Abstract This thesis studies the structure and evolution of the large scale heliospheric magnetic field. The work covers the space age, the period when satellite measurements revolutionized our knowledge about space. Now, this period is known to be the declining phase of the grand modern maximum of solar activity. The thesis addresses how the hemispherical asymmetry of solar activity is seen in the photospheric magnetic field and how it appears in the corona and in the heliosphere until the termination shock. According to geomagnetic and heliospheric observations, the heliospheric current sheet has been southward shifted around the solar minima since 1930s. Using Ulysses probe observations, we derive an accurate estimate of 2° for the southward shift of the heliospheric current sheet during two very different solar minimum in the mid 1990s and 2000s. The overall structure of the heliospheric magnetic field has changed significantly now when the grand modern maximum has come to an end. During the present low solar activity the polar fields are weaker and the heliospheric current sheet covered a wide latitudinal range during the previous minimum. When the heliospheric current sheet is wide the asymmetry is less visible at the Earth’s orbit. We extend our study to the outer heliosphere using measurements made by Voyager and Pioneer probes and show that the hemispherical asymmetry in the coronal hole evolution, and the related southward shift of the heliospheric current sheet, are seen until the termination shock. In order to understand the origin of the hemispherical asymmetry, we complete a multipole analysis of the solar magnetic field since 1976. We find that the minimum time southward shift of the heliospheric current sheet is due to the quadrupole component of the coronal magnetic field. The quadrupole term exists because the generation and transport of the magnetic flux in the Sun tends to proceed differently in the northern and southern hemispheres. During this and the following decade the Sun is most likely going to be less active than it has been since 1920s. Therefore it is probable that the hemispherical asymmetry of the heliospheric magnetic field will be less visible in the ecliptic plane in the near future. Now, when the Sun seems to be at the maximum of cycle 24, we are looking forward to see how the polar fields and the heliospheric magnetic field are formed when approaching the following solar minimum. It is possible that, as the activity rises again after the present and future low cycles, the hemispherical asymmetry will be opposite to that of the 20th century and the minimum time heliospheric current sheet would be northward shifted.

The existence of a Fisk-type heliospheric magnetic field (HMF) is one of the most debated questions in cosmic-ray modulation. Recently, Burger and Hitge [2004] developed a divergence-free Fisk-Parker hybrid magnetic field model to demonstrate the behaviour of cosmic rays in the heliosphere due to such a field. This approach has been refined and the properties of the consequent field are investigated. It is found that randomly directed magnetic field diffusion in and above the photosphere significantly influences the solar magnetic field both at the solar poles and near the polar coronal hole boundary. The solar cycle dependence of this field is investigated, a study which is of particular importance for studies of the long-term behaviour of cosmic rays, such as those undertaken at the SANAE base in Antarctica. The amplitudes of the 26-day recurrent cosmic-ray variations are modelled as function of both latitudinal gradient and heliolatitude and are found to agree qualitatively and in some cases quantitatively with the observational results reported by Zhang 119971 and Paizis et al. 119991. Although magnetic field data do not clearly indicate the existence of the Fisk field [see, e.g., Fursyth et al., 20021, this study supports the existence of a Fisk-type HMF. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2006.

Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

The existence of a Fisk-type heliospheric magnetic field (HMF) is one of the most debated questions in cosmic-ray modulation. Recently, Burger and Hitge [2004] developed a divergence-free Fisk-Parker hybrid magnetic field model to demonstrate the behaviour of cosmic rays in the heliosphere due to such a field. This approach has been refined and the properties of the consequent field are investigated. It is found that randomly directed magnetic field diffusion in and above the photosphere significantly influences the solar magnetic field both at the solar poles and near the polar coronal hole boundary. The solar cycle dependence of this field is investigated, a study which is of particular importance for studies of the long-term behaviour of cosmic rays, such as those undertaken at the SANAE base in Antarctica. The amplitudes of the 26-day recurrent cosmic-ray variations are modelled as function of both latitudinal gradient and heliolatitude and are found to agree qualitatively and in some cases quantitatively with the observational results reported by Zhang 119971 and Paizis et al. 119991. Although magnetic field data do not clearly indicate the existence of the Fisk field [see, e.g., Fursyth et al., 20021, this study supports the existence of a Fisk-type HMF. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2006.

Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

Until recently, numerical modulation models for the solar modulation of cosmic rays have been based primarily on finite difference approaches; however, models based on the solution of an appropriate set of stochastic differential equations have become increasingly popular. This study utilises such a spatially three-dimensional and time-stationary model, based on that of Strauss et al. (2011b). The remarkable numerical stability and powerful illustrative capabilities of this model are utilised extensively and in a distinctly comparative fashion to enable new insights into the processes of modulation. The model is refined to provide for both the Smith-Bieber (Smith and Bieber, 1991) and Jokipii-Kota (Jokipii and Kota, 1989) modifcations to the Parker heliospheric magnetic field (Parker, 1958) and the implications for modulation are investigated. During this investigation it is conclusively illustrated that the Parker field is most conducive to drift dominated modulation, while the Jokipii-Kota and Smith-Bieber modifcations are seen to induce successively larger contributions from diffusive processes. A further refinement to the model is the incorporation of a different profile for the heliospheric current sheet. This profile is defined by its latitudinal extent given by Kota and Jokipii (1983), as opposed to the profile given by Jokipii and Thomas (1981). An extensive investigation into current sheet related matters is launched, illustrating the difference between these current sheet geometries, the associated drift velocity fields and the effect on modulation. At high levels of solar activity, such that the current sheet enters deep enough into the polar regions, the profile of Kota and Jokipii (1983) is found to significantly reduce the effective inward (outward) drifts of positively (negatively) charged particles during A > 0 polarity cycles. The analogous effect is true for A < 0 polarity cycles and the overall effect is of such an extent that the A > 0 and A < 0 solutions are found to coincide at the highest levels of solar activity to form a closed loop. This is a result that has never before been achieved without having to scale down the drift coefficient to zero at solar maximum, as was done by e.g. Ndiitwani et al. (2005). Furthermore, it is found that the drift velocity fields associated with these two current sheet profiles lead to significant differences in modulation even at such low levels of solar activity where no difference in the geometries of these profiles are yet in evidence. The model is finally applied to reproduce four observed galactic proton spectra, selected from PAMELA measurements (Adriani et al., 2013) during the atypical solar minimum of 2006 to 2009; a new proton local interstellar spectrum was employed. The results are found to be in accordance with that found by other authors and in particular Vos (2011), i.e. the diffusion was required to consistently increase from 2006 to 2009 and, in addition, the rigidity dependence below ~ 3 GV was required to change over this time so that the spectra became increasingly softer. / MSc (Space Physics), North-West University, Potchefstroom Campus, 2015

Until recently, numerical modulation models for the solar modulation of cosmic rays have been based primarily on finite difference approaches; however, models based on the solution of an appropriate set of stochastic differential equations have become increasingly popular. This study utilises such a spatially three-dimensional and time-stationary model, based on that of Strauss et al. (2011b). The remarkable numerical stability and powerful illustrative capabilities of this model are utilised extensively and in a distinctly comparative fashion to enable new insights into the processes of modulation. The model is refined to provide for both the Smith-Bieber (Smith and Bieber, 1991) and Jokipii-Kota (Jokipii and Kota, 1989) modifcations to the Parker heliospheric magnetic field (Parker, 1958) and the implications for modulation are investigated. During this investigation it is conclusively illustrated that the Parker field is most conducive to drift dominated modulation, while the Jokipii-Kota and Smith-Bieber modifcations are seen to induce successively larger contributions from diffusive processes. A further refinement to the model is the incorporation of a different profile for the heliospheric current sheet. This profile is defined by its latitudinal extent given by Kota and Jokipii (1983), as opposed to the profile given by Jokipii and Thomas (1981). An extensive investigation into current sheet related matters is launched, illustrating the difference between these current sheet geometries, the associated drift velocity fields and the effect on modulation. At high levels of solar activity, such that the current sheet enters deep enough into the polar regions, the profile of Kota and Jokipii (1983) is found to significantly reduce the effective inward (outward) drifts of positively (negatively) charged particles during A > 0 polarity cycles. The analogous effect is true for A < 0 polarity cycles and the overall effect is of such an extent that the A > 0 and A < 0 solutions are found to coincide at the highest levels of solar activity to form a closed loop. This is a result that has never before been achieved without having to scale down the drift coefficient to zero at solar maximum, as was done by e.g. Ndiitwani et al. (2005). Furthermore, it is found that the drift velocity fields associated with these two current sheet profiles lead to significant differences in modulation even at such low levels of solar activity where no difference in the geometries of these profiles are yet in evidence. The model is finally applied to reproduce four observed galactic proton spectra, selected from PAMELA measurements (Adriani et al., 2013) during the atypical solar minimum of 2006 to 2009; a new proton local interstellar spectrum was employed. The results are found to be in accordance with that found by other authors and in particular Vos (2011), i.e. the diffusion was required to consistently increase from 2006 to 2009 and, in addition, the rigidity dependence below ~ 3 GV was required to change over this time so that the spectra became increasingly softer. / MSc (Space Physics), North-West University, Potchefstroom Campus, 2015