BGO quenching effect on spectral measurements of cosmic-ray nuclei in DAMPE experiment

The Dark Matter Particle Explorer (DAMPE) is a satellite-borne detector designed to measure high energy cosmic-rays and $\gamma$-rays. As a key sub-detector of DAMPE, the Bismuth Germanium Oxide (BGO) imaging calorimeter is utilized to measure the particle energy with a high resolution. The nonlinear fluorescence response of BGO for large ionization energy deposition, known as the quenching effect, results in an under-estimate of the energy measurement for cosmic-ray nuclei. In this paper, various models are employed to characterize the BGO quenching factors obtained from the experimental data of DAMPE. Applying the proper quenching model in the detector simulation process, we investigate the tuned energy responses for various nuclei and compare the results based on two different simulation softwares, i.e. GEANT4 and FLUKA. The BGO quenching effect results in a decrease of the measured energy by approximately $2.5\%$ ($5.7 \%$) for carbon (iron) at $\sim$10 GeV/n and $<1\%$ above 1 TeV/n, respectively. Accordingly, the correction of the BGO quenching effect leads to an increase of the low-energy flux measurement of cosmic-ray nuclei.