In this dissertation, I explore the relationship between solar energetic particles (SEPs) and the interplanetary magnetic field, and I use observations of SEPs to probe the region of space between the Sun and the Earth. After an introduction of major concepts in heliospheric physics, describing some of the history of energetic particles and defining the data sets used in the work, the rest of this dissertation is organized around three major concepts related to energetic particle transport: magnetic field-line length, interplanetary turbulence, and particle scattering and diffusion. In Chapter 2, I discuss how energetic particles can be used to measure the lengths of field lines and how particle scattering complicates the interpretation of these measurements. I then propose applying these measurements to a particular open problem: the origin and properties of heliospheric current sheets. In the next chapter, I move from the large to small scale and apply energetic particle measurements to important problems in interplanetary turbulence. I introduce two energetic-particle features, one of which I discovered in the course of this work, which have size scales roughly that of the correlation scale of the turbulence (the largest scale over which observations are expected to be similar). I discuss how multi-spacecraft measurements of these energetic particle features can provide a measure of the correlation scale independent of the magnetic field measurements. Finally, I consider interplanetary scattering and diffusion in detail. I describe new observations of particle diffusion in the direction perpendicular to the average magnetic field, showing that particles only scatter a few times between their injection at the Sun and observation at the Earth. I also provide numerical simulation results of diffusion parallel to the field which can be used to correct for the effects of transport on the particles. These corrections allow inferences to be made about the particle energies at injection from observations of the event-integrated fluences at 1 AU. By carefully including scattering, cooling, field line meandering and turbulence effects, solar-energetic particles become a powerful tool for studying the inner heliosphere.

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A proper understanding of the effects of turbulence on the diffusion and drift of cosmic-rays in the heliosphere is imperative for a better understanding of cosmic-ray modulation. This study presents an ab initio model for cosmic-ray modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. The latter model is solved for solar minimum heliospheric conditions, utilizing boundary values chosen in such a way that the results of this model are in fair to good agreement with spacecraft observations of turbulence quantities, not only in the ecliptic plane, but also along the out-of-ecliptic trajectory of the Ulysses spacecraft. These results are employed as inputs for modelled slab and 2D turbulence energy spectra, which in turn are used as inputs for parallel mean free paths based on those derived from quasi-linear theory, and perpendicularmean free paths from extended nonlinear guiding center theory. The modelled 2D spectrum is chosen based on physical considerations, with a drop-off at the very lowest wavenumbers commencing at the 2D outerscale. There currently exist no models or observations for this quantity, and it is the only free parameter in this study. The use of such a spectrum yields a non-divergent 2D ultrascale, which is used as an input for the reduction terms proposed to model the effects of turbulence on cosmic-ray drifts. The resulting diffusion and drift coefficients are applied to the study of galactic cosmic-ray protons, electrons, antiprotons, and positrons using a three-dimensional, steady-state numerical cosmic-ray modulation code. The magnitude and spatial dependence of the 2D outerscale is demonstrated to have a significant effect on computed cosmic-ray intensities. A form for the 2D outerscale was found that resulted in computed cosmic-ray intensities, for all species considered, in reasonable agreement with multiple spacecraft observations. Computed galactic electron intensities are shown to be particularly sensitive to choices of parameters pertaining to the dissipation range of the slab turbulence spectrum, and certain models for the onset wavenumber of the dissipation range could be eliminated in this study. / Thesis (PhD (Physics))--North-West University, Potchefstroom Campus, 2013

A proper understanding of the effects of turbulence on the diffusion and drift of cosmic-rays in the heliosphere is imperative for a better understanding of cosmic-ray modulation. This study presents an ab initio model for cosmic-ray modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. The latter model is solved for solar minimum heliospheric conditions, utilizing boundary values chosen in such a way that the results of this model are in fair to good agreement with spacecraft observations of turbulence quantities, not only in the ecliptic plane, but also along the out-of-ecliptic trajectory of the Ulysses spacecraft. These results are employed as inputs for modelled slab and 2D turbulence energy spectra, which in turn are used as inputs for parallel mean free paths based on those derived from quasi-linear theory, and perpendicularmean free paths from extended nonlinear guiding center theory. The modelled 2D spectrum is chosen based on physical considerations, with a drop-off at the very lowest wavenumbers commencing at the 2D outerscale. There currently exist no models or observations for this quantity, and it is the only free parameter in this study. The use of such a spectrum yields a non-divergent 2D ultrascale, which is used as an input for the reduction terms proposed to model the effects of turbulence on cosmic-ray drifts. The resulting diffusion and drift coefficients are applied to the study of galactic cosmic-ray protons, electrons, antiprotons, and positrons using a three-dimensional, steady-state numerical cosmic-ray modulation code. The magnitude and spatial dependence of the 2D outerscale is demonstrated to have a significant effect on computed cosmic-ray intensities. A form for the 2D outerscale was found that resulted in computed cosmic-ray intensities, for all species considered, in reasonable agreement with multiple spacecraft observations. Computed galactic electron intensities are shown to be particularly sensitive to choices of parameters pertaining to the dissipation range of the slab turbulence spectrum, and certain models for the onset wavenumber of the dissipation range could be eliminated in this study. / Thesis (PhD (Physics))--North-West University, Potchefstroom Campus, 2013

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.

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

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.

Abstract The thesis is focused on the reconstruction of long-term cosmic ray variability using proxy data. The 11-year solar cycle in production/deposition rates of cosmogenic nuclides ¹⁰Be and ¹⁴C has been modelled for the conditions of grand minima and maxima of solar activity (namely, Maunder Minimum and Grand Modern Maximum). The result shows that contrary to the observed strongly suppressed amplitude of the solar cycle in sunspots during Maunder Minimum relatively to Grand Modern Maximum, the cosmic ray proxies have the comparable amplitudes during the two periods. This phenomenon is caused by the nonlinear relation between solar activity and production of cosmogenic nuclides. In addition to well-established proxies of cosmic rays, nitrate in polar ice has been recently proposed as a new proxy for the long-term variability of galactic cosmic rays. The thesis contains two tests of its applicability for this purpose with TALDICE and EPICA-Dome C ice core data from Central Antarctica. The results support the proposal for the multimillennial time scales. Lunar samples acquired during the Apollo missions are important data for estimating the averaged energy spectra of galactic cosmic rays and solar energetic particles at the Earth’s orbit. The development in modelling of the interaction between energetic particles and matter makes it necessary to revise the earlier results. Because of that, new production rates of ¹⁰Be and ¹⁴C in lunar samples by galactic cosmic rays and solar energetic particles have been computed. New accurate cosmic ray reconstructions from natural archives containing cosmogenic nuclides use sophisticated climatic models requiring yield functions of the nuclides with high altitude resolution. These functions have been computed for ⁷Be, ¹⁰Be, ¹⁴C, ²²Na, and ³⁶Cl in the Earth’s atmosphere. Overall, the major purpose of the studies presented in the thesis is to increase the quality of reconstructions of the long-term cosmic ray variability for better understanding of the solar and heliospheric physics. / Original papers The original publications are not included in the electronic version of the dissertation. Poluianov, S. V., Usoskin, I. G., &amp; Kovaltsov, G. A. (2014). Cosmogenic Isotope Variability During the Maunder Minimum: Normal 11-year Cycles Are Expected. Solar Physics, 289(12), 4701–4709. https://doi.org/10.1007/s11207-014-0587-6 Poluianov, S., Traversi, R., &amp; Usoskin, I. (2014). Cosmogenic production and climate contributions to nitrate record in the TALDICE Antarctic ice core. Journal of Atmospheric and Solar-Terrestrial Physics, 121, 50–58. https://doi.org/10.1016/j.jastp.2014.09.011 Poluianov, S., Artamonov, A., Kovaltsov, G., &amp; Usoskin, I. (2015). Energetic particles in lunar rocks: Production of cosmogenic isotopes. Proceedings of Science, 30-July-2015, art. no. 051 . Traversi, R., Becagli, S., Poluianov, S., Severi, M., Solanki, S. K., Usoskin, I. G., &amp; Udisti, R. (2016). The Laschamp geomagnetic excursion featured in nitrate record from EPICA-Dome C ice core. Scientific Reports, 6(1). https://doi.org/10.1038/srep20235 Poluianov, S. V., Kovaltsov, G. A., Mishev, A. L., &amp; Usoskin, I. G. (2016). Production of cosmogenic isotopes 7Be, 10Be, 14C, 22Na, and 36Cl in the atmosphere: Altitudinal profiles of yield functions. Journal of Geophysical Research: Atmospheres, 121(13), 8125–8136. https://doi.org/10.1002/2016jd025034

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