An evaluation of electron-photon cascades developing in matter, photon and magnetic fields

Abstract

Electromagnetic cascades in matter, photon fields, and magnetic fields are solved by a standard numerical method, integrating the diffusion equations of respective cascade processes numerically. Our results and those of Aharonian and Plyasheshnikov agree very well for cascades in matter and magnetic fields, though they show some slight discrepancies for cascades in photon fields of high incident energies. Transport properties of electron and photon spectra are also investigated by solving differential-difference equations for cascades with simplified cross-sections, and the spectra under the electron cooldown process are well explained quantitatively

An Exact Analytical Derivation of Energy Spectra for High-Energy Cascade Electron and Photon in Strong Magnetic Fields

“…2 for electron-and photon-incident showers (• dots), compared with those derived through the numerical integration method (lines) [7] and the Monte Carlo results by Anguelov and Vankov (+ dots) [5]. Present results agree very well with the latters.…”

“…1 for electronand photon-incident showers (dots), compared with those derived through the numerical integration method (lines) [7]. Both results agree very well.…”

“…Transition curves of electrons and photons for electron-and gamma-incident showers, from left to right. Those derived through the numerical inverse Mellin transforms (• dots) for E 0 /E of 10 2 , 10 4 , 10 6 , 10 8 , from the bottom to the top, are compared with those derived through the numerical integral method (lines) [7] and Monte Carlo results (+ dots) [5]. Energies of electron and photon are distinguished by E and W.…”

“…As the cross-sections do not depend only on the fractional energies between the primary and the secondary particles, the equation cannot be solved by the traditional Landau-Rumer method [2][3][4]. So an adiabatic method [1], a Monte Carlo method [5], and numerical integration methods [6,7] were applied to solve the equation, though there still remained ambiguities in accuracy and convergence in those results. We attempt to get the exact solution by numerical inverse Mellin transforms.…”

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

“…(5) and (9) are indicated in Fig. 1 for electron-and photonincident showers (lines), compared with those derived through the numerical integration method (dots) [4]. The former well explain the latter, and the both results agree very well after enough penetration in the fields, about t > 1.…”