Systematic Differences due to High Energy Hadronic Interaction Models in Air Shower Simulations in the 100 GeV-100 TeV Range

The predictions of hadronic interaction models for cosmic-ray induced air showers contain inherent uncertainties due to limitations of available accelerator data and theoretical understanding in the required energy and rapidity regime. Differences between models are typically evaluated in the range appropriate for cosmic-ray air shower arrays ($10^{15}$-$10^{20}$ eV). However, accurate modelling of charged cosmic-ray measurements with ground based gamma-ray observatories is becoming more and more important. We assess the model predictions on the gross behaviour of measurable air shower parameters in the energy (0.1-100 TeV) and altitude ranges most appropriate for detection by ground-based gamma-ray observatories. We go on to investigate the particle distributions just after the first interaction point, to examine how differences in the micro-physics of the models may compound into differences in the gross air shower behaviour. Differences between the models above 1 TeV are typically less than 10%. However, we find the largest variation in particle densities at ground at the lowest energy tested (100 GeV), resulting from striking differences in the early stages of shower development.