88 lines
2.5 KiB
TeX
Executable File
88 lines
2.5 KiB
TeX
Executable File
\documentclass[a4paper, 11pt]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[
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a4paper,
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headheight = 20pt,
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margin = 1in,
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tmargin = \dimexpr 1in - 10pt \relax
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]{geometry}
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\usepackage{fancyhdr} % for headers and footers
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\usepackage{graphicx} % for including figures
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\usepackage{booktabs} % for professional tables
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\setlength{\headheight}{14pt}
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\fancypagestyle{plain}{
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\fancyhf{}
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\fancyhead[L]{\sffamily Radboud University Nijmegen}
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\fancyhead[R]{\sffamily Superconductivity (NWI-NM117), Q3+Q4}
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\fancyfoot[R]{\sffamily\bfseries\thepage}
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\renewcommand{\headrulewidth}{0.5pt}
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\renewcommand{\footrulewidth}{0.5pt}
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}
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\pagestyle{fancy}
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\usepackage{siunitx}
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\usepackage{hyperref}
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\usepackage{float}
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\usepackage{mathtools}
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\usepackage{amsmath}
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\usepackage{todonotes}
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\setuptodonotes{inline}
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\usepackage{mhchem}
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\newcommand{\pfrac}[2]{\frac{\partial #1}{\partial #2}}
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\title{Superconductivity - Assignment 3}
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\author{
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Kees van Kempen (s4853628)\\
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\texttt{k.vankempen@student.science.ru.nl}
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}
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\AtBeginDocument{\maketitle}
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% Start from 8
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\setcounter{section}{7}
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\begin{document}
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\section{\ce{Nb3Sn} cylinder}
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Consider a cylinder of \ce{Nb3Sb}.
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From lecture 4, we have the following properties for \ce{Nb3Sn}:
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$T_c = \SI{18.2}{\kelvin}$,
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$\xi = \SI{3.6}{\nano\meter}$,
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$\lambda = \SI{124}{\nano\meter}$,
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$\kappa = \frac{\lambda}{\xi} = 34 > \frac{1}{\sqrt{2}}$,
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which means we are indeed dealing with a type-II superconductor.
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As $B_{c1} < B_E < B_{c2}$, the cylinder is in the vortex state.
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From the previous set of assignments, we know what the currents in the cylinder look like.
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The average field inside the cylinder is gives as
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\[
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\langle \vec{B} \rangle = \frac{1}{V_{\text{cylinder}}} \int_{\text{cylinder}} \vec{B}(\vec{r}) d\vec{r} .
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\]
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To determine this $\vec{B}$ inside the material, we first need to know how many vortices there are.
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We assume that every vortex lets through only one flux quantum $\Phi_0$,
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and that the vortices will arange themselves as far as possible from eachother.
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If their distance then is large enough to assume there is no overlap between regions of finite $\vec{B}$ around them,
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we can calculate the average field by just summing over the quanta and lastly over the field that penetrates the material in the outside of the cylinder.
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For this latter calculation, we can use the field for a type-I superconductor.
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\section{Superconducting wire}
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\section{Fine type-II superconducting wire}
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\section{Critical currents}
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\section{A weak junction}
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\bibliographystyle{vancouver}
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\bibliography{references.bib}
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%\appendix
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\end{document}
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