Reconstruction of beam parameters and betatron radiation spectra measured with a Compton spectrometer

The photon flux resulting from high-energy electron beam interactions with high-field systems, such as those found in the upcoming FACET-II experiments at the SLAC National Accelerator Laboratory, yields deep insight into the electron beam’s underlying dynamics during the interaction. However, extracting this information is an intricate process. To demonstrate how to approach this challenge using modern methods, this paper utilizes simulated data that models plasma wakefield acceleration-derived betatron radiation in experiments to determine reliable methods of reconstructing key beam and beam-plasma interaction properties. For betatron radiation measurements, translating the observed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>200</a:mn><a:mrow><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>keV</a:mi></a:mrow></a:math> to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>30</c:mn><c:mrow><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>MeV</c:mi></c:mrow></c:math> photon double-differential energy-angle spectra obtained from an advanced Compton spectrometer requires testing multiple methods to optimize the pipeline from its response to incident electron beam information. The paper compares maximum likelihood estimation and machine learning to refine the translation of photon spectra into precise electron beam metrics, such as spot size, energy, and emittance, enhancing the understanding of beam behavior within these dense, high-field environments. We also introduce machine learning and the expected maximization algorithm to reconstruct the primary photon spectrum, employing a multilayer neural network for regression analysis of the energy and angle spectra. With appropriate modifications, the advanced methods reproduce relevant incident beam parameters with high accuracy, even for beam sizes in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo form="prefix">&lt;</e:mo><e:mn>10</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi mathvariant="normal">μ</e:mi><e:mi mathvariant="normal">m</e:mi></e:math> range. This capacity is critical to understanding intense beam propagation and its optimization in plasma.