Computational Optimization of Minimum Ionizing Timing Detector Components

Abstract

The objective of particle detectors in high-energy physics research is to reveal the fundamental laws of nature. The Minimum Ionizing Particle Detector (MTD) has been designed to enhance the timing precision of theCMS (Compact Muon Solenoid) detector at CERN to 50 ps under the increased number of particle impacts after upgrading the Large Hadron Collider (LHC) to the High-Luminosity LHC. The Barrel Timing Layer (BTL) segment of the MTD uses silicon photodetectors (SiPMs), whose timing accuracy depends on their operating temperature and the number of photons they detect. This dissertation presents numerical methods to improve the timing precision of these SiPMs through the design of thermoelectrical coolers and scintillation crystals. On the one hand, thermoelectrical coolers (TECs) can lower the SiPMs temperature, reducing signal-to-noise ratio and recovering radiation-induced damage through controlled annealing procedures. We provide an analytical model to study the landscape of TEC topology optimization with a lower temperature objective, power constraints and two density design variables. This study leads to the recommendation of penalization coefficients for SIMP (solid isotropic material with penalization) in the form of kp = kσ > kα with kp the thermal conductivity, kσ the electrical conductivity and kα the Seebeck’s penalization coefficient to reduce the nonconvexity induced by the power constraint. These coefficients reduce nonconvexity from power constraints, allowing FEM topology optimization via SIMP to achieve lower material volumes and temperatures without volume constraints and filtering schemes. FEM optimization examples are provided, which incorporate electrical working points through a voltage gradient design variable and constant material properties. These examples reduce the temperature by up to 10 ◦C compared to the optimal electrical working point of the original designs. Finally, comparing these results with designs with non-linear, temperature-dependent properties shows that the use of constant material properties can lower computational costs and improve design performance. Although optimized designs achieve lower temperatures, TECs are fragile. The construction of the BTL highlights this fragility, prompting an extension of the design to address operational thermal and mechanical loads. This work introduces a FEM-based topology optimization for the coupled thermoelectromechanical problem using SIMP. This also includes the formulation with nonlinear material properties, and how to deal with the checkerboarding with the extended mechanical degree Celsiuss of freedom. The optimized designs reduce stress concentrations by half while enhancing cooling capabilities. On the other hand, we complement the lower signal-to-noise ratio obtained from using TECs, with an increased number of photon impacts enhancing the SiPM signal. The number of photons created or the scintillation light yield depends on the material composition of the scintillators. However, the photon arrival count at SiPMs is influenced by their reflective surfaces and volume. We provide a model of BTL within GEANT4, a ray-tracing particle-matter interaction software. This model incorporates the effect of the particle impact location and is used in conjunction with NSGAII (non-dominated sorting genetic algorithm) to optimize scintillator shapes to increase the photon detection count. The study uses multiple objective functions based on the stochastic nature of the arrival photons. From these results, the recommended objective function is the mean light collection per energy deposition and the ionizing particle track length, reducing statistical errors and accounting for energy deposition. The results provide relative gains to the original designs in the objective function between 15 and 38%. To overcome the computational limits of Monte Carlo methods, we follow up by translating the scintillation equations into a transient wave for FEM simulations, matching GEANT4 pulse shapes. Furthermore, we perform a shape optimization using a static frequency domain scintillation model replicating the variable influence within GEANT4. The optimal designs obtained with FEM are validated within GEANT4, obtaining gains of the order of 7.7%. These gains were achieved with less than 1% of the computational resources needed to perform the GEANT4 optimizations.