Browsing by master's degree program "Magisterprogrammet i elementarpartikelfysik och astrofysikaliska vetenskaper"
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(2023)The thesis presents results for simulating an orbit determination process with leastsquares fitting (LSF) of synthetic observations for noncooperative satellites. Five satellites with different masses, sizes, and orbital inclinations are orbiting in Low Earth Orbit (LEO). Three different inclinations (53°, 85°, and 98°) are simulated using Orekit (Orbit Extrapolation Kit), an opensource astro dynamical software library. Satellites are observed with four hypothetical radars. The thesis is a feasibility study. It addresses four main research questions: How reliable are predictions of the satellite position for 24 h, 48 h, 72 h, and 96 h after the first detection when using the observations from four consecutive overpasses and the LSFestimated orbit? How accurately the Keplerian or bital elements be modelled with LSF? How does the satellite’s mass affect the results’ reliability, and can the satellite’s drag, reflection, and absorption coefficients be estimated with Orekit? The simulation utilizes the Orekit software library in a Python environment, and the simulation incorporates several perturbing forces: Earth’s gravitational potential model EGM2008, an atmo sphere model with space weather data NRLMSISE00, tidal forces, and pointlike masses of the Sun and the Moon. Synthetic observations were simulated by assuming Gaussian distribution for the uncertainties of the measurements. The initial estimate of the orbit is done with Gooding’s method, and the Levenberg–Marquardt algorithm is used for the LSF. The propagation of the actual satellite for 96 h was compared with the 96h propagation of estimated orbital elements and with a satellite with estimated size and mass. Simulations were conducted with overestimated and underestimated initial masses. Each combination of a satellite, an observing radar, and an orbit was repeated 100 times. The results for reliability were promising. The likelihood of the skyplane projected error of the position staying under the 3.0km for up to 3 days was found to be 90% for two of the simulated radars, but only in cases of orbits having an inclination of 53°. Two other orbits had less successful results, but simulations revealed a potential increase in reliability by adjusting the observational strategy. There was a small bias in the results hinting that underestimating the satellite’s mass could result in less accurate orbit estimates than overestimating it. The satellite’s drag, absorption, and reflection coefficients could not be obtained due to the short observational time intervals simulated.

(2020)The aim of this thesis is to explore applications of machine learning to the study of asteroid spectra, and as such, its research question can be summarized as: How can asteroid spectra be analyzed using machine learning? The question is explored through evaluation of the obtained solutions to two tasks: the optimal locations of spectrophotometric filters for asteroid classification success and the formation of an asteroid taxonomy through unsupervised clustering. First, background theory for asteroids and particularly spectroscopy of asteroids is presented. Next, the theory of machine learning is briefly discussed, including a focus on the method utilized to solve the first task: neural networks. The first task is executed by developing an optimization algorithm that has access to a neural network that can determine the classification success rate of data samples that would be obtained using spectrophotometric filters at specific locations within the possible wavelength range. The second task, on the other hand, is evaluated through determining the optimal number of clusters for the given dataset and then developing taxonomies with the clustering algorithm kmeans. The obtained results for the first task involving the optimal locations of filters for spectrophotometry seem reliable, and correlate relatively well with wellknown mineralogical features on asteroid surfaces. The taxonomic systems developed by the unsupervised clustering also succeeded rather well, as many of the formed clusters seem to be meaningful and follow the trends in other asteroid taxonomies. Therefore, it seems that based on the two investigated tasks, machine learning can be applied well to asteroid spectroscopy. For future studies, larger datasets would be required for improving the overall reliability of the results.

(2020)Cadmium Telluride (CdTe) has a high quantum efficiency and a bandgap of 1.44 eV. As a consequence, it is being used to efficiently detect gamma rays. The aim of this thesis is to explore the properties of the CdTe pixelated detector and the procedures conducted in order to finetune the electronic readout system. A fully functional CdTe detector would be useful in medical imaging techniques such as Boron Neutron Capture Therapy (BNCT). BNCT requires a detector with a good energy resolution, a good timing resolution and a good stopping power. Although the CdTe crystal is a promising material, its growing process is difficult due to the fact that different types of defects appear inside the crystal. The quality assurance process has to be thorough in order for suitable crystals to be found. An aluminum oxide layer (Al2O3) was passivated onto the surface of the crystal. The contacts for both sides were created using Titanium Tungsten (TiW) and gold (Au) sputtering deposition, followed by an electroless nickel growth. I tested the CdTe pixelated detector with different radioactive sources such as Am241, Ba133, Co57, Cs137 and Xray quality series in order to study the sensitivity of the device and its capacity to detect gamma and Xrays.

(2023)Tutkielmani käsittelee kullan pysyvän isotoopin Au197 tuottamista neutroniaktivaatiolla luonnollisesta elohopeanäytteestä. Kokeen kannalta pääasiallinen reaktiomenetelmä oli Hg196 neutronikaappaus. Kyseinen transmutaatio suoritettiin myös kokeellisesti. Elohopeaa sisältävänä näytteenä käytettiin Ardentin valmistamia Futura Standard hammasamalgaamikapseleita. Turvallisuussyistä kapselit olivat koejärjestelyssä alkuperäisessä purkissaan. Kapseleita oli kaikkiaan 50 kappaletta, ja jokaisessa oli 400 mg elohopeaa. Yhteensä näytteessä oli siis 20 grammaa elohopeaa. Näytettä säteilytettiin STUKin tiloissa 14 vuorokauden ajan kolmen AmBeneutronilähteen avulla. Valmistajan ilmoittamat neutronituotot käytetyille lähteille ovat 2.0E+7 n/s, 2.1E+6 n/s ja 6.7E+5 n/s. Lähteiden ilmoitetut aktiivisuudet ovat vastaavasti 333 GBq, 37.0 GBq ja 11.1 GBq. Neutronien hidastamiseen käytettiin HDPEtankoa. Säteilytyksen jälkeen näytettä mitattiin STUKin gammaspektrometrian laboratorion B6 pHPGe BE5030 germaniumilmaisimella, ja kullan synty voitiin todentaa spektristä löytyvien karakterististen gamma ja röntgenpiikkien avulla. Koejärjestely onnistui, ja työni osoittaa, että kullan pysyvän isotoopin Au197 valmistaminen luonnollisesta elohopeasta havaittavissa määrin on mahdollista toteuttaa melko yksinkertaisella koejärjestelyllä käyttäen varsin pienitehoisia neutronilähteitä. Varsinaisen kokeen lisäksi käsittelen työssäni myös kullanteon historiaa sekä aiheeseen liittyvää teoriaa.

(2023)A method for deriving the complex refractive index of a mmsized single particle in a specific wavelength using laboratory measurements is presented. Laboratory measurements were done using the 4π scatterometer, which measures Mueller matrix elements of a particle suspended in air using acoustic levitation as a function of scattering angle. To obtain the complex refractive index of the particle, measurements were compared to simulations from a newly developed SIRIS4 Fixed Orientation (SIRIS4 FO) geometric optics simulation. The 4π scatterometer is a unique instrument which measures Mueller matrix elements from a particle using linear polarizers and a detector rotating about the particle on a rotational stage. The scatterometer uses an acoustic levitator as a sample holder which provides nondestructive measurements and full orientation control of the sample. To compare the measurement results to simulations, SIRIS4 singleparticle geometric optics code was modified to handle particles in a fixed orientation. The original code is able to calculate the Mueller matrix elements for a given 3D model, but averages the results over the orientation of the particle. The modified SIRIS4 FO calculates the Mueller matrix elements over the full solid angle as functions of the two scattering angles, which give the direction of observation of the scattered wave compared to the direction of the incident wave. A 3D model of the shape of the measured particle was constructed using Xray microtomography, and was translated to SIRIS4 FO. The complex refractive index was obtained with a nonlinear least squares analysis by minimizing the sum of squared residuals between the measurements and simulations with varying refractive index values. Finally, confidence regions were constrained for the results, by estimating the computed residuals between simulations and measurements as the random errors in the nonlinear model.

(2023)Dark matter direct detection experiments still have found no evidence of the dark matter WIMPs. The search has therefore been expanded for lighter dark matter candidates. Light dark matter is nearly invisible to current detectors through the elastic nuclear recoils. This thesis is meant to provide understanding on the inelastic atomic scatterings, which are one good way to detect dark matter particles with mχ ∼ GeV. In this thesis we consider spinindependent scatterings. Inelastic scatterings are based on the fact that in an atom, electrons do not follow the motion of the recoil nucleus immediately, but instead it takes time. This results in a small probability of observable ionization or excitation of the atom. This is known as the Migdal effect. We will first study the theoretical framework of dark matternucleus scatterings, showing how to get the event rate and how it is factorized into the astrophysical, the particle physics and the target response part. Then we will move to the inelastic processes, Migdal and Bremsstrahlung effects, deriving their event rates. In the first, we try to detect ionized electrons. The latter one, the Bremsstrahlung, is a similar process to the Migdal, but there we try to detect photons emitted from the deexcitations of atoms excited in the inelastic recoils. We will also look into the Migdal in semiconductors. Because of the smaller gap for electron excitations in crystals, we find that the rate for the Migdal effect is much higher in semiconductors than in atomic targets, thus allowing the search for even lighter dark matter particles. The rate can be expressed in terms of the energy loss function of the target material.

(2021)Phase transitions in the early Universe and in condensed matter physics are active fields of research. During these transitions, objects such as topological solitons and defects are produced by the breaking of symmetry. Studying such objects more thoroughly could shed light on some of the modern problems in cosmology such as baryogenesis and explain many aspects in materials research. One example of such topological solitons are the (1+1) dimensional kinks and their respective higher dimensional domain walls. The dynamics of kink collisions are complicated and very sensitive to initial conditions. Making accurate predictions within such a system has proven to be difficult, and research has been conducted since the 70s. Especially difficult is predicting the location of resonance windows and giving a proper theoretical explanation for such a structure. Deeper understanding of these objects is interesting in its own right but can also bring insight in predicting their possibly generated cosmological signatures. In this thesis we have summarized the common field theoretic tools and methods for the analytic treatment of kinks. Homotopy theory and its applications are also covered in the context of classifying topological solitons and defects. We present our numerical simulation scheme and results on kinkantikink and kinkimpurity collisions in the $\phi^4$ model. Kinkantikink pair production from a wobbling kink is also studied, in which case we found that the separation velocity of the produced kinkantikink pair is directly correlated with the excitation amplitude of the wobbling kink. Direct annihilation of the produced pair was also observed. We modify the $\phi^4$ model by adding a small linear term $\delta \phi^3$, which modifies the kinks into accelerating bubble walls. The collision dynamics and pair production of these objects are explored with the same simulation methods. We observe multiple new effects in kinkantikink collisions, such as potentially perpetual bouncing and faster bion formation in comparison to the $\phi^4$ model. We also showed that the $\delta$ term defines the preferred vacuum by inevitably annihilating any kinkantikink pair. During pair production we noticed a momentum transfer between the produced bion and the original kink and that direct annihilation seems unlikely in such processes. For wobbling kink  impurity collisions we found an asymmetric spectral wall. Future research prospects and potential expansions for our analysis are also discussed.

(2021)The solar corona constantly emits a flow of charged particles, called the solar wind, into interplanetary space. This flow is diverted around the Earth by the magnetic pressure of the Earth’s own geomagnetic field, shielding the Earth from the effect of this particle radiation. On occasion the Sun ejects a large amount of plasma outwards from the corona in an event called a Coronal Mass Ejection (CME). Such events can drive discontinuities in the solar wind plasma, called interplanetary shocks. Shocks can affect the Earth’s magnetosphere, compressing it inwards and generating electromagnetic waves inside it. In this thesis we will cover a study of the ultralow frequency (ULF) wave response in the magnetosphere to CMEdriven shocks. Geomagnetic pulsations are ultralow frequency plasma waves in the magnetosphere, observable from groundbased magnetometers. The compression of the magnetosphere by interplanetary shocks generates geomagnetic pulsations in the Pc4 and Pc5 frequency ranges (2  22 mHz). These waves play an important role in magnetospheric dynamics and the acceleration and depletion of high energy electrons in the radiation belts. We consider 39 interplanetary shock events driven by CMEs, and analyse groundbased magnetometer data from stations located near local noon at the time of the shock arrival. Solar wind measurements are used to categorise interplanetary shocks based on their Mach number and the dynamic pressure differential as main indicators of shock strength. The importance of these parameters in determining the strength of the wave response in the geomagnetic field is then studied using wavelet analysis and superposed epoch analysis. Stronger shocks are found to result in larger increases in wave activity, especially in the Pc4 range. Ground stations at higher latitudes observe higher wavepower, but there is an interesting anomaly in the Pc4 range at stations magnetically connected to regions near the plasmapause, which show an enhanced wavepower response. We quantify the decay time of the wave activity and find that it is around 20 hours for Pc5 waves and 7 hours for Pc4 waves.

(2023)Dark matter (DM) is introduced and explored in a holistic perspective. Topics include observational evidence, various DM properties, potential candidates, and the tenets of indirect versus direct DM detection. Then an emphasis is placed on understanding the cryogenic detection of weakly interacting massive particles, with explicit connection to phononbased detection of DM. The importance of improving methods of DM direct detection are emphasised, with specifically the usage of molecular dynamics simulations as an avenue of studying defect creation in cryogenic detector materials. Previous investigations into this area are reviewed and expanded upon through novel experimentation into how defect properties vary when changing thermal motion of the crystal lattice. This experimentation is conducted via the usage of molecular dynamics simulations on sapphire (Al2O3) as a DM direct detection material, and it is found that while atomic velocity does not impact the overall emergent defect structure, it does have an impact on the energy lost in these defects. Changing the temperature of the lattice produces the expected results, generating greater variance in both defect band structure as well as average energy loss.

(2020)The distribution of matter in space is not homogeneous. Large structures such as galaxy groups, clusters or big empty spaces called voids can be observed at large scales in the Universe. The large scale structure of the Universe will depend on both the cosmological parameters and the dynamics of galaxy formation and evolution. One of the main observables that allow us to quantify this structure is the twopoint correlation function, with which we can trace different galaxy properties such as luminosity, stellar mass and also, it enables us to track its evolution with redshift. In galaxy surveys, we do not obtain the location of galaxies in real space. We obtain our data in what it is called redshift space. This redshift space can be defined as a distortion of the real space generated by the redshift introduced by the peculiar velocities of galaxies and from the Hubble expansion of the Universe. Therefore, the distribution of galaxies in redshift space will look different from the one obtained in real space. These differences between both spaces are small but not negligible, and they depend strictly on the cosmology. In this work, we will assume a ΛCDM cosmology. Therefore, in order to find the different 1dimensional or 2dimensional correlations functions, we will use the most updated version of the code provided by the Euclid consortium, which belongs officially to the ESA Euclid mission. Moreover, we will also need different galaxy catalogues. These catalogues have already been simulated and they are called Minerva mocks, which are a set of 300 different cosmological mocks produced with Nbody simulations. Finally, as there is a welldefined relation between real and redshift space, one could also assume that there is a relation between the twopoint correlation functions in both real and redshift space. In this project, we will prove that the realspace onedimensional twopoint correlation function, which is the physically meaningful one, can be derived from the twodimensional twopoint correlation function in redshift space following a geometrical procedure independent of approximations. This method, in theory, should work for all distance scales.

(2023)The search for a profound connection between gravity and quantum mechanics has been a longstanding goal in theoretical physics. One such connection is known as the holographic principle, which suggests that the dynamics within a given region of spacetime can be fully described on its boundary surface. This concept led to the realization that string theory provides a lowerdimensional description that encapsulates essential aspects of spacetime. While the "AdS/CFT correspondence" exemplifies the success of this holographic theory, it was discovered soon after that the Universe has a positive cosmological constant, Λ. This immediately sparked interest in a potential correspondence centered around de Sitter (dS) space, which is also characterized by a positive cosmological constant. This thesis comprehensively explores the de Sitter/Conformal Field Theory (dS/CFT) correspondence from various perspectives, along with the unique challenges posed by the distinct nature of dS space. The original dS/CFT duality proposes that a twodimensional Conformal Field Theory resides on the boundary of threedimensional asymptotic dS space. However, the definition and interpretation of physical observables within the dS/CFT framework remain open questions. Therefore, the discussions in this thesis not only cover the original dS/CFT conjecture, but also extend into more recent advancements in the field. These advancements include a higherspin dS/CFT duality, the relationship between string theory and dS space, and the intriguing proposal of an "elliptical" dS space. While the dS/CFT correspondence is still far from being welldefined, there have been extensive efforts devoted to shedding light on its intricate framework and exploring its potential applications. As the Universe may be evolving towards an approximately de Sitter phase, understanding the dS/CFT correspondence offers a unique opportunity for gaining fresh insights into the link between gravity and quantum field theory.

(2021)Magnetosheath jets are a class of structures in the Earth's magnetosheath usually defined by an enhancement of the dynamic pressure of the plasma. Magnetosheath jets have been observed by several different spacecraft over the past few decades, but their origin and formation mechanism have remained unclear. The aim of this thesis is to use data from a global simulation to investigate the origin of magnetosheath jets. We defined two different kinds of structures, magnetosheath jets and foreshock compressive structures (FCS), and collected a database of individual jets and FCSs from 4 Vlasiator global hybridVlasov simulation runs, all of which simulate only the ecliptic plane. We then conducted a statistical analysis of the properties of jets and FCSs, and their occurrence rates as a function of the definition of the FCS criterion. Jets were separated into two categories: jets that form in contact with FCSs (FCSjets), and those that do not (nonFCSjets). We found that up to 75% of magnetosheath jets form in association with an FCS impacting the Earth's bow shock. We also found that FCSjets penetrate deeper into the magnetosheath than nonFCSjets. Finally, we found no conclusive explanation for the formation of nonFCSjets. The properties of both jets and FCSs agree qualitatively and to some extent quantitatively with spacecraft observations and other simulations in the literature. The formation of jets from FCSs impacting the bow shock is similar to the proposed theory that jets are linked to Short LargeAmplitude Magnetic Structures (SLAMS). In the future, we will study magnetosheath jets and FCSs in polar plane simulation runs as well, and ultimately in full 3D simulation runs. If made possible by new simulations, the effects of electron kinetic effects on jets and FCSs will also be studied. Comparison studies with spacecraft observations of jet formation from FCSs will also be conducted, if and when such observations are found and become available.

(2023)In this thesis, 16 gasfree galaxy merger simulations were run in order to determine the dominant effect that causes the formation of cores, i.e. regions of ”missing light”, in the centers of massive earlytype galaxies. The simulations were run on the Mahti supercomputer at the Finnish IT Centre for Science (CSC), using the simulation codes GADGET3 and KETJU. The merging of galaxies will eventually lead to the merging of their central supermassive black holes (SMBHs). The evolution of a SMBH binary can be divided into three phases: the dynamical friction phase, the threebody interaction phase and gravitational wave (GW) emission phase. After the GW emission phase, the merged SMBH may receive a recoil velocity. To study the effects of these three phases on the formation of the core, three kinds of simulations were run. These include three GADGET runs and thirteen KETJU runs that can be divided into two groups, since eight of the runs had GW recoils enabled. When using only GADGET, the threebody interactions are not modeled due to the softening of gravity. Using KETJU allows for modeling the later evolution of the SMBH binary, including the threebody interaction phase, the GW emission phase and the resulting GW recoil. The initial conditions for the progenitor galaxies were motivated by the galaxy NGC 1600. The same stellar and dark matter profiles were used for each simulated galaxy. Two different SMBH masses were used. One KETJU merger was also run without SMBHs. For the runs with spinning SMBHs, the spin directions and magnitudes were chosen in such a way that different magnitudes of recoil velocity would be achieved. The size of the core can be determined from the brightness profile of the galaxy, assuming a constant masstolight ratio. The commonly used coreSérsic profile was fit to the surface mass density profiles of the merger remnant galaxies. The bestfit parameter values were then used to estimate the sizes of the cores, such as the core radii. The amount of missing mass in the centers of the galaxies, i.e. the mass deficits, were also computed based on the coreSérsic fits. We found that the mass deficit correlates positively with the mass of the SMBH for all the KETJU runs. Including GW recoils in the simulations was found to increase the mass deficits by roughly the equivalent of one SMBH mass compared to the KETJU runs without the recoils. The formation of cores was the weakest for the GADGET runs, since the cores were created only by the largescale dynamics. No core was formed in the run without SMBHs, as expected. Thus, we can conclude that SMBHs are essential for the formation of cores in massive early type galaxies, and the largest cores are formed when GW recoils are included in the model.

(2023)Mars is a rocky planet in the Solar System, fairly similar to the Earth. It is known for its red color and the theory that there has been liquid water and possibly life in Mars at some point in its history. Mars has been a target of study since space exploration began, with the first flyby mission occuring in 1965. In the past, Martian climate could have supported a functioning hydrological system and Mars even could have had an ocean. This system would have been similar to the one happening in Antarctica due to cold weather. The Martian atmosphere is mostly composed of carbon dioxide, much thinner and colder compared to the Earth's atmosphere. Methane is a main point of interest due to it being a possible biosignature, a sign of life. Another interesting feature about the atmosphere are the dust devils that contibute to the climate by lifting dust into the air. The Martian soil is composed of rocks and dust containing toxic perchlorates. To colonize Mars, several requirements need to be met: the transportation and funding, designing the settlement efficiently with everything needed and determining how many people are necessary. The risk assessment to both people and equipment needs to be made and taken into account.

(2020)We study how higherorder gravity aﬀects Higgs inﬂation in the Palatini formulation. We ﬁrst review the metric and Palatini formulations in comparative manner and discuss their diﬀerences. Next cosmic inﬂation driven by a scalar ﬁeld and inﬂationary observables are discussed. After this we review the Higgs inﬂation and compute the inﬂationary observables both in the metric and Palatini formulations. We then consider adding higherorder terms of the curvature to the action. We derive the equations of motion for the most general action quadratic in the curvature that does not violate parity in both the metric and Palatini formulations. Finally we present a new result. We analyse Higgs inﬂation in the Palatini formulation with higherorder curvature terms. We consider a simpliﬁed scenario where only terms constructed from the symmetric part of the Ricci tensor are added to the action. This implies that there are no new gravitational degrees of freedom, which makes the analysis easier. As a new result we found out that the scalar perturbation spectrum is unchanged, but the tensor perturbation spectrum is suppressed by the higherorder curvature couplings.

(2020)The Standard Model is one of the accurate theories that we have. It has demonstrated its success by predictions and discoveries of new particles such as the existence of gauge bosons W and Z and heaviest quarks charm, bottom and top. After discovery of the Higgs boson in 2012 Standard Model became complete in sense that all elementary particles contained in it had been observed. In this thesis I will cover the particle content and interactions of the Standard Model. Then I explain Higgs mechanism in detail. The main feature in Higgs mechanism is spontaneous symmetry breaking which is the key element for this mechanism to work. The Higgs mechanism gives rise to mass of the particles, especially gauge bosons. Higgs boson was found at the Large Hadron Collider by CMS and ATLAS experiments. In the experiments, protons were collided with high energies (813 TeV). This leads to production of the Higgs boson by different production channels like gluon fusion (ggF), vector boson fusion (VBF) or the Higgsstrahlung. Since the lifetime of the Higgs boson is very short, it cannot be measured directly. In the CMS experiment Higgs boson was detected via channel H → ZZ → 4l and via H → γγ. In this thesis I examine the correspondence of the Standard Model to LHC data by using signal strengths of the production and decay channels by parametrizing the interactions of fermionic and bosonic production and decay channels. Data analysis carried by least squares method gave confidence level contours that describe how well the predictions of the Standard Model correspond to LHC data

(2020)The nature of dark matter (DM) is one of the outstanding problems of modern physics. The existence of dark matter implies physics beyond the Standard Model (SM), as the SM doesn’t contain any viable DM candidates. Dark matter manifests itself through various cosmological and astrophysical observations of the rotational speeds of galaxies, structure formation, measurements of the Cosmic Microwave Background (CMB) and gravitational lensing of galaxy clusters. An attractive explanation of the observed dark matter density is provided by the WIMP (Weakly Interacting Massive Particle) paradigm. In the following thesis I explore this idea within the well motivated Higgs portal framework. In particular, I explore three options for dark matter composition: a scalar field and U(1) and SU(2) hidden gauge Fields. I find that the WIMP paradigm is still consistent with the data. Even though it finds itself under pressure from direct detection experiments, it is not yet in crisis. Simple and well motivated WIMP models can fit the observed DM density without violating the collider and direct DM detection constraints.

(2023)Quantum field theory is often presented without clearly defined mathematical structures, especially in the case of field operators. We discuss axiomatic quantum field theory, where quantum fields and states are defined rigorously using distribution theory, alongside their assumed properties in the form of the Wightman axioms. We present the two key results that come from this construction, namely CPT symmetry and the spinstatistics connection. We then consider the construction of quantum fields in curved spacetime so as to discuss their behaviour in regions of large curvature, such as near black holes. This requires us to redefine fields and states in terms of *algebras. We then present the GNS reconstruction theorem which allows us to get back the original definitions of these objects in Minkowski spacetime.

(2022)One of the most noticeable effects of solar–terrestrial physics is the aurora which regularly appears in the polar regions. This polar light is the result of the excitation of atmospheric species by charged particles originating from the solar wind and magnetosphere that enter the Earth’s atmosphere, which are called precipitating particles. We present the first results on auroral proton precipitation into the ionosphere using a global 3dimensional simulation of nearEarth space plasma with the Vlasiator hybridVlasov model, driven with a southward interplanetary magnetic field and steady solar wind parameters. The hybridVlasov approach describes ions through their velocity distribution function in phase space (3dimensional ordinary space and 3dimensional velocity space), while electrons are represented by a massless chargeneutralizing fluid. Vlasiator is a global model describing the whole region of nearEarth space including the Earth’s magnetosphere (whole dayside and part of the magnetotail), the magnetosheath, as well as the foreshock region and some solar wind. The precipitating proton differential number fluxes for this run are determined from the proton phasespace density contained within the bounce losscone, which is set at a constant angle of 10 degrees everywhere. To determine the precipitation of particles at ionospheric altitudes (in this case a height of 110 km above the Earth’s surface), we trace magnetic field lines from the ionosphere to the inner boundary of the Vlasiator domain using the Tsyganenko model. With this, we obtain a magnetic local time–geomagnetic latitude map of differential number flux of precipitating protons in 9 energy bins between 0.5 and 50 keV. From the differential number flux, proton integral energy fluxes and mean energies can be obtained. The integral energy fluxes in the Vlasiator run are then compared to data of the Precipitation Electron/Proton Spectrometer (SSJ) instrument of the Defense Meteorological Satellite Program (DMSP) for several satellite overpasses during events with similar solar wind conditions as in the Vlasiator run. The SSJ instrument bins proton energies between 0.03 and 30 keV. Typical values of the total integral energy flux are between 5 · 10^6 and 5 · 10^7 keV cm−2 s−1 sr−1 in the cusp and between 1 · 10^6 and 3 · 10^7 keV cm−2 s−1 sr−1 in the evening sector for both Vlasiator and DMSP, although DMSP fluxes can locally be up to an order of magnitude higher. Additionally, global precipitation patterns in Vlasiator are compared to Ovation Prime, which is an empirical model based on data from DMSP which can be used to forecast precipitation of auroral electrons and protons. Although Ovation Prime shows a much wider cusp region compared to Vlasiator, both show similar maximum integral energy fluxes around 1 to 2 · 10^7 keV cm−2 s−1 sr−1 in the cusp region, and between 3 · 10^6 and 5 · 10^7 keV cm−2 s−1 sr−1 in the nightside oval.

(2023)A stream of charged particles known as the solar wind constantly flows with supersonic speed in our solar system. As the supersonic solar wind encounters Earth's magnetic field, a bow shock forms where the solar wind is compressed, heated and slowed down. Not all ions of the solar wind pass through the shock but rather a portion are reflected back upstream. What happens to the reflected ions depends on the magnetic field geometry of the shock. In the case where the angle between the upstream magnetic field and the shock normal vector is small, the reflected ions follow the magnetic field lines upstream and form a foreshock region. In this case the shock is called quasiparallel. In the case of a quasiperpendicular shock, where the angle is large, the reflected ions gyrate back to the shock, accelerated by the convection electric field. Upon returning to the shock, the ions have more energy and either pass through the shock or are reflected again, repeating the process. Ion reflection is important for accelerating ions in shocks. In this work we study the properties and ion reflection of the quasiperpendicular bow shock in Vlasiator simulations. Vlasiator is a plasma simulation which models the interaction between solar wind and the Earth's magnetic field. The code simulates the dynamics of plasma using a hybridVlasov model, where ions are represented as velocity distribution functions (VDF) and electrons as magnetohydrodynamic fluid. Two Vlasiator runs are used in this work. The ion reflection is studied by analysing VDFs at various points in the quasiperpendicular shock. The analysis is performed with reflections in multiple different frames. A virtual spacecraft is placed in the simulation to study shock properties and ion dynamics, such as the shock potential and ion reflection efficiency. These are compared to spacecraft observations and other simulations to test how well Vlasiator models the quasiperpendicular bow shock. We find that the ion reflection follows a model for specular reflection well in all tested frames, especially in the plane perpendicular to the magnetic field. In addition, the study was extended to model second specular reflections which were also observed. We conclude that the ions in Vlasiator simulations are nearly specularly reflected. The properties of the quasiperpendicular bow shock are found to be in quantitative agreement with spacecraft observations. Ion reflection efficiency is found to match observations well. Shock potential investigations revealed that spacecraft observations may have large uncertainties compared to the real shock potential.
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