Simulating electromagnetic cascades in magnetospheres of active galactic nuclei

Context: At the low accretion-rates typical for BL Lac-objects, magnetospheres of active galactic nuclei can develop vacuum gaps with strong electric fields accelerating charged seed particles parallel to the magnetic fields up to ultra-relativistic energies. The seed particles sustain electromagnetic cascades by inverse-Compton-scattering and subsequent pair-production in soft background-radiation-fields from the accretion-disk and/or photo-ionised clouds, along the direction of the primary particle beams. Method: The one-dimensional kinetic equation describing this linear inverse-Compton-Klein-Nishina-pair-cascade is inferred. We have developed a novel code, that can numerically solve this kinetic equation for an ample variety of input-parameters. By this, quasi-stationary particle- and photon-spectra are obtained. Application: We use the code to model the cascaded interaction of electrons, that have been accelerated in a vacuum gap in the magnetosphere of Mrk 501, with Lyman-alpha-photons. The resulting spectrum on top of a synchrotron-self-Compton-background can cause a narrow TeV-bump in the spectrum of of Mrk 501.