Inverse Compton-pair cascades are initiated when gamma-rays are absorbed on an ambient soft photon field to produce relativistic pairs, which in turn up-scatter the same soft photons to produce more gamma-rays. If the Compton scatterings take place in the deep Klein-Nishina regime, then triplet pair production (e{γ }b\to {{ee}}+{e}-) becomes relevant and may even regulate the development of the cascade. We investigate the properties of pair-Compton cascades with triplet pair production in accelerating gaps, i.e., regions with an unscreened electric field. Using the method of transport equations for the particle evolution, we compute the growth rate of the pair cascade as a function of the accelerating electric field in the presence of blackbody and power-law ambient photon fields. Informed by the numerical results, we derive simple analytical expressions for the peak growth rate and the corresponding electric field. We show that for certain parameters, which can be realized in the vicinity of accreting supermassive black holes at the centers of active galactic nuclei, the pair cascade may well be regulated by inverse Compton scattering in the deep Klein-Nishina regime and triplet pair production. We present indicative examples of the escaping gamma-ray radiation from the gap, and discuss our results in application to the TeV observations of radio galaxy M87.

The Fermi Gamma-Ray Space Telescope observations of blazars show a strong correlation between the spectral index of their γ-ray spectra and their synchrotron peak frequency ν _{pk}^{syn}; additionally, the rate of Compton dominance of these sources also seems to be a function of ν _{pk}^{syn}. In this work, we adopt the assumption that the non-thermal emission of blazars is primarily due to radiation by a population of Fermi-accelerated electrons in a relativistic outflow (jet) along the symmetry axis of the blazar's accretion disc. Furthermore, we assume that the Compton component is related to an external photon field of photons, which are scattered from particles of the magnetohydrodynamic wind emanating from the accretion disc. Our results reproduce well the aforementioned basic observational trends of blazar classification by varying just one parameter, namely the mass accretion rate on to the central black hole.