Similarities and differences between relativistic electron–photon cascades developed in matter, photon gas and magnetic field

We investigate the properties of astrophysical electromagnetic cascades in matter, photon gas and magnetic fields, and discuss similarities and differences between characteristics of electron–photon showers developed in these three substances. We apply the same computational technique based on solution of the adjoint cascade equations to all three types of cascades, and present precise numerical calculations of cascade curves and broad-band energy spectra of secondary electrons and photons at different penetration lengths.