M.Sc. degree
Univeristy of Naples Federico II, Italy

Stefano Di Gennaro

Supervisor: Prof. Pasquale Arpaia

Keywords:

• Particle physiscs
• Silicon crystals
• channeling
• Autocollimator

Abstract:

The use of bent crystals in high-energy particle accelerators makes it possible to exploit several physical phenomena, such as channeling and volume reflection, to steer particles toward a desired location. Collimation, steering toward absorbers, extraction, and the merging of two extracted beams are among the goals enabled by beam interactions with silicon crystals. To achieve these objectives, an accurate and reliable characterization of the curvature of bent crystals is required. Within the framework of the UA9 experiment at CERN, the precise measurement of both the primary and the anticlastic curvature components is essential to the success of each experiment, as it helps avoid numerous trial bending attempts and saves valuable beam time, while also ensuring the reproducibility of experimental results. This thesis presents the development and validation of an automated optical measure- ment system based on an autocollimator for the characterization of tiny bent silicon crystals. After a review of the physical principles governing particle–crystal inter- actions and of the existing techniques for crystal curvature measurements, a detailed description of the autocollimator operating principle and of the adopted experimental setup is provided.

Dedicated measurement procedures and image processing algorithms are developed for different crystal geometries, including thin strip crystals and RD22 crystals. The system combines motorized translation stages with custom software for automated data acquisi- tion and processing, enabling systematic and repeatable angular mapping of the crystal surface. In order to enhance measurement accuracy, signal processing techniques such as Principal Component Analysis and Savitzky–Golay filtering are employed. The former enables the estimation of the principal component of the data distribution and, consequently, the determination of the central value of that distribution, while the latter is applied to estimate the curvature trend, reducing the influence of measurement noise and preventing spurious local oscillations from affecting the curvature estimation. The obtained curvature measurements are compared with reference beam-based mea- surements performed in the CERN SPS North Area. The results demonstrate that the proposed optical system provides reliable estimates of both primary and anticlas- tic curvature, with a precision compatible with the requirements of crystal-assisted collimation studies.

The system provides primary curvature radii for strip crystals with deviations below 7% for Strip 1 and within 10% for Strip 2, and relative standard uncertainties below 4%. The anticlastic curvature angles measured on strip crystals are consistent with beam-based reference values within ±22 μrad, with a standard uncertainty of 6 μrad. For RD22 crystals, the central anticlastic curvature measured by the automated system differs from beam measurements by less than 5%, demonstrating good consistency with in- beam characterization and confirming the reliability of the proposed laboratory method. Furthermore, the anticlastic curvature gradient of an RD22 crystal is captured with good agreement with the beam-based profile: over the common span x ∈ [−9, 9] mm, the difference between the two parabolic fits shows a bias of −6.01 μrad, an RMS deviation of 8.29 μrad, and a maximum absolute deviation of 15.69 μrad.

The developed approach represents a flexible and efficient laboratory tool for crystal pre-characterization and quality control, reducing the dependence on resource-intensive beam tests.