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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

A New Measurement of Low Energy Antiprotons In the Cosmic Radiation

Hofverberg, Petter January 2008 (has links)
New measurements of the antiproton flux and the antiproton-to-proton flux ratio at the top of the atmosphere between 80 MeV and 2.0 GeV are presented. The measurement was conducted from July 2006 to March 2008 with the PAMELA satellite experiment. This is a period of minimum solar activity and negative solar polarity and the PAMELA measurement is the first observation of antiprotons during this particular solar state. The PAMELA instrument comprises a permanent magnet spectrometer, a scintillator based time-of-flight system, an electromagnetic calorimeter and an anticoincidence shield. These detectors can identify antiprotons from a background of cosmic-ray electrons and locally produced pions. The PAMELA instrument is mounted on the Resurs DK1 satellite that was launched from the Baikonur Cosmodrome on June the 15th into a semi-polar orbit with an inclination of 70o. During approximately 500 days of data collection 170 antiprotons were identified. The derived antiproton spectrum shows a steep increase up to 2 GeV as expected for pure secondary production of galactic antiprotons. The antiproton flux is over-estimated by most current models of secondary production compared to PAMELA results. There are no indications of the excess of antiprotons at low energy predicted by theories of primordial black hole evaporation. The antiproton-to-proton flux ratio is in agreement with drift models of solar modulation, which are also favoured by recent PAMELA measurements of the positron fraction. / QC 20100811
2

Modeling of galactic cosmic rays in the heliosphere / Mabedle Donald Ngobeni

Ngobeni, Mabedle Donald January 2015 (has links)
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
3

Modeling of galactic cosmic rays in the heliosphere / Mabedle Donald Ngobeni

Ngobeni, Mabedle Donald January 2015 (has links)
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
4

Time-dependent modulation of cosmic rays in the outer heliosphere / Rex Manuel

Manuel, Rex January 2013 (has links)
The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a two-dimensional, time-dependent modulation model. The compound approach of Ferreira and Potgieter (2004), which describes changes in the cosmic ray transport coefficients over a solar cycle, is improved by introducing recent theoretical advances in the model. Computed intensities are compared with Voyager 1 and 2, IMP 8 and Ulysses proton observations in search of compatibility. It is shown that this approach gives realistic cosmic ray proton intensities on a global scale at Earth and along both Voyager spacecraft trajectories. The results show that cosmic ray modulation, in particular during the present polarity cycle, is not just determined by changes in the drift coefficient but is also dependent on changes in the diffusion coefficients. Furthermore, a comparison of computations to observations along the Voyager 1 and Voyager 2 trajectories illustrates that the heliosphere is asymmetrical. Assuming the latter, E > 70 MeV and 133-242 MeV cosmic ray proton intensities along Voyager 1 and 2 trajectories are predicted from 2012 onwards. It is shown that the computed intensities along Voyager 1 can increase with an almost constant rate since the spacecraft is close to the heliopause. However, the model shows that Voyager 2 is still under the influence of temporal solar activity changes because of the relatively large distance to the heliopause when compared to Voyager 1. Along the Voyager 2 trajectory the intensities should remain generally constant for the next few years and then should start to steadily increase. It is also found that without knowing the exact location of heliopause and transport parameters one cannot conclude anything about local interstellar spectra. The effect of a dynamic inner heliosheath width on cosmic ray modulation is also studied by implementing a time-dependent termination shock position in the model. This does not lead to improved compatibility with spacecraft observations so that a time-dependent termination shock along with a time-dependent heliopause position is required. The variation of the heliopause position over a solar cycle is found to be smaller compared to that of the termination shock. The model predicts the heliopause and termination shock positions along Voyager 1 in 2012 at 119 AU and 88 AU respectively and along Voyager 2 at 100 AU and 84 AU respectively. / Thesis (PhD (Space Physics))--North-West University, Potchefstroom Campus, 2013
5

Time-dependent modulation of cosmic rays in the outer heliosphere / Rex Manuel

Manuel, Rex January 2013 (has links)
The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a two-dimensional, time-dependent modulation model. The compound approach of Ferreira and Potgieter (2004), which describes changes in the cosmic ray transport coefficients over a solar cycle, is improved by introducing recent theoretical advances in the model. Computed intensities are compared with Voyager 1 and 2, IMP 8 and Ulysses proton observations in search of compatibility. It is shown that this approach gives realistic cosmic ray proton intensities on a global scale at Earth and along both Voyager spacecraft trajectories. The results show that cosmic ray modulation, in particular during the present polarity cycle, is not just determined by changes in the drift coefficient but is also dependent on changes in the diffusion coefficients. Furthermore, a comparison of computations to observations along the Voyager 1 and Voyager 2 trajectories illustrates that the heliosphere is asymmetrical. Assuming the latter, E > 70 MeV and 133-242 MeV cosmic ray proton intensities along Voyager 1 and 2 trajectories are predicted from 2012 onwards. It is shown that the computed intensities along Voyager 1 can increase with an almost constant rate since the spacecraft is close to the heliopause. However, the model shows that Voyager 2 is still under the influence of temporal solar activity changes because of the relatively large distance to the heliopause when compared to Voyager 1. Along the Voyager 2 trajectory the intensities should remain generally constant for the next few years and then should start to steadily increase. It is also found that without knowing the exact location of heliopause and transport parameters one cannot conclude anything about local interstellar spectra. The effect of a dynamic inner heliosheath width on cosmic ray modulation is also studied by implementing a time-dependent termination shock position in the model. This does not lead to improved compatibility with spacecraft observations so that a time-dependent termination shock along with a time-dependent heliopause position is required. The variation of the heliopause position over a solar cycle is found to be smaller compared to that of the termination shock. The model predicts the heliopause and termination shock positions along Voyager 1 in 2012 at 119 AU and 88 AU respectively and along Voyager 2 at 100 AU and 84 AU respectively. / Thesis (PhD (Space Physics))--North-West University, Potchefstroom Campus, 2013
6

Measurement of cosmic ray electrons and positrons with the AMS-02 experiment / Medição de eléctrons e pósitrons em raios cósmicos com o experimento AMS-02

Mikuni, Vinicius Massami 03 August 2017 (has links)
The Alpha Magnetic Spectrometer (AMS-02) is a high-energy particle physics detector operating on the International Space Station (ISS) since May 2011. Since its launch, the AMS-02 provided a large amount of data whose precision was never before achieved, opening a new path for the study of cosmic rays (CRs). The first published results of AMS-021-3 show tension with the current understanding of the cosmic ray theory, particularly at higher energies. These tensions are directly linked to many fundamental questions like the dark matter nature, the CR origin and their propagation through the galaxy. This work presents the measurement of the electron flux and the positron flux in primary cosmic rays, based on the data collected between May 2011 and November 2016, an extended data set with respect to the published AMS-02 results.3 The results extend the energy range explored up to 1 TeV for electrons and up to 700 GeV for positrons, being consistent with the published results when using the same data set. A discrepancy between the new measurement and the published flux is observed in the low energy region of the electron flux, while the positron flux is in good agreement. This can be explained by a charge dependent solar modulation effect. This hypothesis was investigated by studying the time evolution of the fluxes, focusing on the energy region below 40 GeV, where an electron and positron flux is computed over 74 time bins of 27 days width, corresponding to the suns rotation period as seen from the Earth. The time dependent analysis confirms hints of charge dependent solar modulation, that are also observed by other independent analysis that have been carried out in parallel within the collaboration. / O Alpha Magnetic Spectrometer (AMS-02) é um experimento de física de partículas instalado na Estação Espacial Internacional (ISS) desde Maio de 2011. Desde seu lançamento, AMS-02 coleta uma quantidade de dados com tal precisão que até então nunca foram jamais vistos, abrindo o caminho para o estudo dos Raios Cósmicos (CRs). Os primeiros resultados publicados pelo AMS-021-3 apresentam tensões com o modelo atual da teoria de CRs, particularmente nas altas energias. Essas tensões são diretamente ligadas a diversas questões fundamentais como a natureza da Matéria Escura (DM), a origem dos CRs e suas propagações pela galáxia. Este trabalho apresenta a medição do fluxo de elétrons e pósitrons em CRs primários, baseando-se nos dados coletados entre Maio de 2011 e Novembro de 2016, período extendido com relação aos resultados públicados pelo AMS-02.3 Os resultados extendem o intervalo de energia explorado para 1 TeV para elétrons e 700 GeV ára pósitrons, consistentes com os resultados públicados usando o mesmo período. Discrepância entre a nova medição e o fluxo públicado é observada na região de baixas energias para o fluxo de elétrons, enquanto o fluxo de pósitrons continua em bom acordo. O resultado pode ser explicado por uma dependência na carga causada pela modulação solar. Tal hipótese é investigada estudando-se a evolução temporal dos fluxos, focando-se no intervao de energia abaixo de 40 GeV, onde um fluxo de elétrons e pósitrons é medido durante 74 intervalos temporais de 27 dias, correspondendo à rotação do sol vista da Terra. A análise dependente do tempo confirma a existência da dependência de carga da modulação solar, também observada por outras análises independentes que foram feitas dentro da colaboração.
7

Measurement of cosmic ray electrons and positrons with the AMS-02 experiment / Medição de eléctrons e pósitrons em raios cósmicos com o experimento AMS-02

Vinicius Massami Mikuni 03 August 2017 (has links)
The Alpha Magnetic Spectrometer (AMS-02) is a high-energy particle physics detector operating on the International Space Station (ISS) since May 2011. Since its launch, the AMS-02 provided a large amount of data whose precision was never before achieved, opening a new path for the study of cosmic rays (CRs). The first published results of AMS-021-3 show tension with the current understanding of the cosmic ray theory, particularly at higher energies. These tensions are directly linked to many fundamental questions like the dark matter nature, the CR origin and their propagation through the galaxy. This work presents the measurement of the electron flux and the positron flux in primary cosmic rays, based on the data collected between May 2011 and November 2016, an extended data set with respect to the published AMS-02 results.3 The results extend the energy range explored up to 1 TeV for electrons and up to 700 GeV for positrons, being consistent with the published results when using the same data set. A discrepancy between the new measurement and the published flux is observed in the low energy region of the electron flux, while the positron flux is in good agreement. This can be explained by a charge dependent solar modulation effect. This hypothesis was investigated by studying the time evolution of the fluxes, focusing on the energy region below 40 GeV, where an electron and positron flux is computed over 74 time bins of 27 days width, corresponding to the suns rotation period as seen from the Earth. The time dependent analysis confirms hints of charge dependent solar modulation, that are also observed by other independent analysis that have been carried out in parallel within the collaboration. / O Alpha Magnetic Spectrometer (AMS-02) é um experimento de física de partículas instalado na Estação Espacial Internacional (ISS) desde Maio de 2011. Desde seu lançamento, AMS-02 coleta uma quantidade de dados com tal precisão que até então nunca foram jamais vistos, abrindo o caminho para o estudo dos Raios Cósmicos (CRs). Os primeiros resultados publicados pelo AMS-021-3 apresentam tensões com o modelo atual da teoria de CRs, particularmente nas altas energias. Essas tensões são diretamente ligadas a diversas questões fundamentais como a natureza da Matéria Escura (DM), a origem dos CRs e suas propagações pela galáxia. Este trabalho apresenta a medição do fluxo de elétrons e pósitrons em CRs primários, baseando-se nos dados coletados entre Maio de 2011 e Novembro de 2016, período extendido com relação aos resultados públicados pelo AMS-02.3 Os resultados extendem o intervalo de energia explorado para 1 TeV para elétrons e 700 GeV ára pósitrons, consistentes com os resultados públicados usando o mesmo período. Discrepância entre a nova medição e o fluxo públicado é observada na região de baixas energias para o fluxo de elétrons, enquanto o fluxo de pósitrons continua em bom acordo. O resultado pode ser explicado por uma dependência na carga causada pela modulação solar. Tal hipótese é investigada estudando-se a evolução temporal dos fluxos, focando-se no intervao de energia abaixo de 40 GeV, onde um fluxo de elétrons e pósitrons é medido durante 74 intervalos temporais de 27 dias, correspondendo à rotação do sol vista da Terra. A análise dependente do tempo confirma a existência da dependência de carga da modulação solar, também observada por outras análises independentes que foram feitas dentro da colaboração.
8

Analyse des données de l'expérience AMS-02 pour la propagation du rayonnement cosmique dans la cavité solaire et la Galaxie / Data analysis with the AMS-02 experiment for the cosmic ray propagation study

Ghelfi, Alexandre 29 September 2016 (has links)
Le rayonnement cosmique, mis en évidence par Viktor Hess en 1912, est composé de particules chargées, créées et possiblement accélérées dans les restes de supernova, et qui se propagent dans la Galaxie. La mesure des flux du rayonnement cosmique permet de mettre des contraintes sur leurs sources et leur transport, mais aussi de se pencher sur le problème de la matière sombre.C'est pour répondre à ces questions qu'a été construit le détecteur AMS-02, mis en place sur la station spatiale internationale depuis mai 2011. Ce détecteur de haute précision mesure l'ensemble des flux de particules du rayonnement cosmique.Le travail proposé dans cette thèse consiste à estimer le flux de protons avec le détecteur AMS-02. L'accent est mis sur la déconvolution des effets de la réponse en énergie du détecteur sur les flux et sur la caractérisation du flux obtenu à haute énergie (au-dessus de 200 GeV/n) avec la mise en évidence d'une cassure spectrale.D'autre part, le soleil émet un plasma qui interagit avec les particules du rayonnement cosmique, modifiant les flux issus de la propagation dans la Galaxie. Cette modification évolue dans le temps en suivant le cycle d'activité solaire et est appelée modulation solaire. Dans ce cadre, nous avons obtenu une nouvelle détermination robuste des flux interstellaires de protons et d'hélium en nous basant sur les données récentes du rayonnement cosmique (incluant AMS-02). Les niveaux de modulation solaire obtenus sont validés avec une seconde analyse réalisée à partir des données des moniteurs à neutrons, détecteurs au sol, qui permettent d'établir des séries en temps du paramètre de modulation depuis les années 50. / Cosmic rays (CR) were discovered by Viktor Hess in 1912. Charged CR are synthesized and supposedly accelerated in supernova remnants, then propagate through the Galaxy. CR flux measurement set constraints on CR sources and propagation, but may also bring answers to the dark matter problem.AMS-02 is a high precision particle physics detector placed on the international space station since may 2011. It measures the CR fluxes of many species.This thesis deals with the proton flux estimation measured by the AMS-02 instrument. The focus is set on the unfolding of the instrument energy response impacting the flux, and on the caracterisation of the high-energy spectral break.The Sun produces a plasma which interacts with CR particles, modifying the flux obtained from galactic propagation. This modification evolves through time following the solar activity cycle, and is denoted solar modulation. In this framework, decolving from this effect, a robust determination of the proton and helium interstellar fluxes is obtained using recent high precision CR data including AMS-02. The associated solar modulation levels are cross-checked with a second estimation taken from neutron monitors (ground based detectors) data, allowing solar modulation time series reconstruction from the 50s.
9

A comparative study of cosmic ray modulation models / Jan Louis Raath

Raath, Jan Louis January 2015 (has links)
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
10

A comparative study of cosmic ray modulation models / Jan Louis Raath

Raath, Jan Louis January 2015 (has links)
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

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