## Long-term variation in cosmic-ray modulation

##### Abstract

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.
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.