Rozprawy doktorskie na temat „Cosmic ray modulation”

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.<br>Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.

The transport of cosmic rays in the heliosphere is studied by making use of a newly developed modulation model. This model employes stochastic differential equations to numerically solve the relevant transport equation, making use of this approach’s numerical advantages as well as the opportunity to extract additional information regarding cosmic ray transport and the processes responsible for it. The propagation times and energy losses of galactic electrons and protons are calculated for different drift cycles. It is confirmed that protons and electrons lose the same amount of rigidity when they experience the same transport processes. These particles spend more time in the heliosphere, and also lose more energy, in the drift cycle where they drift towards Earth mainly along the heliospheric current sheet. The propagation times of galactic protons from the heliopause to Earth are calculated for increasing heliospheric tilt angles and it is found that current sheet drift becomes less effective with increasing solar activity. Comparing calculated propagation times of Jovian electrons with observations, the transport parameters are constrained to find that 50% of 6 MeV electrons measured at Earth are of Jovian origin. Charge-sign dependent modulation is modelled by simulating the proton to anti-proton ratio at Earth and comparing the results to recent PAMELA observations. A hybrid cosmic ray modulation model is constructed by coupling the numerical modulation model to the heliospheric environment as simulated by a magneto-hydrodynamic model. Using this model, it is shown that cosmic ray modulation persists beyond the heliopause. The level of modulation in this region is found to exhibit solar cycle related changes and, more importantly, is independent of the magnitude of the individual diffusion coefficients, but is rather determined by the ratio of parallel to perpendicular diffusion.<br>PhD (Space Physics), North-West University, Potchefstroom Campus, 2013

Cosmic rays (CRs) are energetic particles mainly originating outside the Solar System in extremely powerful environments like supernovae remnants (SNRs). The cosmic radiation is composed primarily of high-energy protons, helium and atomic nuclei while only a small fraction are electrons, anti-protons and positrons. During propagation through the Galaxy, CRs interact with the interstellar matter and the Galactic magnetic field. Because of these interactions CRs lose energy and change their spectral features with respect to the injection spectrum. Moreover, before reaching the Earth, CRs traverse the heliosphere, a region of space formed by the continuously outward expanding solar wind. Propagation inside the solar environment make the CR spectra decrease in intensity and vary with time following the 11-year solar cycle. During solar minimum the intensity of CRs on Earth is maximum; the situation reverses during solar maximum. Above 30 GeV the effects of solar modulation are negligible. In this work a new measurement of the time dependent Galactic CR positron and electron energy spectra between 70 MeV and 50 GeV is presented. The analysis was conducted on data collected by the space borne PAMELA experiment during the period from July 2006 to January 2009. This was a period of intense solar minimum and negative solar magnetic field polarity. Long flight duration together with high proton rejection power make the PAMELA instrument the ideal apparatus for measuring the long-term variation of CR electrons and positrons. A total of seven spectra was obtained, each measures over six months period. This solution was a compromise between the time resolution and the statistics. Precise measurement of the electron and positron spectra allows to test the numerical 3D models which describe the transport of charged particles through the heliosphere. The results discussed in this thesis are relevant since they provide long-term observation of electron and positron spectra improving both time resolution and statistical precision with respect to previous experiments. Moreover the measurement is performed down to 70 MeV, an energy region not achievable by other space-borne experiments able to perform charge sign separation like AMS-02. A big effort has been invested to achieve precise results below 200 MeV since a change in the spectral shape is expected from the propagation models. Finally, the simultaneous measure of the positron and electron spectra allow a comprehensive study of the charge-sign dependent modulation of CRs.

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.<br>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.

A proper understanding of the effects of turbulence on the diffusion and drift of cosmic-rays in the heliosphere is imperative for a better understanding of cosmic-ray modulation. This study presents an ab initio model for cosmic-ray modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. The latter model is solved for solar minimum heliospheric conditions, utilizing boundary values chosen in such a way that the results of this model are in fair to good agreement with spacecraft observations of turbulence quantities, not only in the ecliptic plane, but also along the out-of-ecliptic trajectory of the Ulysses spacecraft. These results are employed as inputs for modelled slab and 2D turbulence energy spectra, which in turn are used as inputs for parallel mean free paths based on those derived from quasi-linear theory, and perpendicularmean free paths from extended nonlinear guiding center theory. The modelled 2D spectrum is chosen based on physical considerations, with a drop-off at the very lowest wavenumbers commencing at the 2D outerscale. There currently exist no models or observations for this quantity, and it is the only free parameter in this study. The use of such a spectrum yields a non-divergent 2D ultrascale, which is used as an input for the reduction terms proposed to model the effects of turbulence on cosmic-ray drifts. The resulting diffusion and drift coefficients are applied to the study of galactic cosmic-ray protons, electrons, antiprotons, and positrons using a three-dimensional, steady-state numerical cosmic-ray modulation code. The magnitude and spatial dependence of the 2D outerscale is demonstrated to have a significant effect on computed cosmic-ray intensities. A form for the 2D outerscale was found that resulted in computed cosmic-ray intensities, for all species considered, in reasonable agreement with multiple spacecraft observations. Computed galactic electron intensities are shown to be particularly sensitive to choices of parameters pertaining to the dissipation range of the slab turbulence spectrum, and certain models for the onset wavenumber of the dissipation range could be eliminated in this study.<br>Thesis (PhD (Physics))--North-West University, Potchefstroom Campus, 2013

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<br>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

Cosmic rays (CRs) are electrically charged particles accelerated by astrophysical powerful sources. CRs consists mainly of protons and helium nuclei and in minimal part of other nuclei and electrons. Among these, there are the deuterons, i.e. the deuterium nuclei, which are produced as a secondary component from interactions of CRs with the interstellar medium. During their voyage in the Galaxy, CRs experience energy losses, fragmentations in secondary products, trajectory deflections by galactic magnetic fields and generally a change of the spectral features. Before reaching the Earth, CRs propagate through the Heliosphere, the space region permeated by the solar magnetic field embedded in the turbulent solar wind (SW) flowing from the Sun. The interaction with the heliospheric magnetic field (HMF) and the SW makes CR fluxes decrease with respect to the intensity of their energy spectra outside the Heliosphere. A time dependence of the CR fluxes is also induced by the different phases of the 11-year cycle of solar activity and of the 22-year cycle of the HMF. The latter also induces polarity-dependent drift motions, which are followed by CRs of opposite charges in the opposite direction. With the current CR detector sensitivity, all these effects of CR solar modulation are measurable up to about 50 GeV. The charge-sign dependence introduced by the drift motions in the Heliosphere is relevant for the studies of the galactic antinuclei, which are rare CR components considered promising probes for indirect searches for dark matter (DM). Especially the antideuterons, according to a variety of DM models, could be produced by DM annihilation or decay with a flux of orders of magnitude above the astrophysical background of secondary antideuterons for energies below a few GeV/n, where the solar modulation effects are significant. In this work, a new measurement of the time-dependent galactic CR proton and deuteron fluxes between 50 and 800 MeV/n are presented. This analysis was conducted on the data collected by the PAMELA experiment from July 2006 to September 2014. This period is particularly relevant for solar-modulation studies because it covers almost a whole solar cycle and includes a change of solar magnetic polarity in 2013 as well. A set of selections was developed to extract clean samples of galactic protons and deuterons from the data maintaining a high selection efficiency. As a result, nine yearly rigidity spectra from 2006 to 2014 have been measured between 0.6 and 2.8 GV for both galactic protons and deuterons. The obtained deuteron fluxes were compared with those obtained from a numerical 3D model of cosmic-ray propagation in the Heliosphere. Such comparison can be useful to constrain the modulation parameters of the model for the different heliospheric conditions. The deuteron-to-proton flux ratios were also calculated and can be used to study as the solar modulation effects depend on the different local-interstellar-spectrum shapes as well as from the charge-to-mass ratio dependence of the principal propagation mechanisms in the Heliosphere. All these results can help to improve the accuracy of the solar modulation modelling of the cosmic-ray deuteron fluxes, which is paramount to properly model the solar-modulation effects on the expected energy spectra of antideuterons, reducing the current related uncertainty. A preliminary study of the deuteron acceptance achievable with the GAPS experiment was also performed using simulated data. Although the GAPS apparatus has been designed to perform a novel exotic-atom formation and decay technique to detect CR antinuclei, particle detection is possible at low energy. An analysis technique was developed to identify the deuteron Bragg peaks occurring in the GAPS detectors and separate in this way deuterons from the larger background of protons. The obtained results about deuteron acceptance and proton power rejection are provided in the thesis.

Les preuves pour l'existence de la matière noire (MN), sous forme d'une particule inconnue qui rempli les halos galactiques, sont issues d'observations astrophysiques et cosmologiques: son effet gravitationnel est visible dans les rotations des galaxies, des amas de galaxies et dans la formation des grandes structures de l'univers. Une manifestation non-gravitationnelle de sa présence n'a pas encore été découverte. L'une des techniques les plus prometteuse est la détection indirecte de la MN, consistant à identifier des excès dans les flux de rayons cosmiques pouvant provenir de l'annihilation ou la désintégration de la MN dans le halo de la Voie Lactée. Les efforts expérimentaux actuels se focalisent principalement sur une gamme d'énergie de l'ordre du GeV au TeV, où un signal de WIMP (Weakly Interacting Massive Particles) est attendu. L'analyse des mesures récentes et inédites des rayons cosmiques chargés (antiprotons, électrons et positrons) et leurs émissions secondaires et les améliorations des modèles astrophysiques sont présentées.Les données de PAMELA sur les antiprotons contraignent l'annihilation et la désintégration de la MN de manière similaire (et même légèrement meilleurs) que les contraintes les plus fortes venant des rayons gamma, même dans le cas où les énergies cinétiques inférieures à 10 GeV sont écartées. En choisissant des paramètres astrophysiques différents (modèles de propagation et profils de MN), les contraintes peuvent changer d'un à deux ordres de grandeur. Pour exploiter la totalité de la capacité des antiprotons à contraindre la MN, des effets précédemment négligés sont incorporés et se révèlent être importants dans l'analyse des données inédites de AMS-02 : ajouter les pertes d'énergie, la diffusion dans l'espace des moments et la modulation solaire peut modifier les contraintes, même à de hautes masses. Une mauvaise interprétation des données peut survenir si ces effets ne sont pas pris en compte. Avec les flux de protons et d'hélium exposé par AMS-02, le fond astrophysique et ces incertitudes du ratio antiprotons sur protons sont réévalués et comparés aux données inédites de AMS-02. Aucune indication pour un excès n'est trouvé. Une préférence pour un halo confinant plus large et une dépendance en énergie du coefficient de diffusion plus plate apparaissent. De nouvelles contraintes sur l'annihilation et la désintégration de la MN sont ainsi dérivés.Les émissions secondaires des électrons et des positrons peuvent aussi contraindre l'annihilation et la désintégration de la MN dans le halo galactique : le signal radio dû à la radiation synchrotron des électrons et positrons dans le champs magnétique galactique, les rayons gamma des processus de bremsstrahlung avec le gas galactique et de Compton Inverse avec le champs radiatif interstellaire sont considérés. Différentes configurations de champs magnétique galactique et de modèles de propagation et des cartes de gas et de champs radiatif interstellaire améliorés sont utilisées pour obtenir des outils permettant le calculs des émissions synchrotrons et bremsstrahlung venant de MN de type WIMP. Tous les résultats numériques sont incorporés dans la dernière version du Poor Particle Physicist Coookbook for DM Indirect Detection (PPPC4DMID).Une interprétation d'un possible excès dans les données de rayons gamma de Fermi-LAT au centre galactique comme étant dû à l'annihilation de MN en canaux hadronique et leptonique est analysée. Dans une approche de messagers multiples, le calcul des émissions secondaires est amélioré et se révèle être important pour la détermination du spectre pour le canal leptonique. Ensuite, les limites provenant des antiprotons sur l'annihilation en canal hadronique contraignent sévèrement l'interprétation de cet excès comme étant dû à la MN, dans le cas de paramètres de propagation et de modulation solaire standards. Avec un choix plus conservatif de ces paramètres elles s'assouplissent considérablement<br>Overwhelming evidence for the existence of Dark Matter (DM), in the form of an unknownparticle filling the galactic halos, originates from many observations in astrophysics and cosmology: its gravitational effects are apparent on galactic rotations, in galaxy clusters and in shaping the large scale structure of the Universe. On the other hand, a non-gravitational manifestation of its presence is yet to be unveiled. One of the most promising techniques is the one of indirect detection, aimed at identifying excesses in cosmic ray fluxes which could possibly be produced by DM annihilations or decays in the Milky Way halo. The current experimental efforts mainly focus in the GeV to TeV energy range, which is also where signals from WIMPs (Weakly Interacting Massive Particles) are expected. Focussing on charged cosmic rays, in particular antiprotons, electrons and positrons, as well as their secondary emissions, an analysis of current and forseen cosmic ray measurements and improvements on astrophysical models are presented. Antiproton data from PAMELA imposes contraints on annihilating and decaying DM which are similar to (or even slightly stronger than) the most stringent bounds from gamma ray experiments, even when kinetic energies below 10 GeV are discarded. However, choosing different sets of astrophysical parameters, in the form of propagation models and halo profiles, allows the contraints to span over one or two orders of magnitude. In order to exploit fully the power of antiprotons to constrain or discover DM, effects which were previously perceived as subleading turn out to be relevant especially for the analysis of the newly released AMS-02 data. In fact, including energy losses, diffusive reaccelleration and solar modulation can somewhat modify the current bounds, even at large DM masses. A wrong interpretation of the data may arise if they are not taken into account. Finally, using the updated proton and helium fluxes just released by the AMS-02 experiment, the astrophysical antiproton to proton ratio and its uncertainties are reevaluated and compared to the preliminarly reported AMS-02 measurements. No unambiguous evidence for a significant excess with respect to expectations is found. Yet, some preference for thicker halos and a flatter energy dependence of the diffusion coefficient starts to emerge. New stringed constraints on DM annihilation and decay are derived. Secondary emissions from electrons and positrons can also be used to constrain DM annihilation or decay in the galactic halo. The radio signal due to synchrotron radiation of electrons and positrons on the galactic magnetic field, gamma rays from bremsstrahlung processes on the galactic gas densities and from Inverse Compton scattering processes on the interstellar radiation field are considered. With several magnetic field configurations, propagation scenarios and improved gas density maps and interstellar radiation field, state-of-art tools allowing the computaion of synchrotron and bremssttrahlung radiation for any WIMP DM model are provided. All numerical results for DM are incorporated in the release of the Poor Particle Physicist Coookbook for DM Indirect Detection (PPPC4DMID). Finally, the possible GeV gamma-ray excess identified in the Fermi-LAT data from the Galactic Center in terms of DM annihilation, either in hadronic or leptonic channels is studied. In order to test this tantalizing interprestation, a multi-messenger approach is used: first, the computation of secondary emisison from DM with respect to previous works confirms it to be relevant for determining the DM spectrum in leptonic channels. Second, limits from antiprotons severely constrain the DM interpretation of the excess in the hadronic channel, for standard assumptions on the Galactic propagation parameters and solar modulation. However, they considerably relax if more conservative choices are adopted

Questa tesi descrive lo studio di elettroni e positroni nella radiazione cosmica. Nuove misure della frazione di positroni al top dell’atmosfera tra 200 MeV e 3.0 GeV, nonché lo spettro di elettroni fino a 20 GeV, sono presentati. La misura è stata effettuata con l’esperimento PAMELA da Luglio 2006 a Dicembre 2008, periodo di minima attività solare e polarità negativa. PAMELA fornisce le prime osservazioni a lungo termine della frazione di positroni di bassa energia durante questo particolare stato della eliosfera. La grande statistica collezionata permette di studiare la variazione del flusso di particelle a Terra in funzione dell’energia e del tempo, e di investigare effetti dipendenti dal segno della carica. Durante circa 860 giorni di raccolta dati circa 16000 positroni e 178000 elettroni sono stati identificati. Le maggiore fonte di fondo, costituite da protoni e pioni localmente prodotti, sono state studiate. Lo spettro di elettroni derivato mostra chiaramente l’effetto della modulazione solare sotto qualche GeV. La frazione di positroni è risultata in accordo con le predizioni di modelli teorici che descrivono il trasporto di particelle nell’eliosfera che tengono conto di effetti di drift.<br>This thesis describes the study of electrons and positrons in the cosmic radiation. New measurements of the positron fraction at the top of the atmosphere between 200 MeV and 3.0 GeV are presented, together with the electron spectrum up to 20 GeV. The measurement was conducted with the space borne PAMELA experiment from July 2006 to December 2008, that is a period of minimum solar activity and negative solar magnetic field polarity. PAMELA provides the first long term observation of the low energy positron abundance during this particular solar and heliospheric state. The great amount of collected statistics allows to study the variation of the particle intensity at Earth with energy and time, and to investigate effects depending on the particles sign of charge. During approximately 860 days of data collection about 16300 positrons and 178000 electrons were identified. The major sources of background, constituted by cosmic protons and locally produced pions, have been studied. The derived electron spectrum clearly shows the effect of the solar modulation below few GeV. The detected positron fraction has been found to be in accordance with predictions from theoretical models that describe the transport of particles in the heliosphere taking drift effects into account.

In the present study we aim to further our understanding of charged particle transport in a magnetized medium. To this end, we perform direct numerical simulations of particle transport in a turbulent magnetic field. From the particle trajectories we calculate diffusion and drift coefficients. In contrast to previous numerical simulations of this nature, we also consider a background magnetic field that contains a gradient perpendicular to the magnetic field direction. By using a non-uniform background magnetic field, we can investigate the simultaneous large scale drift due to the gradient in the background magnetic field and the diffusion due to the turbulence which is superimposed on this background magnetic field. Upon comparison with the simulated diffusion coefficients, the newly proposed weakly non-linear theory (WNLT) of Shalchi et al. (2004b) seems to be the most appropriate theory for the simultaneous description of parallel and perpendicular diffusion over a wide range of fluctuation amplitude and particle rigidity. As for the effect of large scale drift on perpendicular diffusion, we find that under conditions of small amplitude turbulence and/ or high particle rigidity the transport perpendicular to the background field can exhibit super-diffusive behaviour. Diffusive behaviour seems to be recovered for the cases when the turbulence amplitude is sufficiently large and/ or the particle rigidity is sufficiently small. We furthermore find that both the drift coefficient and the drift speed are reduced from their weak scattering counterparts in the presence of scattering, with the reduction becoming more pronounced with increasing turbulence amplitude. For the drift coefficient in particular, the reduction from its weak scattering counterpart behaves differently for the cases in which the background magnetic field is either uniform or non-uniform. For the former case the reduction is predominantly at small rigidities, while for the latter case the reduction is predominantly at large rigidities. The latter result might be of significance for heliospheric modulation models in which the background magnetic field is highly non-uniform. Finally, we use a two-dimensional steadystate cosmic ray modulation model to see how our improved understanding of the underlying transport processes influences the overall cosmic ray modulation in the heliosphere. We conclude that in the absence of a theory which connects large scale drift with small scale diffusion, any statements about the inadequacy of a two-dimensional steady-state modulation model might be premature.<br>Thesis (Ph.D. (Physics))--North-West University, Potchefstroom Campus, 2006.

Time-dependent cosmic ray modulation in the heliosphere is studied by using a two-dimensional time dependent modulation model. To compute realistic cosmic ray modulation a compound approach is used, which combines the effect of the global changes in the heliospheric magnetic field magnitude and the current sheet tilt angle to establish realistic time dependent diffusion and drift coefficients. This approach is refined by scaling down drifts additionally (compared to diffusion) towards solar maximum. The amount of drifts needed in the model to realistically compute 2.5 GV proton and electron and 1.2GV electron and helium intensities, as measured by Ulysses from 1990 to 2004, is established. It is shown that the model produces the correct latitudinal gradients evident from the observations during both the Ulysses fast latitude scan periods. Also, much can be learned on the magnitude of perpendicular diffusion in the polar direction, K┴θ, especially for solar minimum conditions and for polarity cycles when particles drift in from the poles. For these periods K┴θ = 0.12K║ in the polar regions (with K║ the parallel diffusion coefficient)and K┴θ /K║ can vary between 0.01 to even 0.04 in the equatorial regions depending on the enhancement factor toward the poles. The model is also applied to compute radial gradients for 2.5 GV cosmic ray electrons and protons in the inner heliosphere. It is shown that, for solar minimum, and in the equatorial regions, the protons (electrons) have a radial gradient of 1.9 %/AU (2.9 %/AU), increasing for both species to a very fluctuating gradient varying between 3 to 4 %/AU at solar maximum. Furthermore, the model also computes realistic electron to proton and electron to helium ratios when compared to Ulysses observations, and charge-sign dependent modulation is predicted up to the next solar minimum expected in 2007. Lastly the model is also applied to model simultaneously galactic cosmic ray modulation at Earth and along the Voyager 1 trajectory, and results are compared with> 70 MeV count rates from Voyager 1 and IMP8. To produce realistic modulation, this model gives the magnitude of perpendicular diffusion in the radial direction as K┴r/K║= 0.035 and that the modulation boundary seemed to be situated between at 120 AU and 140 AU.<br>Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2005.

A two-dimensional (2-D) time-dependent cosmic ray modulation model is used to calculate the modulation of cosmic-ray protons and electrons for 11-and 22-year modulation cycles using a compound approach to describe solar cycle related changes in the transport parameters. The compound approach was developed by Ferreira and Potgieter (2004) and incorporates the concept of propagation diffusion barriers, global changes in the magnetic field, time-dependent gradient, curvature and current-sheet drifts, and other basic modulation mechanisms. By comparing model results with 2.5 GV Ulysses observations, for both protons and electrons, it is shown that the compound approach results in computed intensities on a global scale compatible to observations. The model also computes the expected latitudinal dependence, as measured by the Ulysses spacecraft, for both protons and electrons. This is especially highlighted when computed intensities are compared to observations for the different fast latitude scan (FLS) periods. For cosmic ray protons a significant latitude dependence was observed for the first FLS period which corresponded to solar minimum conditions. For the second, which corresponded to solar maximum, no latitude dependence was observed as was the case for the third FLS period, which again corresponded to moderate to minimum solar activity. For the electrons the opposite occurred with only an observable latitude dependence in intensities for the third FLS period. It is shown that the model results in compatible intensities when compared to observations for these periods. Due to the success of the compound approach, it is also possible to compute charge-sign dependent modulation for 2.5 GV protons and electrons. The electron to proton ratio is presented at Earth and along the Ulysses trajectory. Lastly, it is also shown how the modulation amplitude between solar minimum and maximum depends on rigidity. This is investigated by computing cosmic ray intensities for both protons and electrons, not only at 2:5 GV, but also up to 7:5 GV. A refinement for the compound approach at higher rigidities is proposed.<br>Thesis (M.Sc. (Space Physics))--North-West University, Potchefstroom Campus, 2011.

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.<br>Thesis (PhD (Space Physics))--North-West University, Potchefstroom Campus, 2013

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.<br>Thesis (Ph.D. (Physics))--North-West University, Potchefstroom Campus, 2004.

Models describing the modulation of galactic cosmic rays in the heliosphere have been developed and investigated. These models are numerical solutions of the cosmic ray transport equation under idealized heliospheric conditions. Primarily, the models were used to predict the radial gradient g r of galactic cosmic rays in the vicinity of the Earth during solar-minimum conditions specified by a flat neutral sheet and no propagating shock disturbances. It was found that g r was not sensitive to the assumed value of the cosmic ray distribution at the Sun, but was very sensitive to (a) the diffusion coefficients used to specify the rate of diffusion of the cosmic ray distribution near the Sun, and (b) the choice of the integrating algorithm used to determine the distribution from the transport equation. The stability of each integrating algorithm used was also investigated. There have been many measurements of the value of g,. at Earth in the past, mainly derived from data collected by polar-based neutron monitors or detectors on board satellites. From all sources of data and over a wide range of energy (tens of MeV to ~100 GeV) the general consensus is that g,. at Earth is less than 5% AU-1 and probably around 1-2 % AU-1 . The models investigated in this thesis predict a gradient in this range but only if certain diffusion coefficients are specified. The models were also used to investigate the relative importance of shocks, or propagating solar disturbances, to the total eleven year cycle of cosmic ray modulation for medium energy (1-10 GeV) particles. It was found that such disturbances were unable to produce the observed intensity difference seen from solar minimum to solar maximum. It was concluded that these, and higher energy particles, are modulated significantly by changes in the overall global average heliospheric magnetic field through bulk drift motion. An example of this bulk-drift modulation was investigated by looking at the correlation of neutral-sheet position with isotropic intensity wave variations seen in the cosmic ray data. For this analysis, a generalized model of the neutral sheet was developed.. An independent measurement of g r was also calculated from data collected by the network of cosmic ray detectors operated by the Hobart cosmic ray group during the years 1975-78 and 1982-85. This group consists of the Cosmic Ray Section of the Australian Antarctic Division and the Cosmic Ray Section of the University of Tasmania (Physics Department). The gradient g r was determined by applying a north-south anisotropy analysis to the data. The value of g r obtained was sensitive to the assumed energy spectrum of the north-south anisotropy but was not inconsistent with other experimentally determined values. The gradient was generally less than 5% AU -1 . It was necessary to calculate coupling coefficients and atmospheric correction coefficients for the Mawson muon telescopes in order to use the data from these detectors in the north-south anisotropy analysis.

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.<br>MSc (Space Physics), North-West University, Potchefstroom Campus, 2015

The distribution of galactic cosmic ray particles in the heliosphere is influenced (modulated) by the Sun's interplanetary magnetic field (IMF) and the solar wind. The particles diffuse inward, convect outward and have drifts in the motion of their gyro-centres. They are also scattered from their gyro-orbits by irregularities in the IMF. These processes are the components of solar modulation and produce streaming (anisotropies) of particles in the heliosphere. The anisotropies can be investigated at Earth by examining the count rates of cosmic ray detectors. The anisotropic streams appear as diurnal and semi-diurnal variations in the count rates of cosmic ray recorders in solar and sidereal time. Theoretical models of solar modulation predict effects which are dependent on the polarity of the Sun's magnetic dipole (A >0 or A <0). The solar diurnal and North-South anisotropy can be used to test these predictions. The yearly averaged solar and sidereal diurnal variations in data recorded by seven neutron monitors and ten muon telescopes for the period 1957 to 1990 have been deduced by Fourier analysis methods. The rigidities of the galactic cosmic rays to which these instruments respond encompass the range 10 to 1400 Giga volts (GV). The rigidity spectrum of the solar diurnal anisotropy has been inferred to have a mean spectral index extremely close to zero and an idealised upper limiting rigidity of 100± 25 GV. This is in good agreement with previous determinations. It is shown that this upper limit has a temporal variation between 50 GV and 180 GV and is correlated with the magnitude of the IMF. The rigidity spectrum is likely to be dependent on the polarity of the Sun's magnetic dipole, the spectral index being determined as positive in the A >0 magnetic polarity state and negative in the A <0 polarity state. It is also shown that the amplitude of the anisotropy varies with an 11-year variation and the time of maximum varies with 22-year variation. Both of these variations are shown to be independent of any change in the rigidity spectrum. The solar diurnal anisotropy is also used as a tool to calculate the modulation parameters λ∥ Gτ, (the product of the parallel mean-free path and radial density gradient) and Glzl (an indicator of the symmetric latitudinal density gradient). λ∥ Gτ is found to have a 22-year variation at all rigidities studied and furthermore to only have rigidity dependence when the λ∥Gτ heliosphere is in the A >0 magnetic polarity state. It is unlikely that has any rigidity dependence in the A <0 polarity state. Glzl indicates that below 50 GV the symmetric latitudinal density gradient behaves in accordance with the predictions of current modulation theories. Between 50 and 195 GV however, the predicted behaviour is only observed when the rigidity spectrum of the solar diurnal anisotropy is assumed to be flat, static and have an upper limiting rigidity of 100 GV. The sidereal diurnal variation in the data recorded by the instruments has been deduced and used to study the North-South anisotropy. The results indicate that this anisotropy has only a small variation in amplitude. There is strong evidence for heliospheric asymmetric modulation (with respect to above and below the neutral sheet) of a galactic anisotropy in the sense proposed by Nagashima et al. (1982) and that this modulation may have a 22-year variation. From the examination of the North-South anisotropy the radial density gradients (Gτ) at 1 AU of 17 to 195 GV particles were determined. The gradient is slightly smaller around times of solar minimum. No magnetic polarity dependence of the radial gradient was observed, in direct conflict with conventional theoretical predictions. The modulation parameters have been used to determine the parallel mean-free path (λ∥) of galactic cosmic rays with rigidities between 17 and 195 GV near the Earth. It was found that this parameter depends on magnetic polarity at all the rigidities examined and has a linear relationship with rigidity. Perpendicular diffusion has been examined and shown to have very little contribution to the values of the modulation parameters except for years near solar minimum.

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.<br>PhD (Space Physics), North-West University, Potchefstroom Campus, 2015