Analytic description of the radiation spectrum

This repository calculates the analytic betatron radiation spectrum for both single particles and beam distributions in the blowout regime of plasma wakefield acceleration. The model assumes paraxial motion in a uniform ion channel and computes critical energy and spectral shape across undulator regimes. It includes code to evaluate synchrotron radiation functions and compare normalized single-particle vs beam spectra. Useful for theoretical studies and benchmarking particle-in-cell simulation outputs. Related paper: arXiv:2303.04213