The Jiangmen Underground Neutrino Observatory (JUNO) is a next-generation neutrino experiment under construction in China expected to be completed in 2022. As the main goal it aims to determine the neutrino mass ordering with 3-4 $sigma$ significance using a 20 kton liquid scintillator detector. It will measure the oscillated energy spectrum of electron anti-neutrinos from two nuclear power plants at about 53 km baseline with an unprecedented energy resolution of 3% at 1 MeV. A requirement of the JUNO experiment is the knowledge of the energy non-linearity of the detector with a sub-percent precision. As the light yield of the liquid scintillator is not fully linear to the energy of the detected particle and dependent on the particle type, a model for this light yield is presented in this paper. Based on an energy non-linearity model of electrons, this article provides the conversion to the more complex energy response of positrons and gammas. This conversion uses a fast and simple algorithm to calculate the spectrum of secondary electrons generated by a gamma, which is introduced here and made open access to potential users. It is also discussed how the positron non-linearity can be obtained from the detector calibration with gamma sources using the results presented in this article.
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