  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.
