The solar minimum of 2009 has been identified as an exceptional event with regard to cosmic ray (CR)modulation, since conditions in the heliosphere have reached unprecedented quiet levels. This unique minimum has been observed by the Earth–orbiting satellite, PAMELA, launched in June, 2006, from which vast sets of accurate proton and electron preliminary observations have been made available. These simultaneous measurements from PAMELA provide the ideal opportunity to conduct an in–depth study of CR modulation, in particular charge–sign dependent modulation. In utilizing this opportunity, a three–dimensional, steady–state modulation model was used to reproduce a selection of consecutive PAMELA proton and electron spectra from 2006 to 2009. Thiswas done by assuming full drifts and simplified diffusion coefficients, where the rigidity dependence and absolute value of themean free paths for protons and electrons were sequentially adjusted below 3 GV and 300 MV, respectively. Care has been taken in calculating yearly–averaged current–sheet tilt angle and magnetic field values that correspond to the PAMELA spectra. Following this study where the numerical model was used to investigate the individual effects resulting from changes in the tilt angle, diffusion coefficients, and global drifts, it was found that all these modulation processes played significant roles in contributing to the total increase in CR intensities from 2006 to 2009, as was observed by PAMELA. Furthermore, the effect that drifts has on oppositely charged particles was also evident from the difference between the peak–shaped time profiles of protons and the flatter time profiles of electrons, as is expected for an A < 0 polarity cycle. Since protons, which drift into the heliosphere along the heliospheric current–sheet, haven’t yet reached maximum intensity levels by 2008, their intensities increased notably more than electrons toward the end of 2009. The time and energy dependence of the electron to proton ratios were also studied in order to further illustrate and quantify the effect of drifts during this remarkable solar minimum period. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.

The solar minimum of 2009 has been identified as an exceptional event with regard to cosmic ray (CR)modulation, since conditions in the heliosphere have reached unprecedented quiet levels. This unique minimum has been observed by the Earth–orbiting satellite, PAMELA, launched in June, 2006, from which vast sets of accurate proton and electron preliminary observations have been made available. These simultaneous measurements from PAMELA provide the ideal opportunity to conduct an in–depth study of CR modulation, in particular charge–sign dependent modulation. In utilizing this opportunity, a three–dimensional, steady–state modulation model was used to reproduce a selection of consecutive PAMELA proton and electron spectra from 2006 to 2009. Thiswas done by assuming full drifts and simplified diffusion coefficients, where the rigidity dependence and absolute value of themean free paths for protons and electrons were sequentially adjusted below 3 GV and 300 MV, respectively. Care has been taken in calculating yearly–averaged current–sheet tilt angle and magnetic field values that correspond to the PAMELA spectra. Following this study where the numerical model was used to investigate the individual effects resulting from changes in the tilt angle, diffusion coefficients, and global drifts, it was found that all these modulation processes played significant roles in contributing to the total increase in CR intensities from 2006 to 2009, as was observed by PAMELA. Furthermore, the effect that drifts has on oppositely charged particles was also evident from the difference between the peak–shaped time profiles of protons and the flatter time profiles of electrons, as is expected for an A < 0 polarity cycle. Since protons, which drift into the heliosphere along the heliospheric current–sheet, haven’t yet reached maximum intensity levels by 2008, their intensities increased notably more than electrons toward the end of 2009. The time and energy dependence of the electron to proton ratios were also studied in order to further illustrate and quantify the effect of drifts during this remarkable solar minimum period. / 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.

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.