Search

The near-Earth space and upper atmosphere experience a continuous barrage of particles from different sources: The magnetized solar wind flow from the Sun and the highly energetic cosmic rays originating from (extra-)galactic sources or solar eruptions. Energetic cosmic rays can also create particle air showers that reach the ground level at Earth. The flux of cosmic rays arriving at Earth can be measured at different locations by employing neutron monitors (NMs). We can use NM data to study the local variation of cosmic radiation or use a combination of NMs with knowledge about the geomagnetic shielding to model the flux of cosmic rays in near-Earth space. The flux of galactic cosmic rays (GCRs) arriving to the heliosphere, the region of solar plasma influence, is believed to be constant on millenial time scales. Therefore, the variations of cosmic rays we observe inside the heliosphere are related solely on the heliospheric modulation of cosmic rays through deflection in magnetic fields. This modulation is driven by solar activity and is highly periodic. The 11-year solar cycle is the strongest modulator, but also periods of about 1.75 years, 155 days and the solar rotational 27 days can be identified. Also the local anisotropy of cosmic rays at Earth causes a daily variation in CR measurements. Since the heliospheric medium is highly turbulent, magnetic irregularities generated by it cause modulation of GCRs. By studying power spectrum slopes of NM variations, we found evidence that the level of turbulence affecting NM variations is also dependent on the solar cycle phase. Over one hundred NMs have been active since the 1950s. The NM data is available from multiple databases, but it was found that these datasets are not uniform with one another. A subsequent survey of 147 NM stations from over 300 data records analysed the situation and made it possible to construct a recommended data source list for users of NM data. With the improved knowledge of NM station data quality, we used data from multiple NM stations and new NM yield function estimations to construct an updated version of the heliospheric modulation potential, which is a measure of the average energy loss of GCR particles in the heliosphere at 1 AU. This new method is highly scalable and accurate and was used to produce a daily version of the modulation potential reconstruction.

The final publication is available at IOS Press through http://dx.doi.org/10.3847/1538-4357/aaa774 Galactic cosmic-ray (GCR) energy spectra observed in the inner heliosphere are modulated by the solar activity, the solar polarity and structures of solar and interplanetary origin. A high counting rate particle detector (PD) aboard LISA Pathfinder, meant for subsystems diagnostics, was devoted to the measurement of GCR and solar energetic particle integral fluxes above 70 MeV n-1 up to 6500 counts s-1. PD data were gathered with a sampling time of 15 s. Characteristics and energy dependence of GCR flux recurrent depressions and of a Forbush decrease dated 2016 August 2 are reported here. The capability of interplanetary missions, carrying PDs for instrument performance purposes, in monitoring the passage of interplanetary coronal mass ejections is also discussed.

Variability of Galactic cosmic ray (GCR) is often expressed in terms of the modulation potential, which is typically assessed using energy-integrating ground-based detectors, such as neutron monitors (NMs) for the last decades or cosmogenic isotopes on the time scales of centuries and millennia. In order to estimate the energy dependence of the GCR variability we re-assess here the effective energy Eeff of each type of detector, which is defined so that the variability of the GCR particles at this energy is equal to that of the detector's count rate. We found that Eeff is 11-12 GeV/nuc for the standard polar sea-level neutron monitor, but it is essentially smaller for cosmogenic isotopes, being 6-7 GeV/nuc for 14C and 5.5-6 GeV/nuc for 10Be, respectively. It is also discussed that this effective energy is robustly defined and is hardly dependent on the primary assumptions on the local interstellar spectrum (LIS) of GCR. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License (CC BY-NC-ND 4.0).

Fluxes of galactic cosmic rays (GCR) observed at 1 AU are modulated inside the heliosphere at different time scales. Here we study the properties of the power spectral density (PSD) of galactic cosmic ray variability using hourly data from 31 neutron monitors (NM) from 1953 to 2016. We pay particular attention to the reliability of the used datasets and methods. We present the overall PSD and discuss different parts of the spectrum and the related periodicities. We find significant spectral peaks at the periods of 11 years, 1.75 years, 155 days, 27 days and 24 hours and the harmonics of the latter two peaks. We calculate a power law slope of −1.79 ± 0.13 for the period range between 50 and 130 hours and a slope of −1.34 ± 0.17 for the period range between 40 days and 3.4 years (1000 − 30000 h).

PhD (Space Physics), North-West University, Potchefstroom Campus, 2016 The propagation and modulation of electrons in the heliosphere play an important part in improving our understanding and assessment of the processes of solar modulation. A locally developed, full three-dimensional, numerical model is used to study the modulation of Jovian and galactic electrons from 1 MeV to 50 GeV, and from the Earth into the heliosheath. Modeling results are compared with Voyager 1 observations in the outer heliosphere, including the heliosheath, as well as observations at or near the Earth, in particular the 2009 spectrum from the PAMELA space mission and from Voyager 1 for 1977. First, new heliopause spectra for galactic electrons are established. The issue of the intensity levels and the spectral shape of the local interstellar spectrum at lower energies is specifically addressed. The heliopause is assumed at 122 AU in the model. The extra-ordinary large increase of galactic electrons in the 5 MeV to 50 MeV range in the heliosheath is investigated. The modeling confirms that the heliosheath acts as a most effective modulation barrier for these low energy electrons. This is followed by establishing new Jovian electron source functions, also addressing its level of intensity and its spectral shape. Modulated electron spectra from the inner to the outer heliosphere are computed, first separately for Jovian and galactic electrons and then for the combined modulation. After combining these results, the intensity levels of galactic and Jovian electrons at the Earth below 50 MeV could be estimated. The energy range could be established over which the Jovian electrons dominate over galactic electrons in the inner heliosphere, a process which depends strongly on what is assumed for the Jovian electron source function. Conclusions are made about diffusion and drift theory as applicable to electrons in the heliosphere. Ways of reducing particle drifts explicitly and implicitly are investigated with interesting results. Increasing the rigidity dependence of the drift coefficient at lower energies very effectively reduces the extent to which particle drifts play a role in the modulation process. Concerning diffusion, a general result is that the rigidity dependence of both the parallel and perpendicular diffusion coefficients needs to be constant below ~0.4 GV, but to increase above this rigidity to assure compatibility between the modeling and observations at the 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 modulation that is compatible with observations in this region. Doctoral

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.

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. Masters

Research in many areas of modern physics such as, e.g., indirect searches for dark matter and particle acceleration in SNR shocks, rely heavily on studies of cosmic rays (CRs) and associated diffuse emissions (radio, microwave, X-rays, gamma rays). While very detailed numerical models of CR propagation exist, a quantitative statistical analysis of such models has been so far hampered by the large computational effort that those models require. Although statistical analyses have been carried out before using semi-analytical models (where the computation is much faster), the evaluation of the results obtained from such models is difficult, as they necessarily suffer from many simplifying assumptions, The main objective of this paper is to present a working method for a full Bayesian parameter estimation for a numerical CR propagation model. For this study, we use the GALPROP code, the most advanced of its kind, that uses astrophysical information, nuclear and particle data as input to self-consistently predict CRs, gamma rays, synchrotron and other observables. We demonstrate that a full Bayesian analysis is possible using nested sampling and Markov Chain Monte Carlo methods (implemented in the SuperBayeS code) despite the heavy computational demands of a numerical propagation code. The best-fit values of parameters found in this analysis are in agreement with previous, significantly simpler, studies also based on GALPROP., Comment: 19 figures, 3 tables, emulateapj.sty. A typo is fixed. To be published in the Astrophysical Journal v.728 (February 10, 2011 issue). Supplementary material can be found at http://www.g-vo.org/pub/GALPROP/GalpropBayesPaper/

Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007. A time-dependent two-dimensional (2D) modulation model including drifts, the solar wind tennination shock (TS) with diffusive shock acceleration and a heliosheath based on the Parker (1965) transport equation is used to study the modulation of galactic cosmic rays (GCRs) and the anomalous component of cosmic rays (ACRs) in the heliosphere. In particular, the latitude dependence of the TS compression ratio and injection efficiency of the ACRs (source strength) based on the hydrodynamic modeling results of Scherer et al. (2006) is used for the first time in a modulation model. The subsequent effects on differential intensities for both GCRs and ACRs are illustrated, comparing them to the values without a latitude dependence for these parameters. It is found that the latitude dependence of these parameters is important and that it enables an improved description of the modulation of ACRs beyond the TS. With this modeling approach (without fitting observations) to the latitude dependence of the two parameters, it is possible to obtain a TS spectrum for ACRs at a polar angle of B = 55" that qualitatively approximates the main features of the Voyager 1 observations. This positive result has to be investigated further. Additionally, it is shown that the enhancement of the cosmic ray intensity just below the cut-off energy found for the ACR at the TS in an A < 0 magnetic polarity cycle in the equatorial plane with the latitude independent scenario, disappears in this region when the latitude dependence of the compression ratio and injection efficiency is assumed. Subsequent effects of these scenarios are illustrated on the global anisotropy vector of both GCRs and ACRs as the main theme of this work. For this purpose the radial and latitudinal gradients for GCRs and ACRs were accurately computed. The radial and latitudinal anisotropy components were then computed as a function of energy, radial distance and polar angle. It is also the first time that the anisotropy vector is comprehensively calculated in such a global approach to cosmic ray modeling in the heliosphere, in particular for ACRs. It is shown that the anisotropy vector inside (up-stream) and outside (down-stream) the TS behaves in a complicated way, so care must be taken in interpreting it. It is found that the latitude dependence of the two mentioned parameters can alter the direction (sign) of the anisotropy vector. Its behaviour beyond the TS is markedly different from inside the TS, mainly because of the slower solar wind velocity, with less dependence on the magnetic polarity cycles. Masters

A time-dependent two-dimensional (2D) modulation model including drifts, the solar wind tennination shock (TS) with diffusive shock acceleration and a heliosheath based on the Parker (1965) transport equation is used to study the modulation of galactic cosmic rays (GCRs) and the anomalous component of cosmic rays (ACRs) in the heliosphere. In particular, the latitude dependence of the TS compression ratio and injection efficiency of the ACRs (source strength) based on the hydrodynamic modeling results of Scherer et al. (2006) is used for the first time in a modulation model. The subsequent effects on differential intensities for both GCRs and ACRs are illustrated, comparing them to the values without a latitude dependence for these parameters. It is found that the latitude dependence of these parameters is important and that it enables an improved description of the modulation of ACRs beyond the TS. With this modeling approach (without fitting observations) to the latitude dependence of the two parameters, it is possible to obtain a TS spectrum for ACRs at a polar angle of B = 55" that qualitatively approximates the main features of the Voyager 1 observations. This positive result has to be investigated further. Additionally, it is shown that the enhancement of the cosmic ray intensity just below the cut-off energy found for the ACR at the TS in an A < 0 magnetic polarity cycle in the equatorial plane with the latitude independent scenario, disappears in this region when the latitude dependence of the compression ratio and injection efficiency is assumed. Subsequent effects of these scenarios are illustrated on the global anisotropy vector of both GCRs and ACRs as the main theme of this work. For this purpose the radial and latitudinal gradients for GCRs and ACRs were accurately computed. The radial and latitudinal anisotropy components were then computed as a function of energy, radial distance and polar angle. It is also the first time that the anisotropy vector is comprehensively calculated in such a global approach to cosmic ray modeling in the heliosphere, in particular for ACRs. It is shown that the anisotropy vector inside (up-stream) and outside (down-stream) the TS behaves in a complicated way, so care must be taken in interpreting it. It is found that the latitude dependence of the two mentioned parameters can alter the direction (sign) of the anisotropy vector. Its behaviour beyond the TS is markedly different from inside the TS, mainly because of the slower solar wind velocity, with less dependence on the magnetic polarity cycles. Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

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