On the knee in the energy spectrum of cosmic rays
  The knee in the all-particle energy spectrum is scrutinized with a phenomenological model, named poly-gonato model, linking results from direct and indirect measurements. For this purpose, recent results from direct and indirect measurements of cosmic rays in the energy range from 10 GeV up to 1 EeV are examined. The energy spectra of individual elements, as obtained by direct observations, are extrapolated to high energies using power laws and compared to all-particle spectra from air shower measurements. A cut-off for each element proportional to its charge Z is assumed. The model describes the knee in the all-particle energy spectrum as a result of subsequent cut-offs for individual elements, starting with the proton component at 4.5 PeV, and the second change of the spectral index around 0.4 EeV as due to the end of stable elements (Z=92). The mass composition, extrapolated from direct measurements to high energies, using the poly-gonato model, is compatible with results from air shower experiments measuring the electromagnetic, muonic, and hadronic components. But it disagrees with the mass composition derived from X_max measurements using Cerenkov and fluorescence light detectors. 
J.R. Hoerandel