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Emittance Evolution in the MICE Cooling Channel extended » main.tex

Source File - Hunt, Christopher, 05 October 2017 10:31

 
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\begin{document}
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\title{Recent Results from the Study of Emittance Evolution in MICE}
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\author{ Christopher Hunt \\ \vspace{0.1em} \emph{\scriptsize on behalf of} \normalsize \\ \vspace{0.3em} The MICE Collaboration }
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\date{ 29th Sep 2017 }
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\begingroup
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    \centering
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    \vspace{1em}
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    ~\includegraphics[width=2.0cm]{MICE_vector_cropped.pdf} \hfill%
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    \includegraphics[width=5cm]{Logo_for_Imperial_College_London.pdf}
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\endgroup
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\begin{frame}
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  \frametitle{Contents}
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  \centering
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  \vspace{1em}
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  \large
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  \begin{minipage}{0.6\textwidth}
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    \begin{enumerate}\setlength{\itemsep}{1.5em}
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      \item Introduction and Definitions
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      \item Analysing the MICE Cooling Channel
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      \item Event Selection and Reconstruction Tools
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      \item Most Recent Public Results
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      \item The Next Steps
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    \end{enumerate}
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  \end{minipage}%
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  \begin{minipage}{0.4\textwidth}
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    \centerline{\includegraphics[width=1.1\textwidth]{STEP_IV_cooling_channel.jpg}}
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  \end{minipage}
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\end{frame}
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\begin{frame}
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  \frametitle{Introduction}
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  \vspace{1em}
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  The MICE Experiment is currently evaluating several key measurements:
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  \vspace{1em} \small
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  \begin{enumerate}[\hspace{1.5cm}1.] \setlength{\itemsep}{1em}
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    \item High precision emittance measurement from individual muons tracks,
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    \item The first measurement of emittance reduction through a LiH absorber, \\
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      { \scriptsize \hfill [ See F. Drielsma ] }
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    \item An entire programme of materials physics studies, { \scriptsize \hfill [ See J. Nugent ] }
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    \item A detailed study of emittance evolution in the MICE Cooling Channel.
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  \end{enumerate}
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  \vspace{2em}
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  I will focus on 1. and 2., but do please see the excellent work presented by our collaborators.
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\end{frame}
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\begin{frame}
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  \frametitle{Defining Emittance}
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  \centering
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  \begin{minipage}{0.48\textwidth}
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    \vspace{1.5em}
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    The volume of phase-space occupied by an ensemble of particles.
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    \vspace{1em}
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    In MICE we focus on the \emph{4-dimensional, transvserse, normalised, RMS emittance}, $\epsilon_{\perp}$, which corresponds to the central 1-sigma of a Gaussian distribution in $x$, $p_x$, $y$, $p_y$ space.
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    \vspace{1em}
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    Calculated from the covariance matrix of the ensemble $\bm{\Sigma}$, and the muon mass, $m$.
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    \centering
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    \LARGE
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    $\epsilon_{\perp} = \frac{\left| \bm{\Sigma} \right|^\frac{1}{4}}{m}$.
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  \end{minipage}\hfill
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  \begin{minipage}{0.48\textwidth}
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    \centering
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    \small
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    \includegraphics[width=\textwidth]{x-px_phasespace_example+ellipse.pdf}
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    \parbox{5cm}{\centering A typical phase-space projection in $x$-$p_x$.}
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  \end{minipage}
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\end{frame}
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\begin{frame}
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  \frametitle{Defining Amplitude}
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  \centering
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  \begin{minipage}{0.48\textwidth}
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    \centering
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    \includegraphics[width=0.8\textwidth]{amplitude_cartoon.pdf}
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  \end{minipage}\hfill
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  \begin{minipage}{0.48\textwidth}
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    \vspace{1em}
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    Analysing emittance evolution on a muon-by-muon basis.
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    \vspace{1.5em}
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    The Single Particle Amplitude defined as the scalar distance in phase-space of a particle (with vector $\bm{v}$) from the centre of the ensemble (with covariance matrix $\bm{\Sigma}$).
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    \vspace{1.5em}
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    \centering
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    \Large
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    $A_{\perp} = \epsilon_{\perp} \bm{v}^{\intercal} \bm{\Sigma}^{-1} \bm{v}$
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    \vspace{2em}
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  \end{minipage}
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\end{frame}
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\begin{frame}
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  \frametitle{Amplitude and Emittance}
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  \centering
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  \vspace{1.5em}
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  \parbox{12cm}{\centering To demonstrate cooling, we can analyse both RMS emittance measurements and amplitude distributions.}
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  \vspace{1.5em}
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  \centering
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  {\renewcommand{\arraystretch}{2}
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    \begin{tabular}{ >{\centering}p{0.45\textwidth} | >{\centering}p{0.45\textwidth} }
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      RMS Emittance, Cooling: & Amplitude Distribution, Cooling: \tabularnewline
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      Net decrease in the RMS occupied phase-space volume. &  Net migration of particles from higher amplitudes to lower amplitudes. \tabularnewline
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      Can be affected by high field gradients and hard scattering events. & Can remove tail effects and examine the core of the beam.
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    \end{tabular}
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  }
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\end{frame}
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\begin{frame}
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  \centering
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  \LARGE \usebeamercolor[fg]{frametitle}{Analysing the MICE Cooling Channel}
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\end{frame}
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\begin{frame}
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  \frametitle{The Experiment}
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  \centering
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  \vspace{1em}
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  \includegraphics[width=1.0\textwidth]{Step-4-layout-simple.pdf}
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  Net migration of particles from higher amplitudes to lower amplitudes. \\
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  An increase in core density.
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\end{frame}
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\begin{frame}
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  \frametitle{The Experiment}
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  \centering
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  \includegraphics[width=0.85\textwidth]{H4a_details.pdf}
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\end{frame}
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\begin{frame}
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  \centering
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  \LARGE \usebeamercolor[fg]{frametitle}{Selection and Reconstruction}
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\end{frame}
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\begin{frame}
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  \frametitle{Analysis Process}
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  \centering
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  \vspace{1em}
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  \includegraphics[width=\textwidth]{analysis_flow_chart.pdf}
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\end{frame}
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\begin{frame}
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  \frametitle{Global Reconstruction}
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  \centering
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  \includegraphics[clip=true,trim=0 10cm 0 23cm,width=0.65\textwidth]{track_matching_cartoon.png}
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  \vspace{1em}
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  \begin{minipage}{0.40\textwidth}
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    \small
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    \begin{itemize}
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      \item Use reconstruction from all detectors,
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      \item Involves very precise tracking through CAD geometries,
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      \item Predict which tracks scattered and scraped,
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      \item Ensures a ``clean'' muon sample.
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    \end{itemize}
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  \end{minipage}%
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  \begin{minipage}{0.60\textwidth}
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    \centering
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    \includegraphics[width=0.85\textwidth]{track_matching_residuals_mini.pdf}
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    \vspace{0.5em}
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    \scriptsize Tracker$\rightarrow$TOF Residuals 
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  \end{minipage}
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\begin{frame}
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  \frametitle{Event Selection}
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  \centering
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  \begin{minipage}{0.50\textwidth}
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    \vspace{1em}
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    \small
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    Selecting Good Muons:
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    \begin{itemize}
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      \item Single tracker events,
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      \item Muonic time of flight,
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      \item Good reconstruction in all detectors,
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      \item No apertures scraped.
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    \end{itemize}
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    \centering
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    \includegraphics[width=0.8\textwidth]{pion_contamination_TOF.pdf}
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    \tiny Time Of Flight TOF1$\rightarrow$2.
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  \end{minipage}%
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  \begin{minipage}{0.5\textwidth}
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    \centering
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    \small TOF - Momentum Correlation.
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    \vspace{1em}
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    \includegraphics[clip=true,trim=0 0 0cm 1cm,width=0.9\textwidth]{emittance_recon_analysis_tof_vs_tracker.pdf}
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    \vspace{1em}
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    Shown previously a muon purity of >99.85\%
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    \vspace{1em}
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  \end{minipage}
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\begin{frame}
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  \frametitle{Beam Selection}
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  \centering
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  \vspace{1em}
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  \begin{minipage}{0.5\textwidth}
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    \centering
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    \includegraphics[width=0.9\textwidth]{selection_example.pdf}
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    \vspace{1em}
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    \small
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    A rigorous proceedure is used to select a matched beam for the individual magnetic lattice.
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  \end{minipage}%
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    \vspace{0.5em}
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    \small
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    \centering
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    \begin{itemize}
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      \item Accept/reject sampling or statistical weighting,
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      \item Select a different amplitude distribution,
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      \item Select a matched beam from an unmatched one.
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    \end{itemize}
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    \vspace{0.5em}
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    \includegraphics[width=\textwidth]{wonky_distribution.pdf}
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  \end{minipage}
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\end{frame}
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\begin{frame}
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  \centering
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  \LARGE \usebeamercolor[fg]{frametitle}{Recent Results}
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\begin{frame}
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  \frametitle{Recent Results}
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  \centering
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  \vspace{1em}
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  I will present the most recent results from two of the key analyses for MICE:
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  \vspace{2em}
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  \small \raggedright
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  { \usebeamercolor[fg]{frametitle} The Precise Measurement of Beam Emittance }
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  \centering \vspace{1em}
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  \parbox{0.8\textwidth}{ Precise calculation of the normalised emittance within the upstream tracker. }
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  \vspace{2em} \raggedright
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  { \usebeamercolor[fg]{frametitle} A Measurement of Emittance Evolution through a LiH Absorber}
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  \centering \vspace{1em}
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  \parbox{0.8\textwidth}{ Comparison of the upstream and downstream amplitude distributions for a 3~mm beam and a 6~mm beam (nominal normalised emittance). }
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\begin{frame}
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  \frametitle{Precise Measurement of Beam Emittance}
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  \centering
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  \begin{minipage}{0.5\textwidth}
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    \small
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    \begin{itemize} \setlength{\itemsep}{0.5em}
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      \item Time-of-flight counters used for primary event selection,
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      \item Upstream spectrometer used for emittance reconstruction,
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      \item Single-track events with a muonic time of flight and a good reconstruction,
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      \item Analyse beam in 8~MeV/c momentum bins, twice the momentum uncertainty,
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      \item Statistical and systematic errors evaluated from all correlations in covariance matrix.
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    \end{itemize}
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  \end{minipage}%
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  \begin{minipage}{0.5\textwidth}
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    \vspace{4em}
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    \raggedleft
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    \includegraphics[clip=true,trim=0cm 0cm 1cm 1cm,width=\textwidth]{data_emittance_185_to_245_in_8MeV_bins.pdf}
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    \vspace{1em}
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  \end{minipage}%
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\begin{frame}
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  \frametitle{Measurement of Emittance Evolution}
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  \centering
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  \vspace{1em}
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  \small
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  Nominal 3mm Beam \hspace{11em} Nominal 6mm Beam
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  \centerline{\includegraphics[clip=true,trim=0cm 0cm 1cm 1cm,width=0.50\textwidth]{amplitude_distribution_3mm.pdf}%
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  \includegraphics[clip=true,trim=0cm 0cm 1cm 1cm,width=0.50\textwidth]{amplitude_distribution_6mm.pdf} }
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  \begin{minipage}{0.5\textwidth}
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    \centering
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    Consistent with emittance increase/heating.
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    Core density decrease.
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  \end{minipage}%
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  \begin{minipage}{0.5\textwidth}
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    \centering
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    \vspace{0.2em}
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    Consistent with equilibrium emittance.
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    No change in core density.
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\begin{frame}
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  \frametitle{Conclusions}
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  \centering
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  \vspace{1em}
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  \begin{enumerate} \setlength{\itemsep}{2em}
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    \item \emph{Direct Measurement of Emittance Using the Scintillating Fibre Trackers}
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      \vspace{0.5em}
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      \begin{itemize}
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        \item Demonstrated an emittance measurement with single muons,
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        \item Acheived small statistical and systematic errors.
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      \end{itemize}
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    \item \emph{Measurement of Emittance Evolution through LiH Absorber}
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      \begin{itemize}
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        \item First results of evolution of amplitude distribution have been presented,
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        \item Characteristic effects of heating and emittance equilibrium demonstrated,
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        \item Final dataset, 10~mm nominal emittance, currently being finalised.
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      \end{itemize}
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    \item \emph{Liquid Hydrogen Data}
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      \vspace{0.5em}
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      \begin{itemize}
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        \item Currently being recorded\ldots
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  \end{enumerate}
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\vspace{4em}
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  \begin{minipage}{0.4\textwidth}
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    \centering
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    \large
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    Thank you for your attention.
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    \vspace{1em}
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    Watch this space! $\rightarrow$
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  \end{minipage}%
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  \begin{minipage}{0.6\textwidth}
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    \includegraphics[clip=true,trim=0cm 0cm 1cm 1cm,width=\textwidth]{amplitude_distribution_6mm.pdf}
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(12-12/13)