An essentially analytical theory of the transport of high-energy radiation through the Earth's atmosphere is presented here. The transport of primary and secondary particles is described by a solution of the Boltzmann transport equation. The transport of secondary particles is based on a solution of the Boltzmann equation separable into longitudinal and transverse components, applicable to high-energy hadron-nucleus collisions, and based on work by Passow and reported by Alsmiller, and on Elliott and Williams. All secondary particles other than hadrons are mediated by meson production and decay. The breakup of primary nuclei as a result of collisions with atoms of air is treated by means of a generalized Rudstam formula. The theory described here has also been applied to the atmospheres of other solar system bodies.
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