High energy photons from blazars can initiate electromagnetic pair cascades interacting with the extragalactic photon background. The charged component of such cascades is deflected and delayed by extragalactic magnetic fields (EGMF), reducing thereby the observed point-like flux and leading potentially to multi degree images in the GeV energy range. We calculate the fluence of 1ES 0229+200 as seen by Fermi-LAT for different EGMF profiles using a Monte Carlo simulation for the cascade development. The non-observation of 1ES 0229+200 by Fermi-LAT suggests that the EGMF fills at least 60% of space with fields stronger than O(10 −16 − 10 −15 ) G for life times of TeV activity of O(10 2 − 10 4 ) yr. Thus the (non-) observation of GeV extensions around TeV blazars probes the EGMF in voids and puts strong constraints on the origin of EGMFs: Either EGMFs were generated in a space filling manner (e.g. primordially) or EGMFs produced locally (e.g. by galaxies) have to be efficiently transported to fill a significant volume fraction, as e.g. by galactic outflows.

Local interstellar spectra (LIS) for protons, helium and antiprotons are built using the most recent experimental results combined with the state-of-the-art models for propagation in the Galaxy and heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of cosmic ray (CR) species at different modulation levels and at both polarities of the solar magnetic field. To do so in a self-consistent way, an iterative procedure was developed, where the GALPROP LIS output is fed into HelMod that provides modulated spectra for specific time periods of selected experiments to compare with the data; the HelMod parameters optimization is performed at this stage and looped back to adjust the LIS using the new GALPROP run. The parameters were tuned with the maximum likelihood procedure using an extensive data set of proton spectra from 1997-2015. The proposed LIS accommodate both the low energy interstellar CR spectra measured by Voyager 1 and the high energy observations by BESS, Pamela, AMS-01, and AMS-02 made from the balloons and near-Earth payloads; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The found solution is in a good agreement with proton, helium, and antiproton data by AMS-02, BESS, and PAMELA in the whole energy range.

An efficient scheme for one-dimensional extensive air shower simulation and its implementation in the program CONEX are presented. Explicit Monte Carlo simulation of the high-energy part of hadronic and electromagnetic cascades in the atmosphere is combined with a numeric solution of cascade equations for smaller energy sub-showers to obtain accurate shower predictions. The developed scheme allows us to calculate not only observables related to the number of particles (shower size) but also ionization energy deposit profiles which are needed for the interpretation of data of experiments employing the fluorescence light technique. We discuss in detail the basic algorithms developed and illustrate the power of the method. It is shown that Monte Carlo, numerical, and hybrid air shower calculations give consistent results which agree very well with those obtained within the CORSIKA program.