Monte Carlo Study of the Arrival Time Distribution of Particles in   Extensive Air Showers in the Energy Range 1--100 TeV
  A detailed simulation of vertical showers in atmosphere produced by primary gammas and protons, in the energy range 1-100 TeV, has been performed by means of the FLUKA Monte Carlo code, with the aim of studying the time structure of the shower front at different detector heights. It turns out that the time delay distribution can be fitted using few parameters coincident with the distribution central moments. Such parameters exhibit a smooth behaviour as a function of energy. These results can be used both for detector design and for the interpretation of the existing measurements. Differences in the time structure between gamma and proton induced showers are found and explained in terms of the non-relativistic component of extensive air showers. 
G. Battistoni, M. Carboni, A. Ferrari, V. Patera