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: Several short term exogenic forcings affecting Earth's climate are but recently identified. Lunar nutation periodicity has implications for numerical meteorological prediction. Abrupt shifts in solar wind bulk velocity, particle density, and polarity exhibit correlation with terrestrial hemispheric vorticity changes, cyclonic strengthening and the intensification of baroclinic disturbances. Galactic Cosmic ray induced tropospheric ionization modifies cloud microphysics, and modulates the global electric circuit. This dissertation is constructed around three research questions: (1): What are the biweekly declination effects of lunar gravitation upon the troposphere? (2): How do United States severe weather reports correlate with heliospheric current sheet crossings? and (3): How does cloud cover spatially and temporally vary with galactic cosmic rays? Study 1 findings show spatial consistency concerning lunar declination extremes upon Rossby longwaves. Due to the influence of Rossby longwaves on synoptic scale circulation, our results could theoretically extend numerical meteorological forecasting. Study 2 results indicate a preference for violent tornadoes to occur prior to a HCS crossing. Violent tornadoes (EF3+) are 10% more probable to occur near, and 4% less probable immediately after a HCS crossing. The distribution of hail and damaging wind reports do not mirror this pattern. Polarity is critical for the effect. Study 3 results confirm anticorrelation between solar flux and low-level marine-layer cloud cover, but indicate substantial regional variability between cloud cover altitude and GCRs. Ultimately, this dissertation serves to extend short term meteorological forecasting, enhance climatological modeling and through analysis of severe violent weather and heliospheric events, protect property and save lives. / Dissertation/Thesis / Ph.D. Geography 2013

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 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