Krüger, H.Burger, R.A.Mosotho, Moshe Godfrey2017-12-142017-12-142017http://hdl.handle.net/10394/26099MSc (Space Physics), North-West University, Potchefstroom Campus, 2017The transport of cosmic rays inside the heliosphere can be described b the Parker equation (Parker, 1965). Since there are no full analytica solutions to the Parker equation, two first-order approximate solutions o the equation can be derived, namely the Convection-Diffusion and th Force-Field approximations. These approximations were implemented t account for heliospheric modulation only. Utilizing the Force-Fiel approximations, Usoskin et al. (2011) calculated the modulatio potentials between 1936 and 2009 using the ionization chamber an neutron monitor data. The normalized difference between the calculate modulation potentials by Usoskin et al. (2005) and Usoskin et al. (2011 is 3.4 % for solar maximum in June 1991. According to Usoskin et al (2011), their lower calculated values compared with the earlier study ar related to the addition of the third neutron monitor yield function. Despit that, these authors argue that these new calculated modulation potential remain consistent with the old values within the uncertainties. Herbst et al. (2010) have shown that the calculation of modulatio potentials do not only depend on the Local Interstellar Spectrum but als on the energy (or rigidity) range of interest. These authors pointed ou that the use of a different LIS can cause the calculated modulatio potential to either increase or decrease. Based on these findings, this stud re-calculated the modulation potentials by Usoskin et al. (2005, 2011). T investigate modulation this study uses both space-borne (i.e. PAMELA IMP - 8 and Voyager - 1) and ground-based detectors (SANAE Hermanus, Potchefstroom and Tsumeb neutron monitors). Th equivalence, validity and limitations of the Convection-Diffusion an Force-Field approximate solutions are employed at neutron monito energies. The modulation potential results of this study are found to be i accordance with that found by other authors and in particular Ghelfi et al (2016). There is a significant difference though between the results of thi study and Usoskin et al. (2005, 2011) especially during solar maximu periods. Keywords: Galactic cosmic rays, Modulation, Force-Field approximation Convection-Diffusion approximation, Neutron monitors, Yield functions proton fluxes, local interstellar spectrum. i The transport of cosmic rays inside the heliosphere can be described b the Parker equation (Parker, 1965). Since there are no full analytica solutions to the Parker equation, two first-order approximate solutions o the equation can be derived, namely the Convection-Diffusion and th Force-Field approximations. These approximations were implemented t account for heliospheric modulation only. Utilizing the Force-Fiel approximations, Usoskin et al. (2011) calculated the modulatio potentials between 1936 and 2009 using the ionization chamber an neutron monitor data. The normalized difference between the calculate modulation potentials by Usoskin et al. (2005) and Usoskin et al. (2011 is 3.4 % for solar maximum in June 1991. According to Usoskin et al (2011), their lower calculated values compared with the earlier study ar related to the addition of the third neutron monitor yield function. Despit that, these authors argue that these new calculated modulation potential remain consistent with the old values within the uncertainties. Herbst et al. (2010) have shown that the calculation of modulatio potentials do not only depend on the Local Interstellar Spectrum but als on the energy (or rigidity) range of interest. These authors pointed ou that the use of a different LIS can cause the calculated modulatio potential to either increase or decrease. Based on these findings, this stud re-calculated the modulation potentials by Usoskin et al. (2005, 2011). T investigate modulation this study uses both space-borne (i.e. PAMELA IMP - 8 and Voyager - 1) and ground-based detectors (SANAE Hermanus, Potchefstroom and Tsumeb neutron monitors). Th equivalence, validity and limitations of the Convection-Diffusion an Force-Field approximate solutions are employed at neutron monito energies. The modulation potential results of this study are found to be i accordance with that found by other authors and in particular Ghelfi et al (2016). There is a significant difference though between the results of thi study and Usoskin et al. (2005, 2011) especially during solar maximu periods. Keywords: Galactic cosmic rays, Modulation, Force-Field approximation Convection-Diffusion approximation, Neutron monitors, Yield functions proton fluxes, local interstellar spectrum. The transport of cosmic rays inside the heliosphere can be described by the Parker equation (Parker, 1965). Since there are no full analytical solutions to the Parker equation, two first-order approximate solutions of the equation can be derived, namely the Convection-Diffusion and the Force-Field approximations. These approximations were implemented to account for heliospheric modulation only. Utilizing the Force-Field approximations, Usoskin et al. (2011) calculated the modulation potentials between 1936 and 2009 using the ionization chamber and neutron monitor data. The normalized difference between the calculated modulation potentials by Usoskin et al. (2005) and Usoskin et al. (2011) is 3.4 % for solar maximum in June 1991. According to Usoskin et al. (2011), their lower calculated values compared with the earlier study are related to the addition of the third neutron monitor yield function. Despite that, these authors argue that these new calculated modulation potentials remain consistent with the old values within the uncertainties. Herbst et al. (2010) have shown that the calculation of modulation potentials do not only depend on the Local Interstellar Spectrum but also on the energy (or rigidity) range of interest. These authors pointed out that the use of a different LIS can cause the calculated modulation potential to either increase or decrease. Based on these findings, this study re-calculated the modulation potentials by Usoskin et al. (2005, 2011). To investigate modulation this study uses both space-borne (i.e. PAMELA, IMP - 8 and Voyager - 1) and ground-based detectors (SANAE, Hermanus, Potchefstroom and Tsumeb neutron monitors). The equivalence, validity and limitations of the Convection-Diffusion and Force-Field approximate solutions are employed at neutron monitor energies. The modulation potential results of this study are found to be in accordance with that found by other authors and in particular Ghelfi et al. (2016). There is a significant difference though between the results of this study and Usoskin et al. (2005, 2011) especially during solar maximum periods.enGalactic cosmic raysModulationForce-Field approximationConvection-Diffusion approximationNeutron monitorsYield functionsProton fluxesLocal interstellar spectrumThesis