coherent modes are orthogonal and therefore compact; when the emittance approaches λ in both planes we discuss an economical method of defining the relevant coherent fields that samples the electron beam phase space using low-discrepancy sequences.