Abstract
Electromagnetic cascades in matter, photon fields, and magnetic fields are solved by a standard numerical method, integrating the diffusion equations of respective cas- cade processes numerically. Our results and those of Aharo- nian and Plyasheshnikov agree very well for cascades in mat- ter and magnetic fields, though they show some slight dis- crepancies for cascades in photon fields of high incident ener- gies. Transport properties of electron and photon spectra are also investigated by solving differential-difference equations for cascades with simplified cross-sections, and the spec- tra under the electron cooldown process are well explained quantitatively. Rossi and Greisen, when cross-sections are inhomogeneous with primary and secondary energies. So we apply standard numerical methods to integrate the above cascade equations. Our results for transition curves of shower electrons devel- oping in matter, photon fields, and magnetic fields are com- pared with those derived by Aharonian and Plyasheshnikov and by Nishimura (1967). We also indicate changes in the energy spectra of cascade electrons and photons penetrating photon fields, and attempt to explain the transport property of the energy spectra quantitatively by solving differential- difference equations with simplified cross-sections.
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