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

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.

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 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.

Title: Correlation properties of magnetosheath fluctuations Author: Olga Gutynska Department: Department of Surface and Plasma Science Supervisor: Prof. RNDr. Jana Šafránková, DrSc. e-mail address: Jana.Safrankova@mff.cuni.cz Abstract: This thesis deals with fluctuations of the magnetic field (MF) and plasma density in different magnetosheath locations. The statistical study of the correlation length of these quantities has shown that these lengths are surprisingly low for both the ion flux and MF (approx. 1 RE). However, the correlation length increases with an increasing correlation between the magnetosheath and interplanetary magnetic fields (IMF). Further, we have found that the correlation length of MF fluctuations depends on the solar wind speed, on a correlation between IMF and magnetosheath MF fluctua- tions, and on the amplitude of fluctuations. The statistical study of radial profiles of cross-correlations between MF and plasma density at the subsolar and flank regions based on Cluster and THEMIS magnetosheath observa- tions revealed better correlations toward the magnetopause. A study of the modification of the IMF direction in the magnetosheath has shown that a reliable prediction of the magnetosheath BZ sign requires |IMF BZ| > 2 nT and that this prediction is more precise during solar minimum....

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.