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In a strong magnetic field, a high-energy photon can be absorbed and thenproduce an electron-positron pair. The produced electron/positron will in turnradiate a high-energy photon via synchrotron radiation, which then initiates acascade. We built a one-dimensional Monte-Carlo code to study the developmentof the cascade especially after it reaches the saturated status, when almostall the energy of the primary particles transfers to the photons. The photonspectrum in this status has a cut-off due to the absorption by magnetic fields,which is much sharper than the exponential one. Below the cut-off, the spectralenergy distribution (SED) manifest itself as a broken power-law with a spectralindex of $0.5$ and $0.125$, respectively, below and above the broken energy.The SED can be fitted by a simple analytical function, which is solelydetermined by the product of the cascade scale $R$ and the magnetic fieldperpendicular to the motion of the particle B_{\perp}, with an accuracy betterthan 96\%. The similarity of the spectrum to that from the cascade in anisotropic black-body photon field is also studied.

Analytical treatment for the development of electromagnetic cascades in intense magnetic fields