From AMS Glossary
(Also air shower, cascade, extensive air shower, shower.) Multiple generations of secondary cosmic rays produced when primary cosmic rays interact with atoms in the upper atmosphere, yielding subatomic particles and gamma rays. The secondary cosmic rays in turn produce even more down through the atmosphere.
Billions of these particles travel downward at nearly the speed of light and at ground level may extend over several square kilometers (in which instance the shower may be termed an extensive air shower). The maximum flux of cosmic rays, both primary and secondary, is at an altitude of 20 km, and below this the absorption by the atmosphere reduces the flux, though the rays are still readily detectable at sea level. Intensity of cosmic ray showers has also been observed to vary with latitude, being more intense at the poles.
Friedlander, M. W. 1989. Cosmic Rays. pp. 13, 79.