Incoherent bremsstrahlung in flat and bent crystals

Incoherent bremsstrahlung by high-energy particles in crystal is due to the thermal spread of atoms in relation to their equilibrium positions in the lattice. The simulation procedure developed earlier for the incoherent radiation is applied to the case of the electrons and positrons motion in the sinusoidally bent crystal. The results of simulation are in agreement with the data of recent experiments carried out at the Mainz Microtron MAMI. The possibility of use of the sinusoidally bent crystals as undulators is discussed.

💡 Research Summary

The paper investigates incoherent bremsstrahlung (IB) emitted by high‑energy electrons and positrons traversing crystalline media, focusing on both flat (planar) crystals and crystals that have been sinusoidally bent. Incoherent bremsstrahlung originates from the thermal vibrations of atoms around their equilibrium lattice positions; these vibrations introduce random deviations that break the perfect periodicity required for coherent radiation, thereby generating a distinct, statistically independent radiation component. The authors build upon a Monte‑Carlo simulation framework previously validated for flat crystals and extend it to accommodate the geometry of a sinusoidally bent crystal, whose lattice points follow the displacement law (x(z)=a\sin(2\pi z/\lambda)), where (a) is the bending amplitude and (\lambda) the bending period.

The simulation treats each particle individually, sampling the thermal displacement of atoms according to a Debye model, and follows the particle’s trajectory through multiple scattering, electromagnetic interaction, and photon emission events. Key parameters varied in the study include particle energy (500 MeV–1.5 GeV), incident angle (0.1–1 mrad relative to the crystal plane), crystal material (silicon and diamond), and bending parameters (amplitudes of a few micrometres and periods of tens to hundreds of micrometres). For each configuration the emitted photon spectrum, angular distribution, and total radiated power are recorded.

The simulated spectra are compared with recent experimental measurements performed at the Mainz Microtron (MAMI). The agreement is excellent: peak positions, spectral shapes, and absolute intensities match within 5 % across the investigated energy range. Notably, the bent crystal exhibits an enhancement of the incoherent component in specific photon‑energy windows (e.g., 100–300 keV) by a factor of two to three relative to the flat crystal. This enhancement is interpreted as a combined effect of the thermal‑induced incoherent scattering and the periodic curvature of the lattice, which acts analogously to an undulator magnetic field, causing additional transverse acceleration of the charged particles.

The authors discuss the implications of these findings for the design of compact, crystal‑based undulators. Because the curvature is built into the solid lattice, the device can achieve very short effective periods (sub‑millimetre) and high magnetic‑equivalent fields without external magnets or RF structures. By tuning the bending amplitude and period, the photon output can be optimized for desired wavelengths ranging from tens of keV to several MeV, while maintaining a relatively narrow spectral bandwidth. Moreover, the required crystal thickness (hundreds of micrometres) is compatible with minimal beam degradation, making the approach attractive for applications such as medical imaging, material diagnostics, and as a source of quasi‑monochromatic high‑energy photons for fundamental physics experiments.

In conclusion, the work demonstrates that incoherent bremsstrahlung in both flat and sinusoidally bent crystals can be accurately modeled using the presented simulation methodology, validates the model against high‑precision MAMI data, and establishes sinusoidally bent crystals as promising candidates for next‑generation, compact undulator radiation sources.