Taming rotationally supported disks using state of the art numerical methods

Während des gravitativen Kollapses eines Objekts bleibt der Drehimpuls erhalten. Im Fall eines endlichen Drehimpulses im System kann sich eine rotierende Scheibe bilden, die durch die Rotation stabilisiert wird. Aufgrund der Einfachheit dieses Mechanismus sind Scheiben allgegenwärtig in der Astrophysik, beispielsweise als protoplanetare Scheiben, Akkretionsscheiben um Schwarze Löcher oder Spiralgalaxien. Insbesondere kalte Gasscheiben sind allerdings schwierig numerisch zu simulieren, da die Rotationsgeschwindigkeit deutlich über der Schallgeschwindigkeit liegt und bereits geringe Ungenauigkeiten in der verwendeten numerischen Methode zu einem unphysikalischem Wachstum von Fluidinstabilitäten führen können. Dies ist besonders dann problematisch, wenn man echte, physikalische Instabilitäten in diesen Systemen analysieren möchte. Eine Methode, die im Prinzip besonders geeignet für die Analyse von Scheibensystemen sein sollte, ist die Berechnung der magnetohydrodynamischen Gleichungen auf einem mitbewegten Gitter, wie sie in dem kosmologischen Code AREPO realisiert ist. Hierdurch kann die Überschallströmung des Gases aufgrund der Rotationsgeschwindigkeit in die Bewegung des Gitters aufgenommen und dadurch eliminiert werden. Die Bewegung und permanente Verzerrung der Gitterzellen aufgrund differentieller Rotation führt jedoch in der ursprünglichen Version von AREPO zu numerischem Rauschen, was die Nützlichkeit des Codes für kalte Scheiben deutlich reduziert hat. Das Ziel dieser Arbeit war es zunächst, die Ursache des Rauschens zu ermitteln und zu beheben. Anschließend sollte evaluiert werden, wie gut die verbesserte Methode kalte Scheiben beschreiben kann, insbesondere in Situationen, in denen Turbulenz durch Magnetfelder oder durch die Wechselwirkung von Strahlungskühlung und Gravitation erzeugt wird. Im Rahmen dieser Arbeit habe ich zuerst die sogenannte "Shearing-Box" Näherung in AREPO entwickelt, die es ermöglicht, einen kleinen Teil einer rotierenden Scheibe mit sehr hoher Auflösung zu simulieren. Im Gegensatz zu Implementierungen in anderen Codes bietet meine Lösung eine adaptive Gitterauflösung sowie vollständige Translationinvarianz. Daneben konnte ich durch eine präzisere numerische Integration der Flussfunktion über die Grenzflächen aneinanderstoßender Zellen das Rauschen auf Zellebene beheben und damit die Genauigkeit des Codes für Scherströmungen stark erhöhen. Auf Basis dieser Verbesserungen habe ich anschließend die magnetische Rotationsinstabilität (MRI) in der Shearing-Box und die dabei auftretenden magnetischen Dynamo-Effekte analysiert. Sowohl im linearen als auch im nichtlinearen Bereich habe ich gute Übereinstimmung mit früheren Ergebnissen in der Literatur gefunden, die mit statischen Gittercodes erzielt wurden. In einer weiteren Studie habe ich eine Codeerweiterung entwickelt, welche die Gravitationskräfte zwischen Massenelementen innerhalb der Simulationsregion unter Einbeziehung der speziellen Randbedingungen der Shearing-Box und ohne Auflösungsbeschränkungen berechnen kann. Mit Hilfe des sogenannten beta-Kühlens konnte ich zeigen, dass bei schwachem Strahlungskühlen unter Eigengravitation und Scherung ein gravitoturbulenter Zustand entsteht, während sich bei effizienterem Kühlen Fragmente aus kollabierenden Gaswolken herausbilden können. Schließlich habe ich die sogenannte Rossby-Wellen-Instabilität in globalen, zweidimensionalen Scheibensimulationen analysiert. Hierbei konnte ich sowohl im linearen als auch im nichtlinearen Bereich gute Übereinstimmung mit der Literatur erzielen. Die Entwicklung der Shearing-Box-Näherung und die Beseitigung des Rauschens auf Gitterebene in dem Verfahren mit einem bewegten Gitter ermöglicht vielfältige Forschungsanwendungen in der Zukunft. Einerseits kann die Wechselwirkung verschiedener Instabilitäten in Scheiben mit Hilfe der Shearing-Box präzise analysiert werden, andererseits sind nun auch globale Simulationen von ganzen Scheiben mit der Methode des bewegten Gitters möglich. Dieses Verfahren ermöglicht wesentlich größere Zeitschritte und geringere Advektionsfehler als herkömmliche Methoden mit stationären Gittern. Auch können Teile einer galaktischen Scheibe mit meiner Shearing-Box Methode in einem "Zoom" Modus simuliert werden, wobei insbesondere die geometrisch flexible, adaptive Auflösung der Methode von Vorteil ist.During the gravitational collapse of an object, the angular momentum is conserved. In the case of a finite angular momentum in the system, a rotating disk can form, stabilized by the rotation. Due to the simplicity of this mechanism, disks are ubiquitous in astrophysics, with prominent examples being protoplanetary disks, accretion disks around black holes, or spiral galaxies. However, cold gas disks in particular are difficult to be simulated numerically because the rotational velocity is much larger than the speed of sound and even small inaccuracies in the used numerical method can lead to the unphysical growth of fluid instabilities. This is particularly problematic when one tries to analyze real, physical instabilities in these systems. A method that in principle should be particularly suitable for the analysis of disk systems is the solution of the magnetohydrodynamic equations on a moving mesh, as realized in the cosmological code AREPO. This allows the supersonic flow of the gas due to the rotational velocity to be included in the mesh motion and thereby to be eliminated. However, the motion and constant distortion of the grid cells due to differential rotation introduce numerical noise in the original version of AREPO, which has significantly reduced the usefulness of the code for cold disks. The goal of this work was first to identify and remove the origin of this "grid noise'', and second to evaluate how well the improved method can describe cold disks, especially in situations where turbulence is generated by magnetic fields or by the interaction of radiative cooling and gravity. As part of this thesis, I first implemented the so-called "shearing-box'' approximation in AREPO, which allows a small portion of a rotating disk to be simulated at very high resolution. Unlike implementations in other codes, my solution provides an adaptive spatial resolution as well as full translation invariance. Additionally, by integrating the flux function more precisely over the interfaces of neighbouring cells, I was able to remove the grid noise, greatly increasing the accuracy of the code for shear flows. Based on these improvements, I analyzed the magnetorotational instability (MRI) in the shearing box and the magnetic dynamo effects that one can observe. In both the linear and nonlinear regimes, I found good agreement with previous results in the literature obtained with static grid codes. In a further line of work, I have developed a code extension that can compute gravitational forces between mass elements within the simulation box, including the special boundary conditions of the shearing box and without resolution constraints. Using the so-called beta-cooling, I was able to show that weak radiative cooling in combination with self-gravity and shear can produce a gravito-turbulent state, while more efficient cooling can produce fragments in the form of collapsing gas clouds. Finally, I analyzed the so-called Rossby wave instability in global, two-dimensional disk simulations. Here I was able to obtain good agreement with the literature in both the linear and nonlinear regimes. The development of the shearing-box approximation and the elimination of the grid noise in the moving mesh method allows a variety of research applications in the future. On the one hand, the interaction of different fluid instabilities in disks can be precisely analyzed using the shearing box, and on the other hand, global simulations of entire disks are now possible using the moving mesh method. This approach allows much larger time steps and smaller advection errors than conventional methods with stationary grids. Also, parts of a galactic disk can be simulated with my shearing box method in a ``zoom'' mode, where the geometrically flexible, adaptive resolution of the method is a particular advantage

Internal waves in fluid flows. Possible coexistence with turbulence

Waves in fluid flows represents the underlying theme of this research work. Wave interactions in fluid flows are part of multidisciplinary physics. It is known that many ideas and phenomena recur in such apparently diverse fields, as solar physics, meteorology, oceanography, aeronautical and hydraulic engineering, optics, and population dynamics. In extreme synthesis, waves in fluids include, on the one hand, surface and internal waves, their evolution, interaction and associated wave-driven mean flows; on the other hand, phenomena related to nonlinear hydrodynamic stability and, in particular, those leading to the onset of turbulence. Close similarities and key differences exist between these two classes of phenomena. In the hope to get hints on aspects of a potential overall vision, this study considers two different systems located at the opposite limits of the range of existing physical fluid flow situations: first, sheared parallel continuum flows - perfect incompressibility and charge neutrality - second, the solar wind - extreme rarefaction and electrical conductivity. Therefore, the activity carried out during the doctoral period consists of two parts. The first is focused on the propagation properties of small internal waves in parallel flows. This work was partly carried out in the framework of a MISTI-Seeds MITOR project proposed by Prof. D. Tordella (PoliTo) and Prof. G. Staffilani (MIT) on the long term interaction in fluid flows. The second part regards the analysis of solar-wind fluctuations from in situ measurements by the Voyagers spacecrafts at the edge of the heliosphere. This work was supported by a second MISTI-Seeds MITOR project, proposed by D. Tordella (PoliTo), J. D. Richardson (MIT, Kavli Institute), with the collaboration of M. Opher (BU)

On pulsar radio emission

This work intends to contribute to the understanding of the radio emission of pulsars. Pulsars are neutron stars with a radius of about 10^6 cm and a mass of about one to three solar masses, that rotate with a period between seconds and milliseconds. They exhibit tremendous magnetic fields of 10^8 to 10^13 Gauss. These fields facilitate the conversion of rotational energy to mainly dipole radiation, x-ray emission and the pulsar wind. Less than a thousandth of the total energy loss is being emitted as radio emission. This contribution however is generated by a collective plasma radiation process that acts coherently on a time scale of nanoseconds and below. Since the topic has been an active field of research for nearly half a century, we introduce the resulting theoretical concepts and ideas for an emission process and the appearance of the so called “magnetosphere”, the plasma filled volume around a pulsar, in Chapter 1. We show that many basic questions have been answered satisfactorily. Questions concerning the emission process, however, suffer some uncertainty. Especially the exact energy source of the radio emission remains unclear. The early works of Goldreich and Julian [1969] and Ruderman and Sutherland [1975] predict high electric fields to arise that are capable of driving a strong electric current. To supplement the energy to power the radio emission, rather mildly relativistic particle energies and a moderate current are favourable. How the system converts current into flow is unclear. In fact, the earlier theories are opposed by recent simulations that also do not predict a relativistic flow near the pulsar. We examine the observed radiation and its form, especially in light of the illustrated models in Chapter 2. We notice that the radio emission is generated in extremely short time scales, that are comparable to the inverse of the Plasma frequency. We elaborate why this places high demands on the theoretical models leaving in fact only one viable candidate process. We conclude that profound questions of energy flow and energy source remain unanswered by current theory. Furthermore, the compression of available energy in space and time to a few centimetres and nanoseconds remains unclear, especially when facing the fact that only a small fraction of the theoretically available energy is being converted. Since the fluctuations relevant for the compression of the energy take place on an intermediate scale of nanoseconds to micro- and milliseconds, it should be possible to detect these observationally. To facilitate this, we decide to analyse the statistics of the Receiver equation of radio radiation in Chapter 3, also since this is relevant to other topics of Pulsar research. The results presented in Chapter 4 show that the developed Bayesian method excels conventional methods to extract parameters from observation data in both precision and accuracy. The method for example weights rotation phase measurements differently than conventional techniques and assigns a more accurate error estimation to single measurements. This is of great relevance to gravitational wave search with so called “pulsar timing array”, as the validity of the total measurement is substantially dependent on the understanding of the accuracy assigned to the single observations. However, the work on single observation data with Bayesian techniques also exemplifies the numerical limits of this method. It is desirable to enable algorithms to include single observation data in the analysis. Therefore we developed a runtime library that writes out currently unneeded data to hard disk, being capable to manage huge data sets (substantial fractions of the hard disk space, not the main memory) in Chapter 5. This library has been written in a generic form so that it can be also used in other data-intensive areas of research. While we thereby lay the foundations to evaluate fluctuation models by observational data, we approach the problem from theoretical grounds in Chapter 6. We propose that the energetic coupling of radio emission could be of magnetic origin, as this is also a relevant mechanism in solar flare physics. We argue in a general way that the rotation of the pulsar pumps energy into the magnetic field, due to topological reasons. This energy can be released again by current decay. We show that already the annihilation of electrons and positrons may suffice to generate radio emission on non-negligible energy scales. This mechanism is not dependent on relativistic flow and thus does not suffer from the problem of requiring high kinetic particle energies. We conclude that the existing gaps in the theory of the radio emission process could possibly be closed in the future, if we analyse observational data statistically more accurate and especially if we put more effort into understanding the problem of energy transport. This thesis serves as an example that scientific investigation of a very theoretical question such as the origin of radio emission can lead to results that may be used directly in other Areas of research

Rayleigh-Taylor and Richtmyer-Meshkov instabilities: A journey through scales

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordHydrodynamic instabilities such as Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities usually appear in conjunction with the Kelvin-Helmholtz (KH) instability and are found in many natural phenomenon and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. In this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers that are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent.Science and Technology Facilities CouncilScience and Technology Facilities Counci

The Significance of Proton Beams in the Multiscale Solar Wind

The solar wind is a multiscale, near-collisionless plasma. Three significant timescales are decades, days, and seconds. These timescales are associated with the solar cycle, Coulomb collisions, and instabilities, respectively. To low order, the solar wind can be treated as a sum of perturbations on a steady state background. The solar cycle drives long term variation in this background. Coulomb collisions and instabilities are two mechanisms that can locally drive some perturbations towards equilibrium states. They can also be modified by the perturbations themselves. In this thesis, I explore one aspect related to each of these timescales. In the process, I describe proton beams, a subset of solar wind protons that constitute a perturbation on the bulk or core protons. I then illustrate how the presence of a proton beam can impact a prototypical characterization of instabilities. I close by showing how proton beams vary with solar cycle and point to the necessity of describing the multiscale feedback mechanisms that must be disentangled to properly characterize a proton beam.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153427/1/balterma_1.pd

Implementation of a X-mode multichannel edge density profile reflectometer for the new ICRH antenna on ASDEX Upgrade

Ion cyclotron resonance heating (ICRH) is one of the main heating mechanisms for nuclear fusion plas- mas. However, studying the effects of ICRH operation, such as power coupling efficiency and convective transport, requires the measurement of the local edge plasma density profiles. Two new three-strap an- tennas were designed to reduce tungsten impurity release during operation, and installed on ASDEX Upgrade. One of these ICRH antennas embedded ten pairs of small microwave pyramidal horn anten- nas. In this thesis, a new multichannel X-mode microwave reflectometry diagnostic was developed to use these embedded antennas to simultaneously measure the edge electron density profiles in front of the bottom, middle and top regions of the radiating surface of the ICRH antenna. Microwave reflectome- try is a radar technique that measures the round trip delay of probing waves that are reflected at specific cutoff layers, depending on the probing wave frequency, plasma density and local magnetic field. This diagnostic uses a coherent heterodyne quadrature detection architecture and probes the plasma in the range 40-68 GHz to measure plasma edge electron densities up to 2×1019 m-3, with magnetic fields between 1.85 T and 2.7 T, and a repetition interval as low as 25 μs. This work details the implementa- tion and commissioning of the diagnostic, including the calibration of the microwave hardware and the analysis of the raw reflectometry measurements. We study the automatic initialization of the X-mode upper cutoff measurement, which is the main source of error in X-mode density profile reconstruction. Two first fringe estimation algorithms were developed: one based on amplitude and spectral information and another using a neural network model to recognize the first fringe location from spectrogram data. Kalman filters are used to improve radial measurement uncertainty to less than 1 cm. To validate the diagnostic, we compared the density profile measurements with other electron density diagnostics on ASDEX Upgrade, and observed typical plasma phenomena like the L-H transition and ELM activity. The experimental density profile results were used to corroborate ICRH power coupling simulations under different gas puffing conditions and to observe poloidal convective transport during ICRH operation

Energy harvesting of low-grade waste heat with colloid based technology

L'abstract è presente nell'allegato / the abstract is in the attachmen

Working Papers: Astronomy and Astrophysics Panel Reports

The papers of the panels appointed by the Astronomy and Astrophysics survey Committee are compiled. These papers were advisory to the survey committee and represent the opinions of the members of each panel in the context of their individual charges. The following subject areas are covered: radio astronomy, infrared astronomy, optical/IR from ground, UV-optical from space, interferometry, high energy from space, particle astrophysics, theory and laboratory astrophysics, solar astronomy, planetary astronomy, computing and data processing, policy opportunities, benefits to the nation from astronomy and astrophysics, status of the profession, and science opportunities

On pulsar radio emission

This work intends to contribute to the understanding of the radio emission of pulsars. Pulsars are neutron stars with a radius of about 10^6 cm and a mass of about one to three solar masses, that rotate with a period between seconds and milliseconds. They exhibit tremendous magnetic fields of 10^8 to 10^13 Gauss. These fields facilitate the conversion of rotational energy to mainly dipole radiation, x-ray emission and the pulsar wind. Less than a thousandth of the total energy loss is being emitted as radio emission. This contribution however is generated by a collective plasma radiation process that acts coherently on a time scale of nanoseconds and below. Since the topic has been an active field of research for nearly half a century, we introduce the resulting theoretical concepts and ideas for an emission process and the appearance of the so called “magnetosphere”, the plasma filled volume around a pulsar, in Chapter 1. We show that many basic questions have been answered satisfactorily. Questions concerning the emission process, however, suffer some uncertainty. Especially the exact energy source of the radio emission remains unclear. The early works of Goldreich and Julian [1969] and Ruderman and Sutherland [1975] predict high electric fields to arise that are capable of driving a strong electric current. To supplement the energy to power the radio emission, rather mildly relativistic particle energies and a moderate current are favourable. How the system converts current into flow is unclear. In fact, the earlier theories are opposed by recent simulations that also do not predict a relativistic flow near the pulsar. We examine the observed radiation and its form, especially in light of the illustrated models in Chapter 2. We notice that the radio emission is generated in extremely short time scales, that are comparable to the inverse of the Plasma frequency. We elaborate why this places high demands on the theoretical models leaving in fact only one viable candidate process. We conclude that profound questions of energy flow and energy source remain unanswered by current theory. Furthermore, the compression of available energy in space and time to a few centimetres and nanoseconds remains unclear, especially when facing the fact that only a small fraction of the theoretically available energy is being converted. Since the fluctuations relevant for the compression of the energy take place on an intermediate scale of nanoseconds to micro- and milliseconds, it should be possible to detect these observationally. To facilitate this, we decide to analyse the statistics of the Receiver equation of radio radiation in Chapter 3, also since this is relevant to other topics of Pulsar research. The results presented in Chapter 4 show that the developed Bayesian method excels conventional methods to extract parameters from observation data in both precision and accuracy. The method for example weights rotation phase measurements differently than conventional techniques and assigns a more accurate error estimation to single measurements. This is of great relevance to gravitational wave search with so called “pulsar timing array”, as the validity of the total measurement is substantially dependent on the understanding of the accuracy assigned to the single observations. However, the work on single observation data with Bayesian techniques also exemplifies the numerical limits of this method. It is desirable to enable algorithms to include single observation data in the analysis. Therefore we developed a runtime library that writes out currently unneeded data to hard disk, being capable to manage huge data sets (substantial fractions of the hard disk space, not the main memory) in Chapter 5. This library has been written in a generic form so that it can be also used in other data-intensive areas of research. While we thereby lay the foundations to evaluate fluctuation models by observational data, we approach the problem from theoretical grounds in Chapter 6. We propose that the energetic coupling of radio emission could be of magnetic origin, as this is also a relevant mechanism in solar flare physics. We argue in a general way that the rotation of the pulsar pumps energy into the magnetic field, due to topological reasons. This energy can be released again by current decay. We show that already the annihilation of electrons and positrons may suffice to generate radio emission on non-negligible energy scales. This mechanism is not dependent on relativistic flow and thus does not suffer from the problem of requiring high kinetic particle energies. We conclude that the existing gaps in the theory of the radio emission process could possibly be closed in the future, if we analyse observational data statistically more accurate and especially if we put more effort into understanding the problem of energy transport. This thesis serves as an example that scientific investigation of a very theoretical question such as the origin of radio emission can lead to results that may be used directly in other Areas of research