X-ray reflection: a FLUKA model and its application in the design of synchrotron light beamlines and CERN's Future Circular Collider

Relying on atomic scattering factors from evaluated databases, a new model for the reflectivity of x rays on solid surfaces has been developed for FLUKA v4-6.0. This model accounts for the variation of reflectivity as a function of the photon energy, its incidence angle, and linear polarisation; surface roughness effects are also taken into account. FLUKA reflectivities agree well with those obtained from state-of-the-art codes used for the characterization of optical devices, both for homogeneous solids and for multilayer mirrors. This new capability renders FLUKA a nearly one-stop shop for synchrotron radiation simulations: emission from bending magnets and wigglers, photon transport and interaction, electromagnetic (and hadronic when applicable) shower development in complex geometries, as well as x-ray reflection at designated solid surfaces can now be all accounted for in a single FLUKA run. This streamlined FLUKA simulation workflow greatly simplifies the plethora of simulation tools that Monte Carlo practitioners previously needed to rely on. Two application scenarios of this new reflectivity model are showcased: first, the use of a multilayer mirror to deflect x rays from an optical hutch onto an experimental hall at the MINERVA beamline of the ALBA synchrotron and, second, the assessment of the photon flux near the interaction point at the CERN’s Future Circular Collider (in its electron-positron stage) as a result of upstream x-ray reflections.

💡 Research Summary

The paper presents a new X‑ray reflectivity model for the general‑purpose Monte Carlo code FLUKA (versions 4‑6.0) that is based on evaluated atomic scattering factors (ASFs) from several databases (EPICS2014, Henke, NIST). By converting these complex ASFs into a complex index of refraction n(ω)=1−rₑλ²/(2π)∑Nₛ fₛ(ω), the authors obtain a material‑specific optical constant that is valid from 100 eV up to 10 MeV. The Henke tables, originally limited to 30 keV, were extended with EPICS2014 data to cover the full energy range required by FLUKA, and a Kramers‑Kronig consistency check was performed.

The model implements the Fresnel equations for σ (electric field perpendicular to the plane of incidence) and π (parallel) polarizations using the complex n(ω). Reflectivity is calculated as Rσ=|rσ|² and Rπ=|rπ|², and an arbitrary linear polarization is treated as a weighted sum of the two components. Phase shifts between σ and π components are ignored because FLUKA tracks only real linear‑polarization vectors. Surface roughness is accounted for with the Nevot‑Croce factor exp