Modeling the light response of an optically readout GEM based TPC for the CYGNO experiment

The use of gaseous Time Projection Chambers enables the detection and the detailed study of rare events due to particles interactions with the atoms of the gas with energy releases as low as a few keV. Due to this capability, these instruments are being developed for applications in the field of astroparticle physics, such as the study of dark matter and neutrinos. To readout events occurring in the sensitive volume with a high granularity, the CYGNO collaboration is developing a solution where the light generated during the avalanche processes occurring in a multiplication stage based on Gas Electron Multiplier (GEM) is read out by optical sensors with very high sensitivity and spatial resolution. To achieve a high light output, gas gain values of the order of $10^5\text{-}10^6$ are needed. Experimentally, a dependence of the detector response on the spatial density of the charge collected in the GEM holes has been observed, indicating a gain-reduction effect likely caused by space-charge buildup within the multiplication channels. This paper presents data collected with a prototype featuring a sensitive volume of about two liters, together with a model developed by the collaboration to describe and predict the gain dependence on charge density. A comparison with experimental data shows that the model accurately reproduces the gain behaviour over nearly one order of magnitude, with a percent-level precision.