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

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

The interest in the role of the solar wind termination shock (TS) and heliosheath in cosmic ray (CR) modulation studies has increased sigm6cantly as the Voyager 1 and 2 spacecraft approach the estimated position of the TS. For this work the modulation of galactic CR protons, anti-protons, electrons with a Jovian source, positrons, Helium, and anomalous protons and Helium, and the consequent charge-sign dependence, are studied with an improved and extended two-dimensional numerical CR modulation model including a TS with diffusive shock acceleration, a heliosheath and drifts. The modulation is computed using improved local interstellar spectra (LIS) for almost all the species of interest to this study and new fundamentally derived diffusion coefficients, applicable to a number of CR species during both magnetic polarity cycles of the Sun. The model also allows comparisons of modulation with and without a TS and between solar minimum and moderate maximum conditions. The modulation of protons and Helium with their respective anomalous components are also studied to establish the consequent charge-sign dependence at low energies and the influence on the computed p/p, e-/p, and e-/He. The level of modulation in the simulated heliosheath, and the importance of this modulation 'barrier' and the TS for the different species are illustrated. From the computations it is possible to estimate the ratio of modulation occurring in the heliosheath to the total modulation between the heliopause and Earth for the mentioned species. It has been found that the modulation in the heliosheath depends on the particle species, is strongly dependent on the energy of the CRs, on the polarity cycle and is enhanced by the inclusion of the TS. The computed modulation for the considered species is surprisingly different and the heliosheath is important for CR modulation, although 'barrier' modulation is more prominent for protons, anti-protons and Helium, while the heliosheath cannot really be considered a modulation 'barrier' for electrons and positrons above energies of ~150 MeV. The effects of the TS on modulation are more pronounced for polarity cycles when particles are drifting primarily in the equatorial regions of the heliosphere along the heliospheric current sheet to the Sun, e.g. the A < 0 polarity cycle for protons, positrons, and Helium, and the A > 0 polarity cycle for electrons and anti-protons. This study also shows that the proton and Helium LIS may not be known at energies <~ 200 MeV until a spacecraft actually approaches the heliopause because of the strong modulation that occurs in the heliosheath, the effect of the TS, and the presence of anomalous protons and Helium. For anti-protons, in contrast, these effects are less pronounced. For positrons, with a completely different shape LIS, the modulated spectra have very mild energy dependencies <~ 300 MeV, even at Earth, in contrast to the other species. These characteristic spectral features may be helpful to distinguish between electron and positron spectra when they are measured near and at Earth. These simulations can be of use for future missions to the outer heliosphere and beyond. / Thesis (Ph.D. (Physics))--North-West University, Potchefstroom Campus, 2004.

A two dimensional hydrodynamic model describing the solar wind interaction with the local interstellar medium, which surrounds the solar system, is used to study the heliosphere both as a steady-state- and dynamic structure. The finite volume method used to solve the associated system of hydrodynamic equations numerically is discussed in detail. Subsequently the steady state heliosphere is studied for both the case where the solar wind and the interstellar medium are assumed to consist of protons only, as well as the case where the neutral hydrogen population in the interstellar medium is taken into account. It is shown that the heliosphere forms as three waves, propagating away from the initial point of contact between the solar wind and interstellar matter, become stationary. Two of these waves become stationary at sonic points, forming the termination shock and bow shock respectively. The third wave becomes stationary as a contact discontinuity, called the heliopause. It is shown that the position and geometry of the termination shock, heliopause and bow shock as well as the plasma flow characteristics of the heliosphere largely depend on the dynamic pressure of either the solar wind or interstellar matter. The heliosphere is modelled as a dynamic structure, including both the effects of the solar cycle and short term variations in the solar wind observed by a range of spacecraft over the past ~ 30 years. The dynamic model allows the calculation of an accurate record of the heliosphere state over the past ~ 30 years. This record is used to predict the time at which the Voyager 2 spacecraft will cross the termination shock. Voyager 1 observations of 10 MeV cosmic ray electrons are then used in conjunction with a cosmic ray modulation model to constrain the record of the heliosphere further. It is shown that the dynamic hydrodynamic model describes the heliosphere accurately within a margin of error of ±0.7 years and ±3 AU. The model predicts that Voyager 2 crossed the termination shock in 2007, corresponding to preliminary results from observations indicating that the crossing occurred in August 2007. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

The interest in the role of the solar wind termination shock (TS) and heliosheath in cosmic ray (CR) modulation studies has increased sigm6cantly as the Voyager 1 and 2 spacecraft approach the estimated position of the TS. For this work the modulation of galactic CR protons, anti-protons, electrons with a Jovian source, positrons, Helium, and anomalous protons and Helium, and the consequent charge-sign dependence, are studied with an improved and extended two-dimensional numerical CR modulation model including a TS with diffusive shock acceleration, a heliosheath and drifts. The modulation is computed using improved local interstellar spectra (LIS) for almost all the species of interest to this study and new fundamentally derived diffusion coefficients, applicable to a number of CR species during both magnetic polarity cycles of the Sun. The model also allows comparisons of modulation with and without a TS and between solar minimum and moderate maximum conditions. The modulation of protons and Helium with their respective anomalous components are also studied to establish the consequent charge-sign dependence at low energies and the influence on the computed p/p, e-/p, and e-/He. The level of modulation in the simulated heliosheath, and the importance of this modulation 'barrier' and the TS for the different species are illustrated. From the computations it is possible to estimate the ratio of modulation occurring in the heliosheath to the total modulation between the heliopause and Earth for the mentioned species. It has been found that the modulation in the heliosheath depends on the particle species, is strongly dependent on the energy of the CRs, on the polarity cycle and is enhanced by the inclusion of the TS. The computed modulation for the considered species is surprisingly different and the heliosheath is important for CR modulation, although 'barrier' modulation is more prominent for protons, anti-protons and Helium, while the heliosheath cannot really be considered a modulation 'barrier' for electrons and positrons above energies of ~150 MeV. The effects of the TS on modulation are more pronounced for polarity cycles when particles are drifting primarily in the equatorial regions of the heliosphere along the heliospheric current sheet to the Sun, e.g. the A < 0 polarity cycle for protons, positrons, and Helium, and the A > 0 polarity cycle for electrons and anti-protons. This study also shows that the proton and Helium LIS may not be known at energies <~ 200 MeV until a spacecraft actually approaches the heliopause because of the strong modulation that occurs in the heliosheath, the effect of the TS, and the presence of anomalous protons and Helium. For anti-protons, in contrast, these effects are less pronounced. For positrons, with a completely different shape LIS, the modulated spectra have very mild energy dependencies <~ 300 MeV, even at Earth, in contrast to the other species. These characteristic spectral features may be helpful to distinguish between electron and positron spectra when they are measured near and at Earth. These simulations can be of use for future missions to the outer heliosphere and beyond. / Thesis (Ph.D. (Physics))--North-West University, Potchefstroom Campus, 2004.

A two dimensional hydrodynamic model describing the solar wind interaction with the local interstellar medium, which surrounds the solar system, is used to study the heliosphere both as a steady-state- and dynamic structure. The finite volume method used to solve the associated system of hydrodynamic equations numerically is discussed in detail. Subsequently the steady state heliosphere is studied for both the case where the solar wind and the interstellar medium are assumed to consist of protons only, as well as the case where the neutral hydrogen population in the interstellar medium is taken into account. It is shown that the heliosphere forms as three waves, propagating away from the initial point of contact between the solar wind and interstellar matter, become stationary. Two of these waves become stationary at sonic points, forming the termination shock and bow shock respectively. The third wave becomes stationary as a contact discontinuity, called the heliopause. It is shown that the position and geometry of the termination shock, heliopause and bow shock as well as the plasma flow characteristics of the heliosphere largely depend on the dynamic pressure of either the solar wind or interstellar matter. The heliosphere is modelled as a dynamic structure, including both the effects of the solar cycle and short term variations in the solar wind observed by a range of spacecraft over the past ~ 30 years. The dynamic model allows the calculation of an accurate record of the heliosphere state over the past ~ 30 years. This record is used to predict the time at which the Voyager 2 spacecraft will cross the termination shock. Voyager 1 observations of 10 MeV cosmic ray electrons are then used in conjunction with a cosmic ray modulation model to constrain the record of the heliosphere further. It is shown that the dynamic hydrodynamic model describes the heliosphere accurately within a margin of error of ±0.7 years and ±3 AU. The model predicts that Voyager 2 crossed the termination shock in 2007, corresponding to preliminary results from observations indicating that the crossing occurred in August 2007. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

A time-dependent two-dimensional (2D) modulation model including drifts, the solar wind tennination shock (TS) with diffusive shock acceleration and a heliosheath based on the Parker (1965) transport equation is used to study the modulation of galactic cosmic rays (GCRs) and the anomalous component of cosmic rays (ACRs) in the heliosphere. In particular, the latitude dependence of the TS compression ratio and injection efficiency of the ACRs (source strength) based on the hydrodynamic modeling results of Scherer et al. (2006) is used for the first time in a modulation model. The subsequent effects on differential intensities for both GCRs and ACRs are illustrated, comparing them to the values without a latitude dependence for these parameters. It is found that the latitude dependence of these parameters is important and that it enables an improved description of the modulation of ACRs beyond the TS. With this modeling approach (without fitting observations) to the latitude dependence of the two parameters, it is possible to obtain a TS spectrum for ACRs at a polar angle of B = 55" that qualitatively approximates the main features of the Voyager 1 observations. This positive result has to be investigated further. Additionally, it is shown that the enhancement of the cosmic ray intensity just below the cut-off energy found for the ACR at the TS in an A < 0 magnetic polarity cycle in the equatorial plane with the latitude independent scenario, disappears in this region when the latitude dependence of the compression ratio and injection efficiency is assumed. Subsequent effects of these scenarios are illustrated on the global anisotropy vector of both GCRs and ACRs as the main theme of this work. For this purpose the radial and latitudinal gradients for GCRs and ACRs were accurately computed. The radial and latitudinal anisotropy components were then computed as a function of energy, radial distance and polar angle. It is also the first time that the anisotropy vector is comprehensively calculated in such a global approach to cosmic ray modeling in the heliosphere, in particular for ACRs. It is shown that the anisotropy vector inside (up-stream) and outside (down-stream) the TS behaves in a complicated way, so care must be taken in interpreting it. It is found that the latitude dependence of the two mentioned parameters can alter the direction (sign) of the anisotropy vector. Its behaviour beyond the TS is markedly different from inside the TS, mainly because of the slower solar wind velocity, with less dependence on the magnetic polarity cycles. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

A time-dependent two-dimensional (2D) modulation model including drifts, the solar wind tennination shock (TS) with diffusive shock acceleration and a heliosheath based on the Parker (1965) transport equation is used to study the modulation of galactic cosmic rays (GCRs) and the anomalous component of cosmic rays (ACRs) in the heliosphere. In particular, the latitude dependence of the TS compression ratio and injection efficiency of the ACRs (source strength) based on the hydrodynamic modeling results of Scherer et al. (2006) is used for the first time in a modulation model. The subsequent effects on differential intensities for both GCRs and ACRs are illustrated, comparing them to the values without a latitude dependence for these parameters. It is found that the latitude dependence of these parameters is important and that it enables an improved description of the modulation of ACRs beyond the TS. With this modeling approach (without fitting observations) to the latitude dependence of the two parameters, it is possible to obtain a TS spectrum for ACRs at a polar angle of B = 55" that qualitatively approximates the main features of the Voyager 1 observations. This positive result has to be investigated further. Additionally, it is shown that the enhancement of the cosmic ray intensity just below the cut-off energy found for the ACR at the TS in an A < 0 magnetic polarity cycle in the equatorial plane with the latitude independent scenario, disappears in this region when the latitude dependence of the compression ratio and injection efficiency is assumed. Subsequent effects of these scenarios are illustrated on the global anisotropy vector of both GCRs and ACRs as the main theme of this work. For this purpose the radial and latitudinal gradients for GCRs and ACRs were accurately computed. The radial and latitudinal anisotropy components were then computed as a function of energy, radial distance and polar angle. It is also the first time that the anisotropy vector is comprehensively calculated in such a global approach to cosmic ray modeling in the heliosphere, in particular for ACRs. It is shown that the anisotropy vector inside (up-stream) and outside (down-stream) the TS behaves in a complicated way, so care must be taken in interpreting it. It is found that the latitude dependence of the two mentioned parameters can alter the direction (sign) of the anisotropy vector. Its behaviour beyond the TS is markedly different from inside the TS, mainly because of the slower solar wind velocity, with less dependence on the magnetic polarity cycles. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

A two-dimensional hydrodynamic numerical model is extended and applied to simulate the interaction between stellar winds and the interstellar medium (ISM). In particular, the stellar wind evolution of O- and B-type stars is calculated. First, the evolution of a stellar wind into the ambient interstellar medium and also a more dense molecular cloud are considered for the case of no relative motion between the star and the interstellar medium. This interaction results in a cavity being blown into the ISM. Of importance in this work is the boundary radius (astropause) of the stellar wind and also the location where the outflow speed decreases from supersonic to subsonic speeds, called the termination shock. Different parameters like ISM density, outflow speed and mass-loss rate were varied to study the effect these have on the computed astropause (AP) and termination shock (TS) radii. The evolution of these structures is presented up to a simulation time of 1 My. However, stars are not stationary relative to the ISM, and the evolution of stellar winds into the interstellar medium including relative motion is also considered. It is shown that the positions of the TS and AP are dependent on the mass-loss rate and stellar wind outflow speed of the star and the interstellar medium density and relative speed. When these massive stars reach the end of their life, they end their life in a supernova explosion. The explosion results in a blast wave moving outward, called the forward shock (FS) and a reverse shock (RS) also forms which moves inward. Previous work done by Ferreira and de Jager (2008) to simulate supernova remnant (SNR) evolution, was only done for the case of evolution into the undisturbed ISM (no cavity). In this work, the evolution of SNR is simulated taking also into account the pre-existing cavity blown out by the stellar winds of these massive stars. The results of this study showed that the evolution of the SNR is definitely influenced by the presence of a stellar wind cavity even if the cavity is only a few pc in extent. / Thesis (MSc (Space Physics))--North-West University, Potchefstroom Campus, 2011.