A propagation model of galactic cosmic protons through the Heliosphere was implemented using a 2-D Monte Carlo approach to determine the differential intensities of protons during the solar cycle 23. The model includes the effects due to the variation of solar activity during the propagation of cosmic rays from the boundary of the heliopause down to Earth's position. Drift effects are also accounted for. The simulated spectra were found in agreement with those obtained with experimental observations carried out by BESS, AMS and PAMELA collaborations. In addition, the modulated spectrum determined with the present code for the year 1995 exhibits the latitudinal gradient and equatorial southward offset minimum found by Ulysses fast scan in 1995.

We evaluate the exposure during nadir observations with JEM-EUSO, the Extreme Universe Space Obser-\ud vatory, on-board the Japanese Experiment Module of the International Space Station. Designed as a mis-\ud sion to explore the extreme energy Universe from space, JEM-EUSO will monitor the Earth’s nighttime\ud atmosphere to record the ultraviolet light from tracks generated by extensive air showers initiated by\ud ultra-high energy cosmic rays. In the present work, we discuss the particularities of space-based obser-\ud vation and we compute the annual exposure in nadir observation. The results are based on studies of the\ud expected trigger aperture and observational duty cycle, as well as, on the investigations of the effects of\ud clouds and different types of background light. We show that the annual exposure is about one order of\ud magnitude higher than those of the presently operating ground-based observatories

The cosmic rays propagation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation, several approaches were followed in the past. Recently, a Monte Carlo approach became widely used in force of its advantages with respect to other numerical methods. In this approach the transport equation is associated to a fully equivalent set of stochastic differential equations (SDE). This set is used to describe the stochastic path of quasi‐particle from a source, e.g., the interstellar space, to a specific target, e.g., a detector at Earth. We present a comparison of forward‐in‐time and backward‐in‐time methods to solve the cosmic rays transport equation in the heliosphere. The Parker equation and the related set of SDE in the several formulations are treated in this paper. For the sake of clarity, this work is focused on the one‐dimensional solutions. Results were compared with an alternative numerical solution, namely, Crank‐Nicolson method, specifically developed for the case under study. The methods presented are fully consistent each others for energy greater than 400 MeV. The comparison between stochastic integrations and Crank‐Nicolson allows us to estimate the systematic uncertainties of Monte Carlo methods. The forward‐in‐time stochastic integrations method showed a systematic uncertainty <5%, while backward‐in‐time stochastic integrations method showed a systematic uncertainty <1% in the studied energy range.

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