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Numerical Analysis of Coupled Thermal-Electromagnetic Problems in Superconducting Cables
Superconducting materials, being characterized by a negligible electrical resistance under peculiar working conditions, provide extraordinary electromagnetic performances. The research field on electromagnets has taken a lot of advantages from this technology, since the huge electrical current densities that these materials sustain enable to produce very strong magnetic fields, up to more than 10 T, with negligible losses compared to the normal-conducting coils. The development of superconductors technology during the last years has enabled projects that only some decades ago were considered not feasible, both technically and economically. Among them, the most notable are fusion reactors like ITER, presently under construction in Cadarache (France), and particle accelerators for high energy physics such as the Large Hadron Collider (LHC) operating at CERN in Geneva (Switzerland).
The present work regards the THELMA code, a coupled thermal-electromagnetic numerical model for the description of superconducting cables and magnets. This software was initially intended for the simulation of the electromagnetic behavior in the so-called Cable-In-Conduit-Conductors (CICC), largely used in fusion machines like ITER. During the PhD activity, a brand-new thermal model has been developed and added to the pre-existing code to describe problems in which the system thermal evolution cannot be assessed a priori. Moreover, the code has been extended to deal also with the Rutherford cables, a type of superconducting cable widely used in accelerator magnets like those of LHC. Finally, the code has been applied to several case studies, both in the field of accelerator and fusion magnets.
This thesis is structured in the following way.
The first two chapters are a general introduction to superconductivity: the first is a presentation of this phenomenon and its applications, intended for readers that are not familiar with this technology, whereas the second is a more detailed description of the superconducting wires and cables studied during this PhD activity.
In the second part of the thesis, the THELMA numerical code is widely described. In chapter 3, the geometrical, electromagnetic and thermal models are presented, with a particular focus on the brand-new parts developed during this PhD activity, such as the Rutherford cable geometrical model, the thermal model and the coupling among electromagnetic and thermal routines. The THELMA model for electrical and thermal contact resistances is instead widely explained in chapter 4, together with the numerical analysis of several experimental measurements on both Rutherford and CICC cables.
The third part of the work is instead focused on some examples of the application of the THELMA coupled code, performed during the PhD activity. In chapter 5 the analysis of the voltage-temperature characteristic on a CICC sample is presented, as a validation and an example of the code capability of reproducing non-trivial experimental findings. In chapter 6, the problem of the longitudinal propagation of a thermal-electromagnetic instability (quench) in impregnated Rutherford coils is analyzed with experimental, analytical and numerical tools. In chapter 7, the predictive analyses in terms of current distribution and losses in the CICC magnet NAFASSY are reported. Further details regarding useful material properties and some analytical and numerical models can be found in the appendices.I materiali superconduttori, essendo caratterizzati in particolari condizioni da una
resistenza elettrica trascurabile, offrono straordinarie prestazioni elettromagnetiche.
La ricerca sugli elettromagneti ha ottenuto notevoli vantaggi da questa tecnologia, in
quanto le enormi densità di corrente elettrica che questi materiali sopportano possono
essere usate per generare campi magnetici estremamente intensi, anche maggiori
di 10 T, con delle perdite trascurabili in confronto agli avvolgimenti normoconduttivi.
Lo sviluppo della tecnologia dei superconduttori avvenuto negli ultimi anni ha
permesso progetti che solo pochi decenni fa erano considerati irrealizzabili, sia dal
punto di vista tecnico che economico. Tra questi, i più importanti sono senz’altro i
reattori per fusione nucleare come ITER, attualmnente in costruzione a Cadarache
(Francia), e acceleratori di particelle per la fisica delle alte energie come il Large
Hadron Collider (LHC) del CERN a Ginevra (Svizzera).
In questa tesi viene presentato il codice THELMA, un modello numerico per
la descrizione accoppiata del comportamento termo-elettromagnetico di cavi e magneti
superconduttori. Questo codice era stato inizialmente creato per la simulazione
del comportamento elettromagnetico dei cosiddetti Cable-In-Conduit-Conductors
(CICC), ampiamente usati in macchine per la fusione nucleare come ITER. Durante
l’attività di dottorato, è stato implementato un nuovo modello termico in aggiunta
al codice preestitente, in grado di descrivere problemi nei quali l’evoluzione termica
del sistema non può essere prevista a priori. Inoltre, il codice è stato esteso per
descrivere i cavi di tipo Rutherford, usati comunemente nei magneti per acceleratori
di particelle come quelli di LHC. Infine, il codice è stato applicato per l’analisi di
diversi casi di studio, sia nell’ambito dei magneti per acceleratori di particelle che
per fusione nucleare.
La tesi è strutturata nella seguente maniera.
I primi due capitoli sono un’ampia introduzione alla superconduttività: il primo
è una presentazione generale di questo fenomeno e sulle sue applicazioni, pensata per
chi non dovesse avere familiarità con questa tecnologia, mentre il secondo contiene
una descrizione più dettagliata dei fili e cavi superconduttori presi in considerazione
durante questo dottorato di ricerca.
Una descrizione dettagliata del codice numerico THELMA è invece riportata nella
seconda parte della tesi. Nel capitolo 3 vengono presentati i modelli geometrici,
elettromagnetici e termici, con particolare dettaglio relativamente alle parti sviluppate durante l’attività di dottorato, quali il modello geometrico del cavo Rutherford,
il modello termico e l’accoppiamento tra il modello termico e quello elettromagnetico.
Il modello di THELMA per le resistenze di contatto elettriche e termiche è invece
descritto nel capitolo 4, insieme all’analisi numerica di alcuni misure sperimentali
sia su cavi Rutherford che CICC.
La terza parte della tesi è invece focalizzata su alcuni esempi di applicazione
del codice accoppiato THELMA, svolti durante l’attività di dottorato. Nel capitolo
5 viene analizzata la caratteristica tensione-temperatura di un campione di cavo
CICC, quale esempio di validazione sperimentale nella quale il codice è in grado di
riprodurre fenomeni di difficile comprensione. Il capitolo 6 presenta il problema della
propagazione longitudinale di un’instabilità termo-elettromagnetica in avvolgimenti
impregnati di cavi Rutherford, analizzato con strumenti sperimentali, analitici e
numerici. Nel capitolo 7 sono invece descritte le analisi predittive in termini di
perdite e distribuzione di corrente riguardo il magnete CICC NAFASSY. Ulteriori
dettagli riguardanti le proprietà dei materiali e alcuni modelli analitici e numerici
sono infine riportati nelle appendici
Models of the resistive contact distribution in superconducting ITER CICC full size joints and terminations
The paper describes the numerical analysis, carried out with the THELMA code, of an ITER-type superconducting cable-in-conduit termination test made by the Paul Sherrer Institute with the JORDI device. In the test, a set of inter-strand and termination-strand resistances was measured, which have been used here to trim the model parameters and to evaluate the model accuracy. A statistical approach is proposed to enhance the accuracy of the results in the presence of random test parameters like the cable bundles angular initial positions
Critical current statistical distribution and voltage–current characteristics in superconducting wires
Type II superconductors, like Nb–Ti and Nb3Sn, play a central role in the design of magnets for fusion and particle accelerators. These materials show experimentally a longitudinal electric field which depends in a nonlinear way on the current. Different models have been developed to analyse this phenomenon, mainly based on the role of defects and inhomogeneities in the superconducting sample. Some of these models are based on a statistical description of the critical current distribution along the wire, that can explain the presence of a curvature in the volt–ampere characteristic (VAC). In the work we have studied the impact of different critical current statistical distributions on the VAC and their implications, and compared some experimental data with our theoretical results
Going Beyond Counting First Authors in Author Co-citation Analysis
The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
We provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
We conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Coupled Thermal and Electromagnetic analysis of the NAFASSY magnet
The paper presents an analysis of the current distribution and electromagnetic losses in the NAFASSY magnet carried out with the THELMA code, thanks to a brand-new thermal module coupled with the pre-existing electromagnetic module. The non-linear thermal and electrical properties of both superconducting and copper strands, depending on the local temperature, current density and magnetic field, are taken into account. The model analyses a single turn of the magnet, located in the highest field zone, focusing on the current distribution in the cable, the coupling AC and DC losses during ramped waveforms. The results are then extrapolated to estimate the behaviour of the overall magnet. A description of the models is given, together with a parametric analysis of different boundary conditions and cable discretizations. The analysis shows that, in nominal working conditions, no thermal instability should take place. However, local current redistribution among the strands may occur, mainly driven by the interstrand contact pattern, the local magnetic field and the strand current density
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