### Main journal articles on HelMod model and code

M J Boschini, S Della Torre, M Gervasi, G La Vacca and P G Rancoita.

**Propagation of Cosmic Rays in Heliosphere: the HelMod Model**.*Submitted to Adv. Space Res.*, page 0, 2017.

Abstract The heliospheric modulation model HelMod is a two dimensional treatment dealing with the helio-colatitude and radial distance from Sun and is employed to solve the transport-equation for the GCR propagation through the heliosphere down to Earth. The treatment includes the so-called particle drift effects –~e.g., those resulting, for instance, from the extension of the neutral current sheet inside the heliosphere and from the curvature and gradient of the IMF –, which affect the transport of particles entering the solar cavity as a function of their charge sign. The HelMod model is capable to provide modulated spectra which well agree within the experimental errors with those measured by AMS-01, BESS, PAMELA and AMS-02 during the solar cycles 23 and 24. Furthermore, the counting rate measured by Ulysses at \(\pm 80^\circ\) of solar latitude and 1 to 5 AU was also found in agreement with that expected by HelMod code version 3.0.

DOI BibTeX@article{DellaTorre2017, author = "{Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {La Vacca}, G. and {Rancoita}, P.G.", title = "{Propagation of Cosmic Rays in Heliosphere: the HelMod Model}", journal = "Submitted to Adv. Space Res.", year = 2017, month = "", pages = 0, doi = 0, abstract = "The heliospheric modulation model HelMod is a two dimensional treatment dealing with the helio-colatitude and radial distance from Sun and is employed to solve the transport-equation for the GCR propagation through the heliosphere down to Earth. The treatment includes the so-called particle drift effects --~e.g., those resulting, for instance, from the extension of the neutral current sheet inside the heliosphere and from the curvature and gradient of the IMF --, which affect the transport of particles entering the solar cavity as a function of their charge sign. The HelMod model is capable to provide modulated spectra which well agree within the experimental errors with those measured by AMS-01, BESS, PAMELA and AMS-02 during the solar cycles 23 and 24. Furthermore, the counting rate measured by Ulysses at \(\pm 80^\circ\) of solar latitude and 1 to 5 AU was also found in agreement with that expected by HelMod code version 3.0." }

P Bobik, M J Boschini, S Della Torre, M Gervasi, D Grandi, G La Vacca, S Pensotti, M Putis, P G Rancoita, D Rozza, M Tacconi and M Zannoni.

**On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case**.*Journal of Geophysical Research: Space Physics*121(5):3920–3930, 2016.

2015JA022237.

Abstract 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.

URL, DOI BibTeX@article{JGRA:JGRA52618, author = "Bobik, P. and Boschini, M. J. and Della Torre, S. and Gervasi, M. and Grandi, D. and La Vacca, G. and Pensotti, S. and Putis, M. and Rancoita, P. G. and Rozza, D. and Tacconi, M. and Zannoni, M.", title = "On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case", journal = "Journal of Geophysical Research: Space Physics", volume = 121, number = 5, issn = "2169-9402", url = "http://dx.doi.org/10.1002/2015JA022237", doi = "10.1002/2015JA022237", pages = "3920--3930", keywords = "Numerical algorithms, Software tools and services, Cosmic rays, General or miscellaneous, Mathematical and numerical techniques, Monte Carlo, cosmic rays propagation, heliosphere", year = 2016, note = "2015JA022237", abstract = "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." }

P Bobik, G Boella, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti, P G Rancoita, D Rozza and M Tacconi.

**Latitudinal Dependence of Cosmic Rays Modulation at 1 AU and Interplanetary Magnetic Field Polar Correction**.*Advances in Astronomy*2013, 2013.

Abstract The cosmic rays differential intensity inside the heliosphere, for energy below 30 GeV/nuc, depends on solar activity and interplanetary magnetic field polarity. is variation, termed solar modulation, is described using a 2D (radius and colatitude) Monte Carlo approach for solving the Parker transport equation that includes diffusion, convection, magnetic drift, and adiabatic energy loss. Since the whole transport is strongly related to the interplanetary magnetic field (IMF) structure, a better understanding of his description is needed in order to reproduce the cosmic rays intensity at the Earth, as well as outside the ecliptic plane. In this work an interplanetary magnetic field model including the standard description on ecliptic region and a polar correction is presented. this treatment of the IMF, implemented in the HelMod Monte Carlo code (version 2.0), was used to determine the effects on the differential intensity of Proton at 1 AU and allowed one to investigate how latitudinal gradients of proton intensities, observed in the inner heliosphere with the Ulysses spacecra during 1995, can be affected by the modification of the IMF in the polar regions.

URL, DOI BibTeX@article{DellaTorre2013AdvAstro, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J.. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D. and {Tacconi}, M.", title = "{Latitudinal Dependence of Cosmic Rays Modulation at 1 AU and Interplanetary Magnetic Field Polar Correction}", journal = "Advances in Astronomy", archiveprefix = "arXiv", eprint = "1212.1559", primaryclass = "astro-ph.SR", year = 2013, volume = 2013, eid = 793072, doi = "10.1155/2013/793072", adsurl = "http://adsabs.harvard.edu/abs/2013AdAst2013E...1B", adsnote = "Provided by the SAO/NASA Astrophysics Data System", abstract = "The cosmic rays differential intensity inside the heliosphere, for energy below 30 GeV/nuc, depends on solar activity and interplanetary magnetic field polarity. is variation, termed solar modulation, is described using a 2D (radius and colatitude) Monte Carlo approach for solving the Parker transport equation that includes diffusion, convection, magnetic drift, and adiabatic energy loss. Since the whole transport is strongly related to the interplanetary magnetic field (IMF) structure, a better understanding of his description is needed in order to reproduce the cosmic rays intensity at the Earth, as well as outside the ecliptic plane. In this work an interplanetary magnetic field model including the standard description on ecliptic region and a polar correction is presented. this treatment of the IMF, implemented in the HelMod Monte Carlo code (version 2.0), was used to determine the effects on the differential intensity of Proton at 1 AU and allowed one to investigate how latitudinal gradients of proton intensities, observed in the inner heliosphere with the Ulysses spacecra during 1995, can be affected by the modification of the IMF in the polar regions.", url = "https://arxiv.org/abs/1212.1559" }

S Della Torre, P Bobik, M J Boschini, C Consolandi, M Gervasi, D Grandi, K Kudela, S Pensotti, P G Rancoita, D Rozza and M Tacconi.

**Effects of solar modulation on the cosmic ray positron fraction**.*Adv. Space Res.*49:1587-1592, 2012.

Abstract We implemented a 2D Monte Carlo model to simulate the solar modulation of galactic cosmic rays. The model is based on the Par- ker’s transport equation which contains diffusion, convection, particle drift and energy loss. Following the evolution in time of the solar activity, we are able to modulate a local interstellar spectrum (LIS), that we assumed isotropic beyond the termination shock, down to the Earth position inside the heliosphere. In this work we focused our attention to the cosmic ray positron fraction at energy below ~10 GeV, showing how the particle drift processes could explain different results for AMS-01 and PAMELA. We compare our modu- lated spectra with observations at Earth, and then make a prediction of the cosmic ray positron fraction for the AMS-02 experiment.

DOI BibTeX@article{DellaTorre2012, author = "{Della Torre}, S. and {Bobik}, P. and {Boschini}, M.J.. and {Consolandi}, C. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D. and {Tacconi}, M.", title = "{Effects of solar modulation on the cosmic ray positron fraction}", journal = "Adv. Space Res.", year = 2012, month = "", volume = 49, pages = "1587-1592", doi = "10.1016/j.asr.2012.02.017", abstract = "We implemented a 2D Monte Carlo model to simulate the solar modulation of galactic cosmic rays. The model is based on the Par- ker’s transport equation which contains diffusion, convection, particle drift and energy loss. Following the evolution in time of the solar activity, we are able to modulate a local interstellar spectrum (LIS), that we assumed isotropic beyond the termination shock, down to the Earth position inside the heliosphere. In this work we focused our attention to the cosmic ray positron fraction at energy below ~10 GeV, showing how the particle drift processes could explain different results for AMS-01 and PAMELA. We compare our modu- lated spectra with observations at Earth, and then make a prediction of the cosmic ray positron fraction for the AMS-02 experiment.", adsurl = "http://adsabs.harvard.edu/abs/2012AdSpR..49.1587D", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

P Bobik, G Boella, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti, P G Rancoita and M Tacconi.

**Systematic Investigation of Solar Modulation of Galactic Protons for Solar Cycle 23 Using a Monte Carlo Approach with Particle Drift Effects and Latitudinal Dependence**.*Astrophys. J.*745:132, 2012.

Abstract A propagation model of galactic cosmic protons through the heliosphere was implemented using a two-dimensional Monte Carlo approach to determine the differential intensities of protons during 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 to be in agreement with those obtained from experimental observations carried out by the 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 the Ulysses fast scan in 1995.

URL, DOI BibTeX@article{Bobik2011ApJ, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G. and {Tacconi}, M.", title = "Systematic Investigation of Solar Modulation of Galactic Protons for Solar Cycle 23 Using a Monte Carlo Approach with Particle Drift Effects and Latitudinal Dependence", journal = "Astrophys. J.", archiveprefix = "arXiv", eprint = "1110.4315", primaryclass = "astro-ph.SR", abstract = "A propagation model of galactic cosmic protons through the heliosphere was implemented using a two-dimensional Monte Carlo approach to determine the differential intensities of protons during 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 to be in agreement with those obtained from experimental observations carried out by the 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 the Ulysses fast scan in 1995.", keywords = "cosmic rays, solar-terrestrial relations, solar wind, Sun: heliosphere", year = 2012, month = "", volume = 745, eid = 132, pages = 132, doi = "10.1088/0004-637X/745/2/132", adsurl = "http://adsabs.harvard.edu/abs/2012ApJ...745..132B", adsnote = "Provided by the SAO/NASA Astrophysics Data System", url = "https://arxiv.org/abs/1110.4315" }

P Bobik, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**Antiproton modulation in the Heliosphere and AMS-02 antiproton over proton ratio prediction**.*Astrophys. Space Sci. Trans.*7(3):245–249, 2011.

Abstract We implemented a quasi time-dependent 2D stochastic model of solar modulation describing the transport of cosmic rays (CR) in the heliosphere. Our code can modulate the Local Interstellar Spectrum (LIS) of a generic charged particle (light cosmic ions and electrons), calculating the spectrum at 1AU. Several measurements of CR antiparticles have been performed. Here we focused our attention on the CR antiproton component and the antiproton over proton ratio. We show that our model, using the same heliospheric parameters for both particles, fit the observed anti-p/p ratio. We show a good agreement with BESS-97 and PAMELA data and make a prediction for the AMS-02 experiment.

URL, DOI BibTeX@article{AstraArticle2011, author = "{Bobik}, P. and {Boschini}, M.J.. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G.", title = "Antiproton modulation in the Heliosphere and AMS-02 antiproton over proton ratio prediction", journal = "Astrophys. Space Sci. Trans.", year = 2011, volume = 7, pages = "245--249", number = 3, abstract = "We implemented a quasi time-dependent 2D stochastic model of solar modulation describing the transport of cosmic rays (CR) in the heliosphere. Our code can modulate the Local Interstellar Spectrum (LIS) of a generic charged particle (light cosmic ions and electrons), calculating the spectrum at 1AU. Several measurements of CR antiparticles have been performed. Here we focused our attention on the CR antiproton component and the antiproton over proton ratio. We show that our model, using the same heliospheric parameters for both particles, fit the observed anti-p/p ratio. We show a good agreement with BESS-97 and PAMELA data and make a prediction for the AMS-02 experiment.", doi = "10.5194/astra-7-245-2011", file = "1102.0215:http\://arxiv.org/pdf/1102.0215:PDF", keywords = "Earth and Planetary Astrophysics (astro-ph.EP)", url = "http://arxiv.org/abs/1102.0215" }

### Conference proceedings

S Della Torre, M Gervasi, D Grandi, G Johannesson, G La Vacca, N Masi, I V Moskalenko, E Orlando, T A Porter, L Quadrani, P G Rancoita and D Rozza.

**From Observations near the Earth to the Local Interstellar Spectra**.

In*Proceedings of the 25th European Cosmic Rays Symposyum (ECRS2016) eConf C16-09-04.3, Septembers 4-9,2016 (Torino, Italy), arXiv: 1701.02363*. 2016.

URL BibTeX@inproceedings{ECRS2016b, author = "Della Torre, S. and Gervasi, M. and Grandi, D. and Johannesson, G. and {La Vacca}, G. and Masi, N. and Moskalenko, I.V. and Orlando, E. and Porter, T.A. and Quadrani, L. and Rancoita, P.G. and Rozza, D.", title = "{From Observations near the Earth to the Local Interstellar Spectra}", year = 2016, booktitle = "Proceedings of the 25th European Cosmic Rays Symposyum (ECRS2016) eConf C16-09-04.3, Septembers 4-9,2016 (Torino, Italy), arXiv: 1701.02363", url = "https://arxiv.org/abs/1701.02363" }

S Della Torre, M Gervasi, D Grandi, G Johannesson, G La Vacca, N Masi, I V Moskalenko, E Orlando, T A Porter, L Quadrani, P G Rancoita and D Rozza.

**HelMod: a Comprehensive Treatment of the Cosmic Ray transport through the Heliosphere**.

In*Proceedings of the 25th European Cosmic Rays Symposyum (ECRS2016) eConf C16-09-04.3, Septembers 4-9,2016 (Torino, Italy), arXiv: 1612.08445*. 2016.

URL BibTeX@inproceedings{ECRS2016, author = "Della Torre, S. and Gervasi, M. and Grandi, D. and Johannesson, G. and {La Vacca}, G. and Masi, N. and Moskalenko, I.V. and Orlando, E. and Porter, T.A. and Quadrani, L. and Rancoita, P.G. and Rozza, D.", title = "{HelMod: a Comprehensive Treatment of the Cosmic Ray transport through the Heliosphere}", year = 2016, booktitle = "Proceedings of the 25th European Cosmic Rays Symposyum (ECRS2016) eConf C16-09-04.3, Septembers 4-9,2016 (Torino, Italy), arXiv: 1612.08445", url = "https://arxiv.org/abs/1612.08445" }

S Della Torre, P Bobik, M J Boschini, M Gervasi, D Grandi, G La Vacca, S Pensotti, M Putis, P G Rancoita, D Rozza, M Tacconi and M Zannoni.

**Cosmic Rays Propagation with HelMod: Difference between forward-in-time and backward-in-time approaches**.

In*Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), July 30 - August 6, 2015 (The Hague, The Netherlands)*. 2015.

URL BibTeX@inproceedings{DellaTorreICRC2015, author = "Della Torre, S. and Bobik, P and Boschini, M.J. and Gervasi, M. and Grandi, D and La Vacca, G. and Pensotti, S. and Putis, M. and Rancoita, P.G. and Rozza, D. and Tacconi, M. and Zannoni, M.", title = "{Cosmic Rays Propagation with HelMod: Difference between forward-in-time and backward-in-time approaches}", year = "2015 arXiv:1511.00541", booktitle = "Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), July 30 - August 6, 2015 (The Hague, The Netherlands)", url = "https://arxiv.org/abs/1511.00541" }

P Bobik, M J Boschini, S Della Torre, M Gervasi, D Grandi, K Kudela, G La Vacca, M Mallamaci, S Pensotti, P G Rancoita, D Rozza and M Tacconi.

**Solar Modulation along last solar minimum**.

In S Giani and al. (eds.).*Astroparticle, Particle, Space Physics and Detectors for Physics Applications - Proceedings of the 14th ICATPP Conference*. 2014, 177-181.

DOI BibTeX@inproceedings{2014ICATPP_DellaTorre, author = "{Bobik}, P. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {La Vacca}, G. and {Mallamaci}, M. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D. and {Tacconi}, M.", title = "{Solar Modulation along last solar minimum}", booktitle = "Astroparticle, Particle, Space Physics and Detectors for Physics Applications - Proceedings of the 14th ICATPP Conference", year = 2014, editor = "{Giani}, S. and {et al.}", month = "", pages = "177-181", doi = "10.1142/9789814603164_0027", adsurl = "http://adsabs.harvard.edu/abs/2014apsp.conf..177B", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

P Bobik, G Boella, M J Boschini, S Della Torre, M Gervasi, D Grandi, G La Vacca, K Kudela, S Pensotti, P G Rancoita, D Rozza and M Tacconi.

**Cosmic Ray Modulation studied with HelMod Monte Carlo tool and comparison with Ulysses Fast Scan Data during consecutive Solar Minimums**.

In*Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), July 2-9 2013 (Rio de Janeiro, Brazil), arXiv: 1307.5199*. 2013, 1100.

URL BibTeX@inproceedings{ICRC13_DellaTorre, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {La Vacca}, G. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D. and {Tacconi}, M.", title = "Cosmic Ray Modulation studied with HelMod Monte Carlo tool and comparison with Ulysses Fast Scan Data during consecutive Solar Minimums", booktitle = "Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), July 2-9 2013 (Rio de Janeiro, Brazil), arXiv: 1307.5199", year = 2013, pages = 1100, series = "International Cosmic Ray Conference", journal = "arXiv: 1307.5199", archiveprefix = "arXiv", eprint = "1307.5199", slaccitation = "%%CITATION = ARXIV:1307.5199;%%", url = "https://arxiv.org/abs/1307.5199" }

P Bobik, M J Boschini, C Consolandi, S Della Torre, M Gervasi and others.

**GeoMag and HelMod webmodels version for magnetosphere and heliosphere transport of cosmic rays**.

In*Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), July 2-9 2013 (Rio de Janeiro, Brazil), arXiv: 1307.5196*. 2013.

URL BibTeX@inproceedings{ICRC13_Bobik, author = "Bobik, P. and Boschini, M.J. and Consolandi, C. and Della Torre, S. and Gervasi, M. and others", title = "GeoMag and HelMod webmodels version for magnetosphere and heliosphere transport of cosmic rays", year = 2013, booktitle = "Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), July 2-9 2013 (Rio de Janeiro, Brazil), arXiv: 1307.5196", journal = "arXiv: 1307.5196", eprint = "1307.5196", archiveprefix = "arXiv", primaryclass = "astro-ph.IM", slaccitation = "%%CITATION = ARXIV:1307.5196;%%", url = "https://arxiv.org/abs/1307.5196" }

P Bobik, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, K Kudela, F Noventa, S Pensotti, P G Rancoita and D Rozza.

**Heliosphere Dimension and Cosmic Ray Modulation**.

In S Giani, C Leroy, L Price, P G Rancoita and R Ruchti (eds.).*Astroparticle, Particle, Space Physics, and Detectors for Physics Applications - Vol. 7*. 2012, 249-257 arXiv:1112.5730.

URL BibTeX@inproceedings{ICATPP2011_DimHelio, author = "{Bobik}, P. and {Boschini}, M.J. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Noventa}, F. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D.", title = "{Heliosphere Dimension and Cosmic Ray Modulation}", booktitle = "Astroparticle, Particle, Space Physics, and Detectors for Physics Applications - Vol. 7", editor = "Giani, S. and Leroy, C. and Price, L. and Rancoita, P.G. and Ruchti, R.", publisher = "World Scientific", pages = "249-257 arXiv:1112.5730", archiveprefix = "arXiv", eprint = "1112.5730", primaryclass = "astro-ph.SR", keywords = "Astrophysics - Solar and Stellar Astrophysics, Astrophysics - Earth and Planetary Astrophysics", year = 2012, url = "https://arxiv.org/abs/1112.5730", adsnote = "Provided by the SAO/NASA Astrophysics Data System", adsurl = "http://adsabs.harvard.edu/abs/2011arXiv1112.5730B" }

P Bobik, M J Boschini, C Consolandi, M Della Torre S. Gervasi, D Grandi, K Kudela, F Noventa, S Pensotti, P G Rancoita and D Rozza.

**Cosmic Rays propagation in the Heliosphere**.

In S Giani, C Leroy, L Price, P G Rancoita and R Ruchti (eds.).*Proceedings of the 13th Conference on Astroparticle, Particle and Space Physics, Detectors and medical physics applications*. 2012, 226-231.

BibTeX@inproceedings{ICATPP2011_Trasmission, author = "{Bobik}, P. and {Boschini}, M.J. and {Consolandi}, C. and {Della Torre}, S. {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Noventa}, F. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D.", title = "{Cosmic Rays propagation in the Heliosphere}", booktitle = "Proceedings of the 13th Conference on Astroparticle, Particle and Space Physics, Detectors and medical physics applications", editor = "Giani, S. and Leroy, C. and Price, L. and Rancoita, P.G. and Ruchti, R.", year = 2012, pages = "226-231", publisher = "World Scientific", journal = "Proc. of the 13th International Conference on Particle Physics and Advanced Technology, Como 5--9/10/2011, World Scientific, Singapore" }

P Bobik, G Boella, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, M Elmo, K Kudela, E Memola, S Pensotti, P G Rancoita, D Rozza and M Tacconi.

**Energy Loss for Electrons in the Heliosphere and Local Interstellar Spectrum for Solar Modulation**.

In S Giani, C Leroy and P G Rancoita (eds.).*Cosmic Rays for Particle and Astropart. Phys.*. June 2011, 482-489.

DOI BibTeX@inproceedings{ICATPP10_energyloss, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Elmo}, M. and {Kudela}, K. and {Memola}, E. and {Pensotti}, S. and {Rancoita}, P.G. and {Rozza}, D. and {Tacconi}, M.", title = "{Energy Loss for Electrons in the Heliosphere and Local Interstellar Spectrum for Solar Modulation}", keywords = "cosmic rays, heliosphere, solar modulation, energy losses", booktitle = "Cosmic Rays for Particle and Astropart. Phys.", year = 2011, editor = "{Giani}, S. and {Leroy}, C. and {Rancoita}, P.G.", month = "jun", pages = "482-489", doi = "10.1142/9789814329033_0060", adsurl = "http://adsabs.harvard.edu/abs/2011crpa.conf..482B", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

P Bobik, G Boella, M ~J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, K Kudela, E Memola, S Pensotti, P ~G Rancoita and M Tacconi.

**Proton Modulation in the Heliosphere for Different Solar Conditions and Prediction for AMS-02**.

In S Giani, C Leroy and P ~G Rancoita (eds.).*Cosmic Rays for Particle and Astroparticle Physics*. June 2011, 352-359 arXiv:1012.0938.

URL, DOI BibTeX@inproceedings{2011crpa.conf..352B, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.~J. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Memola}, E. and {Pensotti}, S. and {Rancoita}, P.~G. and {Tacconi}, M.", title = "{Proton Modulation in the Heliosphere for Different Solar Conditions and Prediction for AMS-02}", keywords = "Heliosphere, Cosmic Rays, Solar Magnetic Field", booktitle = "Cosmic Rays for Particle and Astroparticle Physics", year = 2011, archiveprefix = "arXiv", eprint = "1012.0938", primaryclass = "astro-ph.EP", editor = "{Giani}, S. and {Leroy}, C. and {Rancoita}, P.~G.", month = "jun", pages = "352-359 arXiv:1012.0938", url = "https://arxiv.org/abs/1012.0938", doi = "10.1142/9789814329033_0045", adsurl = "http://adsabs.harvard.edu/abs/2011crpa.conf..352B", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

P Bobik, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**Electron and Positron solar modulation and prediction for AMS02**.

In S Giani, C Leroy and P G Rancoita (eds.).*Cosmic Rays for Particle and Astropart. Phys.*. June 2011, 337-342 arXiv:1011.4843.

URL, DOI BibTeX@inproceedings{ICATPP2010_Electron, author = "{Bobik}, P. and {Boschini}, M.J. and {Consolandi}, C. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G.", title = "{Electron and Positron solar modulation and prediction for AMS02}", keywords = "cosmic rays, heliosphere, positron ratio, solar modulation", booktitle = "Cosmic Rays for Particle and Astropart. Phys.", year = 2011, archiveprefix = "arXiv", eprint = "1011.4843", primaryclass = "astro-ph.SR", editor = "{Giani}, S. and {Leroy}, C. and {Rancoita}, P.G.", month = "jun", pages = "337-342 arXiv:1011.4843", doi = "10.1142/9789814329033_0043", url = "https://arxiv.org/abs/1011.4843", adsurl = "http://adsabs.harvard.edu/abs/2011crpa.conf..337B", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

P Bobik, M J Boschini, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**Proton and antiproton modulation in the heliosphere for different solar conditions and AMS-02 measurements prediction**.

In C Leroy, P G Rancoita, M Barone, A Gaddi, L Price and R Ruchti (eds.).*Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications - Proc. of the 12th ICATPP Conference on Cosmic Rays for Particle and Astropart. Phys.*. 2011, 360–368 arXiv:1012.3086.

URL BibTeX@inproceedings{DavArticle2010, author = "{Bobik}, P. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G.", title = "{Proton and antiproton modulation in the heliosphere for different solar conditions and AMS-02 measurements prediction}", booktitle = "Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications - Proc. of the 12th ICATPP Conference on Cosmic Rays for Particle and Astropart. Phys.", year = 2011, editor = "Leroy, C. and Rancoita, P.G. and Barone, M. and Gaddi, A. and Price, L. and Ruchti, R.", pages = "360--368 arXiv:1012.3086", url = "https://arxiv.org/abs/1012.3086", keywords = "Cosmic Rays, Heliosphere, Particle Drift" }

P Bobik, G Boella, M J Boschini, C Consolandi, S Della Torre, M Gervasi, D Grandi, M Elmo, K Kudela, E Memola, S Pensotti, D Rozza, P G Rancoita and M Tacconi.

**Energy Loss for electrons in the heliosphere and local interstellar spectrum for solar modulation**.*Proc. of the ICATPP Conference on Cosmic Rays for Particle and Astropart. Phys., Como 7–8/10/2010, World Scientific, Singapore*, 2010.

BibTeX@article{mauroPoster2010, author = "{Bobik}, P. and {Boella}, G. and {Boschini, M.J.} and {Consolandi}, C. and {Della Torre},S. and {Gervasi}, M. and {Grandi}, D. and {Elmo}, M. and {Kudela, K.} and {Memola}, E. and {Pensotti,S.} and {Rozza}, D. and {Rancoita}, P. G. and {Tacconi}, M.", title = "{Energy Loss for electrons in the heliosphere and local interstellar spectrum for solar modulation}", journal = "Proc. of the ICATPP Conference on Cosmic Rays for Particle and Astropart. Phys., Como 7--8/10/2010, World Scientific, Singapore", year = 2010 }

P Bobik, M J Boschini, S Della Torre, M Gervasi, D Grandi, K Kudela and P G Rancoita.

**Galactic Cosmic Rays Modulation and Prediction for the AMS-02 Mission**.

In C Leroy, P -G Rancoita, M Barone, A Gaddi, L Price and R Ruchti (eds.).*Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications*. 2010, 210-219.

DOI BibTeX@inproceedings{bobik2010a, author = "{Bobik}, P. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Rancoita}, P.G.", title = "{Galactic Cosmic Rays Modulation and Prediction for the AMS-02 Mission}", keywords = "Heliosphere, Cosmic Rays, Solar Magnetic Field", booktitle = "Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications", year = 2010, editor = "{Leroy}, C. and {Rancoita}, P.-G. and {Barone}, M. and {Gaddi}, A. and {Price}, L. and {Ruchti}, R.", month = "", pages = "210-219", doi = "10.1142/9789814307529_0036", adsurl = "http://adsabs.harvard.edu/abs/2010apsp.conf..210B", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

P Bobik, G Boella, M J Boschini, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**Drift models and polar field for cosmic rays propagatin in the heliosphere**.*Proc. of the 11th International Conference on Particle Physics and Advanced Technology, Como 5–9/10/2009, World Scientific, Singapore*, pages 760–764, October 2009.

BibTeX@article{DellaTorre2009, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G.", title = "{Drift models and polar field for cosmic rays propagatin in the heliosphere}", journal = "Proc. of the 11th International Conference on Particle Physics and Advanced Technology, Como 5--9/10/2009, World Scientific, Singapore", year = 2009, pages = "760--764", month = "october", booktitle = "Proceedings of the 11th Conference on Astroparticle, Particle and Space Physics, Detectors and medical physics applications", publisher = "World Scientific" }

P Bobik, G Boella, M J Boschini, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**2D stochastic Monte Carlo to evaluate the modulation of GCR for positive and negative periods**.*Proc. of 21st European Cosmic Ray Symposium, Košice (Slovakia) 9-12/9/2008*, page 248, 2009.

BibTeX@article{symposium2008, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G.", title = "2D stochastic Monte Carlo to evaluate the modulation of GCR for positive and negative periods", journal = "Proc. of 21st European Cosmic Ray Symposium, Ko\v{s}ice (Slovakia) 9-12/9/2008", year = 2009, pages = 248, organization = "21st European Cosmic Ray Symposium" }

P Bobik, G Boella, M J Boschini, S Della Torre, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**Helisphere modulation of Primary Cosmic Rays for the AMS-02 mission**.*Proc. of the 31st ICRC, Lodz*, 2009.

BibTeX@article{ICRC09, author = "{Bobik}, P. and {Boella}, G. and {Boschini}, M.J. and {Della Torre}, S. and {Gervasi}, M. and {Grandi}, D. and {Kudela}, K. and {Pensotti}, S. and {Rancoita}, P.G.", title = "{Helisphere modulation of Primary Cosmic Rays for the AMS-02 mission}", journal = "Proc. of the 31st ICRC, Lodz", year = 2009, organization = "31st ICRC" }

P Bobik, M J Boschini, M Gervasi, D Grandi and P G Rancoita.

**2D Stochastic Monte Carlo to evaluate the modulation of GCR for inner and outer solar system planets**.

In*Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications*. 2008, 881-885.

URL, DOI BibTeX@inproceedings{doi:10.1142/9789812819093_0147, author = "P. Bobik and M. J. Boschini and M. Gervasi and D. Grandi and P. G. Rancoita", title = "2D Stochastic Monte Carlo to evaluate the modulation of GCR for inner and outer solar system planets", booktitle = "Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications", pages = "881-885", doi = "10.1142/9789812819093_0147", url = "http://www.worldscientific.com/doi/abs/10.1142/9789812819093_0147", eprint = "http://www.worldscientific.com/doi/pdf/10.1142/9789812819093_0147", publisher = "WORLD SCIENTIFIC", year = 2008 }

P Bobik, M J Boschini, M Gervasi, D Grandi and P G Rancoita.

**A 2D stochastic Montecarlo for the solar modulation of GCR: a procedure to fit interplanetary parameters comparing to the experimental data**.

In*Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications*. 2006, 206-211.

URL, DOI BibTeX@inproceedings{doi:10.1142/9789812773678_0034, author = "P. Bobik and M. J. Boschini and M. Gervasi and D. Grandi and P. G. Rancoita", title = "A 2D stochastic Montecarlo for the solar modulation of GCR: a procedure to fit interplanetary parameters comparing to the experimental data", booktitle = "Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications", pages = "206-211", doi = "10.1142/9789812773678_0034", url = "http://www.worldscientific.com/doi/abs/10.1142/9789812773678_0034", eprint = "http://www.worldscientific.com/doi/pdf/10.1142/9789812773678_0034", publisher = "WORLD SCIENTIFIC", year = 2006 }

P Bobik, G Boella, M J Boschini, M Gervasi, D Grandi, K Kudela, S Pensotti and P G Rancoita.

**A stochastic Montecarlo approach to Solar modulation of GCR: evaluation of the proton flux at several distances from the Sun**.

In*Proc. of the 20th European Cosmic Rays Symposium (ECRS2006), September 5-9, 2006 (Lisbon, Portugal)*. 2006.

BibTeX@inproceedings{Bobik2007, author = "Bobik, P. and Boella, G. and Boschini, M.J. and Gervasi, M. and Grandi, D. and Kudela, K. and Pensotti,S. and Rancoita, P.G.", title = "A stochastic Montecarlo approach to Solar modulation of GCR: evaluation of the proton flux at several distances from the Sun", year = 2006, booktitle = "Proc. of the 20th European Cosmic Rays Symposium (ECRS2006), September 5-9, 2006 (Lisbon, Portugal)" }

P Bobik, M Gervasi, D Grandi, P G Rancoita and I G Usoskin.

**Solar modulation Models: a comparison through a 2D stochastic simulation**.

In*Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications*. 2004, 23-28.

URL, DOI BibTeX@inproceedings{doi:10.1142/9789812702708_0004, author = "P. Bobik and M. Gervasi and D. Grandi and P. G. Rancoita and I. G. Usoskin", title = "Solar modulation Models: a comparison through a 2D stochastic simulation", booktitle = "Astroparticle, Particle and Space Physics, Detectors and Medical Physics Applications", pages = "23-28", doi = "10.1142/9789812702708_0004", url = "http://www.worldscientific.com/doi/abs/10.1142/9789812702708_0004", eprint = "http://www.worldscientific.com/doi/pdf/10.1142/9789812702708_0004", publisher = "WORLD SCIENTIFIC", year = 2004 }

P Bobik, M Gervasi, D Grandi, P G Rancoita and I G Usoskin.

**2D stochastic simulation model of cosmic ray modulation: comparison with experimental data**.

In A Wilson (ed.).*Solar Variability as an Input to the Earth's Environment*535. 2003, 637-640.

BibTeX@inproceedings{2003ESASP.535..637B, author = "{Bobik}, P. and {Gervasi}, M. and {Grandi}, D. and {Rancoita}, P.G. and {Usoskin}, I.G.", title = "{2D stochastic simulation model of cosmic ray modulation: comparison with experimental data}", keywords = "Galactic Cosmic Rays, Modulation, Heliosphere", booktitle = "Solar Variability as an Input to the Earth's Environment", year = 2003, series = "ESA Special Publication", volume = 535, editor = "{Wilson}, A.", month = "", pages = "637-640", adsurl = "http://adsabs.harvard.edu/abs/2003ESASP.535..637B", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

M Gervasi, P G Rancoita, I G Usoskin and G A Kovaltsov.

**Monte-Carlo approach to Galactic Cosmic Ray propagation in the Heliosphere**.*Nuclear Physics B Proceedings Supplements*78:26-31, 1999.

DOI BibTeX@article{1999NuPhS..78...26G, author = "{Gervasi}, M. and {Rancoita}, P.G. and {Usoskin}, I.G. and {Kovaltsov}, G.A.", title = "{Monte-Carlo approach to Galactic Cosmic Ray propagation in the Heliosphere}", journal = "Nuclear Physics B Proceedings Supplements", year = 1999, month = "", volume = 78, pages = "26-31", doi = "10.1016/S0920-5632(99)00518-6", adsurl = "http://adsabs.harvard.edu/abs/1999NuPhS..78...26G", adsnote = "Provided by the SAO/NASA Astrophysics Data System" }

M Gervasi, P G Rancoita and I G Usoskin.

**Transport of Galactic Cosmic Rays in the Heliosphere: Stochastic Simulation Approach**.

In*Proceedings of the 26th International Cosmic Ray Conference (ICRC2016), August 17-25, 1999 (Salt Lake City, USA)*. 1999, 69.

BibTeX@inproceedings{Gervasi1999b, author = "Gervasi, M. and Rancoita, P.G. and Usoskin, I.G.", title = "Transport of Galactic Cosmic Rays in the Heliosphere: Stochastic Simulation Approach", year = 1999, booktitle = "Proceedings of the 26th International Cosmic Ray Conference (ICRC2016), August 17-25, 1999 (Salt Lake City, USA)", pages = 69 }