ExHaLe-jet: An extended hadro-leptonic jet model for blazars. I. Code description and initial results

The processes operating in blazar jets are still an open question. Modeling the radiation emanating from an extended part of the jet allows one to capture these processes on all scales. Kinetic codes solving the Fokker-Planck equation along the jet flow are well suited to this task, as they can efficiently derive the radiation and particle spectra without the need for computationally demanding plasma-physical simulations. Here, we present a new extended hadro-leptonic jet code -- ExHaLe-jet -- which considers simultaneously the processes of relativistic protons and electrons. Within a pre-set geometry and bulk flow, the particle evolution is derived self-consistently. Highly relativistic secondary electrons (and positrons) are created through $\gamma$-$\gamma$ pair production, Bethe-Heitler pair production, and pion/muon decay. These secondaries are entrained in the jet flow decreasing the ratio of protons to electrons with distance from the jet base. For particle-photon interactions, we consider all internal and many external photon fields, such as the accretion disk, broad-line region, and the dusty torus. The external fields turn out to be the most important source for particle-photon interactions governing the resulting photon and neutrino spectra. In this paper, we present the code and an initial parameter study, while in follow-up works we present extensions of the code and more specific applications.