Asymptotic Properties of Energy Spectra for High-Energy Cascade Electron and Photon in Strong Magnetic Fields

Abstract

We solve the diffusion equation of high-energy electromagnetic cascades in the strong magnetic fields by asymptotic expansions in power series based on the quasi-stable energy spectra. The results of spectra well explain those evaluated by the numerical integration method and show good agreement with the latter at about the shower peak and later. The asymptotic energy spectra of E −5/3 dE, the (E 0 /E) 2/3 -dependence of peak value, and the approximate peak positions are also explained.