The modulation of galactic cosmic ray (GCR) Carbon in a north-south asymmetrical heliosphere is studied, using a two-dimensional numerical model that contains a solar wind termination shock (TS), a heliosheath, as well as particle drifts and diffusive shock re-acceleration of GCRs. The asymmetry in the geometry of the heliosphere is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. As a result, the model allows comparisons of modulation in the north and south hemispheres during both magnetic polarity cycles of the Sun, and from solar minimum to moderate maximum conditions. When comparing the computed spectra between polar angles of 55o (approximating the Voyager 1 direction) and 125o (approximating the Voyager 2 direction), it is found that at kinetic energies E < 1:0 GeV/nuc the effects of the assumed asymmetry in the geometry of the heliosphere on the modulated spectra are insignificant up to 60 AU from the Sun, but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with E > 1:0 GeV/nuc, these effects remained insignificant throughout the heliosphere even very close to the heliopause (HP). However, when the enhancement of both polar and radial perpendicular diffusion coefficients off the equatorial plane is assumed to differ from heliographic pole to pole, reflecting different modulation conditions between the two hemispheres, major differences in the computed intensities between the two Voyager directions are obtained throughout the heliosphere. The model is further improved by incorporating new information about the HP location and the relevant heliopause spectrum for GCR Carbon at E < 200 MeV/nuc based on the recent Voyager 1 observations. When comparing the computed solutions at the Earth with ACE observations taken during different solar modulation conditions, it is found that it is possible for the level of modulation at the Earth, when solar activity changes from moderate maximum conditions to solar minimum conditions, to exceed the total modulation between the HP and the Earth during solar minimum periods. In the outer heliosphere, reasonable compatibility with the corresponding Voyager observations is established when drifts are scaled down to zero in the heliosheath in both polarity cycles. The effects of neglecting drifts in the heliosheath are found to be more significant than neglecting the enhancement of polar perpendicular diffusion. Theoretical expressions for the scattering function required for the reduction of the drift coefficient in modulation studies are illustrated and implemented in the numerical model. It is found that when this scattering function decreases rapidly over the poles, the computed A < 0 spectra are higher than the A > 0 spectra at all energies at Earth primarily because of drifts, which is unexpected from a classical drift modeling point of view. Scenarios of this function with strong decreases over the polar regions seem realistic at and beyond the TS, where the solar wind must have a larger latitudinal dependence. / PhD (Space Physics), North-West University, Potchefstroom Campus, 2015

The modulation of galactic cosmic ray (GCR) Carbon in a north-south asymmetrical heliosphere is studied, using a two-dimensional numerical model that contains a solar wind termination shock (TS), a heliosheath, as well as particle drifts and diffusive shock re-acceleration of GCRs. The asymmetry in the geometry of the heliosphere is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. As a result, the model allows comparisons of modulation in the north and south hemispheres during both magnetic polarity cycles of the Sun, and from solar minimum to moderate maximum conditions. When comparing the computed spectra between polar angles of 55o (approximating the Voyager 1 direction) and 125o (approximating the Voyager 2 direction), it is found that at kinetic energies E < 1:0 GeV/nuc the effects of the assumed asymmetry in the geometry of the heliosphere on the modulated spectra are insignificant up to 60 AU from the Sun, but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with E > 1:0 GeV/nuc, these effects remained insignificant throughout the heliosphere even very close to the heliopause (HP). However, when the enhancement of both polar and radial perpendicular diffusion coefficients off the equatorial plane is assumed to differ from heliographic pole to pole, reflecting different modulation conditions between the two hemispheres, major differences in the computed intensities between the two Voyager directions are obtained throughout the heliosphere. The model is further improved by incorporating new information about the HP location and the relevant heliopause spectrum for GCR Carbon at E < 200 MeV/nuc based on the recent Voyager 1 observations. When comparing the computed solutions at the Earth with ACE observations taken during different solar modulation conditions, it is found that it is possible for the level of modulation at the Earth, when solar activity changes from moderate maximum conditions to solar minimum conditions, to exceed the total modulation between the HP and the Earth during solar minimum periods. In the outer heliosphere, reasonable compatibility with the corresponding Voyager observations is established when drifts are scaled down to zero in the heliosheath in both polarity cycles. The effects of neglecting drifts in the heliosheath are found to be more significant than neglecting the enhancement of polar perpendicular diffusion. Theoretical expressions for the scattering function required for the reduction of the drift coefficient in modulation studies are illustrated and implemented in the numerical model. It is found that when this scattering function decreases rapidly over the poles, the computed A < 0 spectra are higher than the A > 0 spectra at all energies at Earth primarily because of drifts, which is unexpected from a classical drift modeling point of view. Scenarios of this function with strong decreases over the polar regions seem realistic at and beyond the TS, where the solar wind must have a larger latitudinal dependence. / PhD (Space Physics), North-West University, Potchefstroom Campus, 2015

The solar minimum of 2009 has been identified as an exceptional event with regard to cosmic ray (CR)modulation, since conditions in the heliosphere have reached unprecedented quiet levels. This unique minimum has been observed by the Earth–orbiting satellite, PAMELA, launched in June, 2006, from which vast sets of accurate proton and electron preliminary observations have been made available. These simultaneous measurements from PAMELA provide the ideal opportunity to conduct an in–depth study of CR modulation, in particular charge–sign dependent modulation. In utilizing this opportunity, a three–dimensional, steady–state modulation model was used to reproduce a selection of consecutive PAMELA proton and electron spectra from 2006 to 2009. Thiswas done by assuming full drifts and simplified diffusion coefficients, where the rigidity dependence and absolute value of themean free paths for protons and electrons were sequentially adjusted below 3 GV and 300 MV, respectively. Care has been taken in calculating yearly–averaged current–sheet tilt angle and magnetic field values that correspond to the PAMELA spectra. Following this study where the numerical model was used to investigate the individual effects resulting from changes in the tilt angle, diffusion coefficients, and global drifts, it was found that all these modulation processes played significant roles in contributing to the total increase in CR intensities from 2006 to 2009, as was observed by PAMELA. Furthermore, the effect that drifts has on oppositely charged particles was also evident from the difference between the peak–shaped time profiles of protons and the flatter time profiles of electrons, as is expected for an A < 0 polarity cycle. Since protons, which drift into the heliosphere along the heliospheric current–sheet, haven’t yet reached maximum intensity levels by 2008, their intensities increased notably more than electrons toward the end of 2009. The time and energy dependence of the electron to proton ratios were also studied in order to further illustrate and quantify the effect of drifts during this remarkable solar minimum period. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.

The solar minimum of 2009 has been identified as an exceptional event with regard to cosmic ray (CR)modulation, since conditions in the heliosphere have reached unprecedented quiet levels. This unique minimum has been observed by the Earth–orbiting satellite, PAMELA, launched in June, 2006, from which vast sets of accurate proton and electron preliminary observations have been made available. These simultaneous measurements from PAMELA provide the ideal opportunity to conduct an in–depth study of CR modulation, in particular charge–sign dependent modulation. In utilizing this opportunity, a three–dimensional, steady–state modulation model was used to reproduce a selection of consecutive PAMELA proton and electron spectra from 2006 to 2009. Thiswas done by assuming full drifts and simplified diffusion coefficients, where the rigidity dependence and absolute value of themean free paths for protons and electrons were sequentially adjusted below 3 GV and 300 MV, respectively. Care has been taken in calculating yearly–averaged current–sheet tilt angle and magnetic field values that correspond to the PAMELA spectra. Following this study where the numerical model was used to investigate the individual effects resulting from changes in the tilt angle, diffusion coefficients, and global drifts, it was found that all these modulation processes played significant roles in contributing to the total increase in CR intensities from 2006 to 2009, as was observed by PAMELA. Furthermore, the effect that drifts has on oppositely charged particles was also evident from the difference between the peak–shaped time profiles of protons and the flatter time profiles of electrons, as is expected for an A < 0 polarity cycle. Since protons, which drift into the heliosphere along the heliospheric current–sheet, haven’t yet reached maximum intensity levels by 2008, their intensities increased notably more than electrons toward the end of 2009. The time and energy dependence of the electron to proton ratios were also studied in order to further illustrate and quantify the effect of drifts during this remarkable solar minimum period. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.

The transport of cosmic rays in the heliosphere is studied by making use of a newly developed modulation model. This model employes stochastic differential equations to numerically solve the relevant transport equation, making use of this approach’s numerical advantages as well as the opportunity to extract additional information regarding cosmic ray transport and the processes responsible for it. The propagation times and energy losses of galactic electrons and protons are calculated for different drift cycles. It is confirmed that protons and electrons lose the same amount of rigidity when they experience the same transport processes. These particles spend more time in the heliosphere, and also lose more energy, in the drift cycle where they drift towards Earth mainly along the heliospheric current sheet. The propagation times of galactic protons from the heliopause to Earth are calculated for increasing heliospheric tilt angles and it is found that current sheet drift becomes less effective with increasing solar activity. Comparing calculated propagation times of Jovian electrons with observations, the transport parameters are constrained to find that 50% of 6 MeV electrons measured at Earth are of Jovian origin. Charge-sign dependent modulation is modelled by simulating the proton to anti-proton ratio at Earth and comparing the results to recent PAMELA observations. A hybrid cosmic ray modulation model is constructed by coupling the numerical modulation model to the heliospheric environment as simulated by a magneto-hydrodynamic model. Using this model, it is shown that cosmic ray modulation persists beyond the heliopause. The level of modulation in this region is found to exhibit solar cycle related changes and, more importantly, is independent of the magnitude of the individual diffusion coefficients, but is rather determined by the ratio of parallel to perpendicular diffusion. / PhD (Space Physics), North-West University, Potchefstroom Campus, 2013

The transport of cosmic rays in the heliosphere is studied by making use of a newly developed modulation model. This model employes stochastic differential equations to numerically solve the relevant transport equation, making use of this approach’s numerical advantages as well as the opportunity to extract additional information regarding cosmic ray transport and the processes responsible for it. The propagation times and energy losses of galactic electrons and protons are calculated for different drift cycles. It is confirmed that protons and electrons lose the same amount of rigidity when they experience the same transport processes. These particles spend more time in the heliosphere, and also lose more energy, in the drift cycle where they drift towards Earth mainly along the heliospheric current sheet. The propagation times of galactic protons from the heliopause to Earth are calculated for increasing heliospheric tilt angles and it is found that current sheet drift becomes less effective with increasing solar activity. Comparing calculated propagation times of Jovian electrons with observations, the transport parameters are constrained to find that 50% of 6 MeV electrons measured at Earth are of Jovian origin. Charge-sign dependent modulation is modelled by simulating the proton to anti-proton ratio at Earth and comparing the results to recent PAMELA observations. A hybrid cosmic ray modulation model is constructed by coupling the numerical modulation model to the heliospheric environment as simulated by a magneto-hydrodynamic model. Using this model, it is shown that cosmic ray modulation persists beyond the heliopause. The level of modulation in this region is found to exhibit solar cycle related changes and, more importantly, is independent of the magnitude of the individual diffusion coefficients, but is rather determined by the ratio of parallel to perpendicular diffusion. / PhD (Space Physics), North-West University, Potchefstroom Campus, 2013