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In gamma-ray astronomy through Imaging Atmospheric Cherenkov Telescopes(IACT), the atmosphere is used as a calorimeter. Incident gamma-rays in theGeV-TeV energy range are observed through the electromagnetic showers theyproduce in the atmosphere and the Cherenkov light emitted by them. We aim toobtain a parameterisation of the longitudinal profiles of electromagneticshowers in the atmosphere. The longitudinal Cherenkov emission profiles ofthese showers can be used for the reconstruction of the parameters of thegamma-photon as well gamma-hadron discrimination. Obtaining an accurateparameterisation of these profiles can therefore be used in the analysis ofIACT images as well as fast simulation of the Cherenkov emission fromgamma-induced showers in the atmosphere. Such parameterisations are not knownto have been systematically carried out prior to this. We carry out Monte Carlosimulations of gamma-induced showers in the atmosphere. The parameterisation oftheir Cherenkov emission longitudinal profiles is based on the well-knowngamma-function used in particle detector physics. We evaluate the dependence ofthe depth of the maximum and the average depth of the longitudinal Cherenkovemission profile, as well as the parameter $1/\beta$ on the energy of theinitial shower. We also study the distributions of various parametersassociated with the gamma-function and find that $\beta/\alpha$ and $1/\alpha$have Gaussian distributions and are not correlated with each other which makesthem appropriate variables for evaluating the fluctuations of the Cherenkovemission profiles. We finally present parameterisations of the fluctuations ofthese two variables.

A parameterisation of the longitudinal Cherenkov emission profiles of  gamma induced electromagnetic showers in the atmosphere in the GeV-TeV energy  range