The model HDPM of CORSIKA has been updated and developed on the base of the recent measurements by ALICE, CMS, TOTEM, LHCb, LHCf... The new model, GHOST, involving a four-source production reproduces correctly the pseudo-rapidity distributions of charged secondaries and has been tested with the data in the mid and forward rapidity region, especially in the complex case of TOTEM, and also with the recent measurements of CMS, up to $ \sqrt s = 13\,{\rm{TeV}} $ (9.0 1016 eV in laboratory system). Special calculations have been devoted to the semi-inclusive data playing an important role in the cosmic ray simulation (fluctuations in earliest collisions, individual cascades measured at high altitude with high energy emulsion chambers). Taking into account the violation of KNO scaling, the negative binomial distribution (NegBin-expressed in terms of scaled elements) $ z = {n \mathord{\left/ {\vphantom {n {\bar {n}}}} \right. \kern-\nulldelimiterspace} {\bar {n}}} $ (n is the number of charged secondaries) has been used pointing out a possible asymptotic behaviour of total charged multiplicities at primary energies exceeding 40 TeV (8.5 1017 eV). Thus, larger reduction of the energies devoted to the leading cluster and very large multiplicity of secondary particles could suggest for EAS generated by primary protons a larger production of muons and a shower maximum at higher altitude.
Leading cluster approach to simulations of hadron collisions with GHOST generator