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

TL;DR

This work presents a FLUKA-based model for x-ray reflection on solid surfaces and multilayer mirrors, grounded in evaluated atomic scattering factors and extended data libraries. Reflectivity is computed as a function of photon energy $E$, incidence angle $\theta$, linear polarization, and surface roughness $R_q$ for both homogeneous media and multilayer stacks, with polarization treated via $R_{\sigma}$ and $R_{\pi}$. The model is validated against XOP, XOPPY, and IMD using common data libraries and demonstrates excellent agreement across materials and multilayers up to high energies. It enables a truly integrated workflow where SR emission, transport, mirror reflection, and downstream photon transport can be simulated in a single FLUKA run, simplifying design studies for synchrotron beamlines and accelerator interfaces. Practical demonstrations on the MINERVA beamline at ALBA and the FCC-ee MDI region highlight the method’s utility for beamline optimization and background assessment, underscoring its potential to streamline SR simulations in complex geometries.

Abstract

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.

Figures (17)

• Figure 1: Real (top) and imaginary (bottom) parts of the AIASF, Eq. \ref{['eq:henkef1f2']}, for Cu. Curves represent the values from EPICS2014 (solid), the extended Henke database employed in FLUKA (dashed), the original Henke data library (dot-dashed), and NIST (dotted).
• Figure 2: Real (top) and imaginary (bottom) parts of the index of refraction of Cu, calculated with Eq \ref{['eq:nw']} and the FLUKA extended Henke AIASF displayed in Fig. \ref{['fig:f1f2']}.
• Figure 3: Schematic layout of the wavevectors and electric field vectors employed in the evaluation of the reflection coefficient, Eqs. \ref{['eq:rsigma']} and \ref{['eq:rpi']}, for $\sigma$- (top) and $\pi$-polarised (bottom) x rays. Magnetic field components shown for completeness.
• Figure 4: Absolute value of the phase shift for $\sigma$- (top) and $\pi$-polarised (bottom) photons reflected from a homogeneous Cu slab as a function of the photon energy for 1 mrad (solid), 10 mrad (dashed), and 100 mrad (dot-dashed) incidence angle.
• Figure 5: Photon reflectivity of Cu as a function of energy and incidence angle for $\sigma$ (left) and $\pi$ (right) polarisation.