Microscopic simulation and statistical analysis of gas gain fluctuations in gaseous detectors

Performance in contemporary gaseous detectors is limited by stochastic fluctuations during charge multiplication. This investigation employs a high-fidelity microscopic framework using Garfield++ and Magboltz to analyze gas gain fluctuations in a baseline ternary mixture (97% C₂H₂F₄, 2.5% iC₄H₁₀, 0.5% SF₆). We evaluated the relative variance (f) and first Townsend coefficient (α) for reduced electric fields (E/p) up to 450 kV/cm Torr and gap widths from 0.01 mm to 0.022 mm. Systematic uncertainty analysis, involving a ±30% scaling of excitation cross-sections, identifies non-ionizing inelastic collisions as primary drivers of gain stochasticity. Crucially, the relative variance converges at high fields; for E/p> 250 kV/cm Torr, f becomes independent of gap width, stabilizing between 0.3 and 0.5. Additionally, the work quantifies the competition between ionization and excitation mechanisms. Ionization yield simulations demonstrate that the transition from exponential Furry statistics to peaked Polya distributions is driven by ionizing collision saturation at high field strengths. Results are synthesized into a universal gain curve relating f to ionization efficiency (α/E), providing a robust predictive model for detector resolution. These findings establish a vital baseline for the transition toward eco-friendly, low-GWP gas mixtures in high-flux radiation environments, such as those encountered at the Large Hadron Collider (LHC).