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 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.

The three-dimensional (3D) steady-state electron modulation model of Ferreira (2002), based on Parker (1965) transport equation, is used to study the modulation of the 7 MeV galactic and Jovian electron anisotropies in the inner heliosphere. The Jovian electrons are produced in Jupiter's magnetosphere which is situated at ~ 5 AU in the ecliptic plane. The propagation of these particles is mainly described by the diffusion tensor applicable for the inner heliosphere. Some of the elements of the diffusion tensor are revisited in order to establish what contribution they make to the three-dimensional anisotropy vector and its components in the inner heliosphere. The 'drift' term is neglected since the focus of this study is on low-energy electrons. The effects on the electron anisotropy of different scenarios when changing the solar wind speed from minimum to maximum activity is illustrated. The effects on both the galactic and Jovian electron anisotropy of changing the polar perpendicular coefficient, in particular, are illustrated. It is shown that the computed Jovian electron anisotropy dominates the galactic anisotropy close to the Jovian electron source at ~5 AU, as expected, testifying to the validity of the3D-model. For the latitudinal anisotropy, the polar perpendicular diffusion plays a dominant role for Jovian electrons close to the source, with the polar gradient becoming the dominant factor away from the electron source. Of all three anisotropy components, the azimuthal anisotropy is dominant in the equatorial plane close to the source. It is found that there is a large azimuthal gradient close to the source because the low-energy electrons tend to follow the heliospheric magnetic field more closely than higher energy particles. The transition of the solar wind speed from minimum to intermediate to maximum solar activity condition was used to illustrate the modulation of the magnitude of the 7 MeV total anisotropy vector along the Ulysses trajectory. It was found that during the two encounters with the planet a maximum anisotropy of 38% was computed but with different anisotropy-timepeaks as the approach to Jupiter was different. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

The three-dimensional (3D) steady-state electron modulation model of Ferreira (2002), based on Parker (1965) transport equation, is used to study the modulation of the 7 MeV galactic and Jovian electron anisotropies in the inner heliosphere. The Jovian electrons are produced in Jupiter's magnetosphere which is situated at ~ 5 AU in the ecliptic plane. The propagation of these particles is mainly described by the diffusion tensor applicable for the inner heliosphere. Some of the elements of the diffusion tensor are revisited in order to establish what contribution they make to the three-dimensional anisotropy vector and its components in the inner heliosphere. The 'drift' term is neglected since the focus of this study is on low-energy electrons. The effects on the electron anisotropy of different scenarios when changing the solar wind speed from minimum to maximum activity is illustrated. The effects on both the galactic and Jovian electron anisotropy of changing the polar perpendicular coefficient, in particular, are illustrated. It is shown that the computed Jovian electron anisotropy dominates the galactic anisotropy close to the Jovian electron source at ~5 AU, as expected, testifying to the validity of the3D-model. For the latitudinal anisotropy, the polar perpendicular diffusion plays a dominant role for Jovian electrons close to the source, with the polar gradient becoming the dominant factor away from the electron source. Of all three anisotropy components, the azimuthal anisotropy is dominant in the equatorial plane close to the source. It is found that there is a large azimuthal gradient close to the source because the low-energy electrons tend to follow the heliospheric magnetic field more closely than higher energy particles. The transition of the solar wind speed from minimum to intermediate to maximum solar activity condition was used to illustrate the modulation of the magnitude of the 7 MeV total anisotropy vector along the Ulysses trajectory. It was found that during the two encounters with the planet a maximum anisotropy of 38% was computed but with different anisotropy-timepeaks as the approach to Jupiter was different. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

The Voyager 1 spacecraft is now about 25 AU beyond the heliospheric termination shock and soon it should encounter the outer boundary of the heliosphere, the heliopause. This is set to be at 120 AU in the modulation model used for this study. This implies that Voyager 1, and soon afterwards also Voyager 2, should be able to measure the heliopause spectrum, to be interpreted as the lowest possible local interstellar spectrum, for low energy galactic electrons (1 MeV to 120 MeV). This could give an answer to a long outstanding question about the spectral shape (energy dependence) of the galactic electron spectrum at these low energies. These in situ electron observations from Voyager 1, until the year 2010 when it was already beyond 112 AU, are used for a comparative study with a comprehensive three dimensional numerical model for the solar modulation of galactic electrons from the inner to the outer heliosphere. A locally developed steady state modulation model which numerically solves the relevant heliospheric transport equation is used to compute and study modulated electron spectra from Earth up to the heliopause. The issue of the spectral shape of the local interstellar spectrum at these low energies is specifically addressed, taking into account modulation in the inner heliosheath, up to the heliopause, including the effects of the transition of the solar wind speed from supersonic to subsonic in the heliosheath. Modulated electron spectra from the inner to the outer heliosphere are computed, together with radial and latitudinal profiles, focusing on 12 MeV electrons. This is compared to Voyager 1 observations for the energy range 6–14 MeV. A heliopause electron spectrum is computed and presented as a new plausible local interstellar spectrum from 30 GeV down to 10 MeV. The comparisons between model predictions and observations from Voyager 1 and at Earth (e.g. from the PAMELA mission and from balloon flights) and in the inner heliosphere (e.g. from the Ulysses mission) are made. This enables one to make conclusions about diffusion theory applicable to electrons in the heliosphere, in particular the rigidity dependence of diffusion perpendicular and parallel to the local background solar magnetic field. A general result is that the rigidity dependence of both parallel and perpendicular diffusion coefficients needs to be constant below P < 0.4 GV and only be allowed to increase above this rigidity to assure compatibility between the modeling and observations at Earth and especially in the outer heliosphere. A modification in the radial dependence of the diffusion coefficients in the inner heliosheath is required to compute realistic modulation in this region. With this study, estimates of the intensity of low energy galactic electrons at Earth can be made. A new local interstellar spectrum is computed for these low energies to improve understanding of the modulation galactic electrons as compared to previous results described in the literature. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.

The Voyager 1 spacecraft is now about 25 AU beyond the heliospheric termination shock and soon it should encounter the outer boundary of the heliosphere, the heliopause. This is set to be at 120 AU in the modulation model used for this study. This implies that Voyager 1, and soon afterwards also Voyager 2, should be able to measure the heliopause spectrum, to be interpreted as the lowest possible local interstellar spectrum, for low energy galactic electrons (1 MeV to 120 MeV). This could give an answer to a long outstanding question about the spectral shape (energy dependence) of the galactic electron spectrum at these low energies. These in situ electron observations from Voyager 1, until the year 2010 when it was already beyond 112 AU, are used for a comparative study with a comprehensive three dimensional numerical model for the solar modulation of galactic electrons from the inner to the outer heliosphere. A locally developed steady state modulation model which numerically solves the relevant heliospheric transport equation is used to compute and study modulated electron spectra from Earth up to the heliopause. The issue of the spectral shape of the local interstellar spectrum at these low energies is specifically addressed, taking into account modulation in the inner heliosheath, up to the heliopause, including the effects of the transition of the solar wind speed from supersonic to subsonic in the heliosheath. Modulated electron spectra from the inner to the outer heliosphere are computed, together with radial and latitudinal profiles, focusing on 12 MeV electrons. This is compared to Voyager 1 observations for the energy range 6–14 MeV. A heliopause electron spectrum is computed and presented as a new plausible local interstellar spectrum from 30 GeV down to 10 MeV. The comparisons between model predictions and observations from Voyager 1 and at Earth (e.g. from the PAMELA mission and from balloon flights) and in the inner heliosphere (e.g. from the Ulysses mission) are made. This enables one to make conclusions about diffusion theory applicable to electrons in the heliosphere, in particular the rigidity dependence of diffusion perpendicular and parallel to the local background solar magnetic field. A general result is that the rigidity dependence of both parallel and perpendicular diffusion coefficients needs to be constant below P < 0.4 GV and only be allowed to increase above this rigidity to assure compatibility between the modeling and observations at Earth and especially in the outer heliosphere. A modification in the radial dependence of the diffusion coefficients in the inner heliosheath is required to compute realistic modulation in this region. With this study, estimates of the intensity of low energy galactic electrons at Earth can be made. A new local interstellar spectrum is computed for these low energies to improve understanding of the modulation galactic electrons as compared to previous results described in the literature. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.