A sampling procedure to regenerate particles in a ground detector from a “thinned” air shower simulation output

Atmospheric showers induced by ultra-high energy cosmic rays contain a huge number of particles. Simulation packages cannot generate, follow and store all of them within a reasonable time. The “thinning” procedure was invented to cope with this problem; it provides a file containing a limited sample of weighted particles. We describe here a method to regenerate a set of particles entering a ground detector from such a file, reproducing as far as possible the properties of the signal, without using tabulations or building smoothed densities in the parameter space of particles. We discuss the possible biases on the amplitude and the time distribution of the signal and practical ways to suppress them. We also evaluate the artificial fluctuations due to the reduced size of the thinned sample and the dispersion of the weights, compared to the natural fluctuations due to the discrete nature of the shower and to the finite size of the detector. We define practical criteria to control the statistical quality, that is, to maintain the artificial fluctuations at an acceptable level.