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\@writefile{toc}{\contentsline {title}{Muon g-2 storage ring beam and spin dynamics}{1}{section*.2}}
\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}}
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\@writefile{toc}{\contentsline {section}{\numberline {I} Introduction}{1}{section*.3}}
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\@writefile{toc}{\contentsline {section}{\numberline {II} Experimental Method}{1}{section*.4}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A} Polarized Muon Production}{1}{section*.5}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {B} Spin Precession}{1}{section*.6}}
\citation{Crnkovic:IPAC2018-WEPAF015}
\citation{Grange:2015fou}
\citation{Grange:2015fou}
\citation{Grange:2015fou}
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\newlabel{tab:ringparams}{{I}{2}{\textcolor {orange}{Jason} Muon \gmtwo ~storage ring magnet parameters.\relax }{table.caption.8}{}}
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\newlabel{fig:bfield}{{1}{3}{\textcolor {orange}{Mike} Preliminary storage ring magnetic field data. \textcolor {red}{\textit {Maybe we should show preliminary field data, as it is used to calculate closed orbit distortions.}}\relax }{figure.caption.9}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {IV} Simulation Tools}{3}{section*.15}}
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\newlabel{fig:picture}{{2a}{3}{Annotated storage ring picture \textcolor {red}{\textit {[still need to annotate the picture]}}.\relax }{figure.caption.11}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \leavevmode {\color {orange}Jason} Injected beam enters the \ensuremath  {g\tmspace  -\thinmuskip {.1667em}-\tmspace  -\thinmuskip {.1667em}2}\nobreakspace  {}ring through a hole in the back leg iron. It emerges from the back leg and enters the inflector which cancels the field of the storage ring magnet. Beam exits the inflector, and enters the ring through the kicker gap. The circumference of the ring is \SI {44.69}{\meter } (revolution period \SI {149}{\nano \second }). The \SI {1.45}{\tesla } bending field is continuous around the ring.\relax }}{3}{figure.caption.11}}
\newlabel{fig:schematic}{{2}{3}{\textcolor {orange}{Jason} Injected beam enters the \gmtwo ~ring through a hole in the back leg iron. It emerges from the back leg and enters the inflector which cancels the field of the storage ring magnet. Beam exits the inflector, and enters the ring through the kicker gap. The circumference of the ring is \SI {44.69}{\meter } (revolution period \SI {149}{\nano \second }). The \SI {1.45}{\tesla } bending field is continuous around the ring.\relax }{figure.caption.11}{}}
\citation{Sagan:2016}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces \leavevmode {\color {orange}David R.} Horizontal position of centroid measured with the \SI {180}{\degree } fiber harp (blue) and \SI {270}{\degree } harp (red) for the first \SI {30}{\micro \second } of the fill. A discrete Fourier transform yields the horizontal tune.\relax }}{4}{figure.caption.12}}
\newlabel{fig:fibercentroid}{{3}{4}{\textcolor {orange}{David R.} Horizontal position of centroid measured with the \SI {180}{\degree } fiber harp (blue) and \SI {270}{\degree } harp (red) for the first \SI {30}{\micro \second } of the fill. A discrete Fourier transform yields the horizontal tune.\relax }{figure.caption.12}{}}
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\newlabel{fig:trackercentroid}{{4}{4}{\textcolor {orange}{David R.} Radial centroid as measured with the \SI {180}{\degree } tracker over the first \SI {220}{\micro \second } of the fill. Red curve is a fitted damped sinusoid. Measurement is increasingly noisy at longer times as statistics are limited.\relax }{figure.caption.13}{}}
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\citation{Sagan:2006sy}
\citation{Sagan:2006sy}
\citation{Semertzidis:2003zs}
\citation{Grange:2015fou}
\@writefile{toc}{\contentsline {subsection}{\numberline {E}Quadrupoles}{5}{section*.20}}
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\newlabel{fig:tuneplane}{{6}{6}{\textcolor {orange}{Jason} Dependence of tune on quadrupole voltage computed with a Bmad\cite {Sagan:2006sy} based model of the guide field. Resonance lines are shown. Tentative operating point is \SI {20.4}{\kilo \volt } (red dot).\relax }{figure.caption.25}{}}
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\newlabel{fig:tuneshift}{{9}{7}{\textcolor {orange}{David R.} Simulated contribution to amplitude dependent tune shift from each of the quad multipoles, their sum, and the decoherence rate $\Gamma $ as determined by tracking.\relax }{figure.caption.28}{}}
\newlabel{fig:2dtuneshift_perf_bfield}{{10a}{7}{\relax }{figure.caption.29}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces \leavevmode {\color {orange}David T.} Amplitude-dependent tune shifts ($\left .\delta p\middle /\ensuremath  {p_{0}}\right .= 0,\left .p_{x}\middle /\ensuremath  {p_{0}}\right .=0,\left .p_{y}\middle /\ensuremath  {p_{0}}\right .=0$) within the storage region ($r\leq \SI {45}{\milli \meter }$) for an ideal (a) and measured (b) magnetic field.\relax }}{7}{figure.caption.29}}
\newlabel{fig:2dtuneshift}{{10}{7}{\textcolor {orange}{David T.} Amplitude-dependent tune shifts ($\left .\delta p\middle /\pmagic \right .= 0,\left .p_{x}\middle /\pmagic \right .=0,\left .p_{y}\middle /\pmagic \right .=0$) within the storage region ($r\leq \SI {45}{\milli \meter }$) for an ideal (a) and measured (b) magnetic field.\relax }{figure.caption.29}{}}
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\citation{Grange:2015fou,Schreckenberger:IPAC2018-THPML093}
\newlabel{fig:tunevsp}{{11a}{8}{Tune value vs. relative momentum.\relax }{figure.caption.30}{}}
\newlabel{sub@fig:tunevsp}{{a}{8}{Tune value vs. relative momentum.\relax }{figure.caption.30}{}}
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\newlabel{fig:tunedepp}{{11}{8}{\textcolor {orange}{Mike and David T.} Tune dependence on muon momentum \textcolor {red}{\textit {[See DocDB15538 and DocDB16661]}}.\relax }{figure.caption.30}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces \leavevmode {\color {orange}David T.} Chromaticity dependence on quadrupole voltage.\relax }}{8}{figure.caption.31}}
\newlabel{fig:chromat}{{12}{8}{\textcolor {orange}{David T.} Chromaticity dependence on quadrupole voltage.\relax }{figure.caption.31}{}}
\newlabel{fig:20180210quadscan}{{13a}{9}{\relax }{figure.caption.32}{}}
\newlabel{sub@fig:20180210quadscan}{{a}{9}{\relax }{figure.caption.32}{}}
\newlabel{fig:20180324quadscan}{{13b}{9}{\relax }{figure.caption.32}{}}
\newlabel{sub@fig:20180324quadscan}{{b}{9}{\relax }{figure.caption.32}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces \leavevmode {\color {orange}Jason} Relative number of decay positrons in a fill as a function of quadrupole voltage \leavevmode {\color {red}\textit  {[remove run numbers and renormalize to \SI {20.4}{\kilo \volt } setting]}}. Storage efficiency is degraded by betatron resonances at 18.8 and \SI {21.2}{\kilo \volt }.\relax }}{9}{figure.caption.32}}
\newlabel{fig:quadscan}{{13}{9}{\textcolor {orange}{Jason} Relative number of decay positrons in a fill as a function of quadrupole voltage \textcolor {red}{\textit {[remove run numbers and renormalize to \SI {20.4}{\kilo \volt } setting]}}. Storage efficiency is degraded by betatron resonances at 18.8 and \SI {21.2}{\kilo \volt }.\relax }{figure.caption.32}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces \leavevmode {\color {orange}David T.} Tune footprint of a beam distribution at \SI {149}{\micro \second } after injection and for a magnetic field measurement.\relax }}{9}{figure.caption.33}}
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\newlabel{fig:mismatchap}{{15}{9}{\textcolor {orange}{David R.} Propagating beam betatron and energy width through narrow aperture inflector and into the storage ring. The dashed line is the horizontal aperture.\relax }{figure.caption.35}{}}
\newlabel{fig:xbeamphasespace}{{16a}{10}{Horizontal phase space at the exit of the inflector.\relax }{figure.caption.36}{}}
\newlabel{sub@fig:xbeamphasespace}{{a}{10}{Horizontal phase space at the exit of the inflector.\relax }{figure.caption.36}{}}
\newlabel{fig:ybeamphasespace}{{16b}{10}{Vertical phase space at the inflector exit.\relax }{figure.caption.36}{}}
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\newlabel{fig:beamphasespace}{{16}{10}{\textcolor {orange}{David R.} Simulated muon beam phase space at the downstream end of the inflector \textcolor {red}{[be careful with the coordinate systems]}.\relax }{figure.caption.36}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces \leavevmode {\color {orange}David R.} Kick angle \SI {\sim 80}{\percent } of nominal. The green lines mark the envelope of the motion of a muon that exits the inflector with zero angle. The on momentum muon oscillates between \SI {\pm 2}{\centi \meter }. If momentum offset is \SI {0.2}{\percent } the peak to peak oscillation is \SI {\sim 5}{\milli \meter }. A muon with momentum offset of \SI {-0.18}{\percent } is outside the \SI {4.5}{\centi \meter } aperture.\relax }}{10}{figure.caption.37}}
\newlabel{fig:EnergyAcceptance1}{{17}{10}{\textcolor {orange}{David R.} Kick angle \SI {\sim 80}{\percent } of nominal. The green lines mark the envelope of the motion of a muon that exits the inflector with zero angle. The on momentum muon oscillates between \SI {\pm 2}{\centi \meter }. If momentum offset is \SI {0.2}{\percent } the peak to peak oscillation is \SI {\sim 5}{\milli \meter }. A muon with momentum offset of \SI {-0.18}{\percent } is outside the \SI {4.5}{\centi \meter } aperture.\relax }{figure.caption.37}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces \leavevmode {\color {orange}David R.} For the nominal kick angle (\SI {10.8}{\milli \radian }), the trajectory of the on momentum muon coincides with the closed orbit. The on momentum muon injected with angle of \SI {\pm 3}{\milli \radian } will oscillate within a \SI {\pm 2}{\centi \meter } envelope.\relax }}{10}{figure.caption.38}}
\newlabel{fig:EnergyAcceptance3}{{18}{10}{\textcolor {orange}{David R.} For the nominal kick angle (\SI {10.8}{\milli \radian }), the trajectory of the on momentum muon coincides with the closed orbit. The on momentum muon injected with angle of \SI {\pm 3}{\milli \radian } will oscillate within a \SI {\pm 2}{\centi \meter } envelope.\relax }{figure.caption.38}{}}
\citation{Semertzidis:2003zs}
\citation{Semertzidis:2003zs}
\citation{Semertzidis:2003zs}
\@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces  \leavevmode {\color {orange}Jason} Measured $\left <f_{c}\right >$ and $\left <f_{\textnormal  {cbo}}\right >$ (only statistical errors are given) and corresponding $\left <\nu _{x}\right >$ calculated via Eq.\nobreakspace  {}(\ref  {eq:tunedef}). This data was collected during Run-1. The FBM measurements use the 6 o'clock horizontal FBM central fiber (no. 4), where the first \SI {3}{\micro \second } of data are not used for these measurements.\relax }}{11}{table.caption.40}}
\newlabel{tab:horz_tune_data}{{II}{11}{\textcolor {orange}{Jason} Measured $\left <f_{c}\right >$ and $\left <f_{\textnormal {cbo}}\right >$ (only statistical errors are given) and corresponding $\left <\nu _{x}\right >$ calculated via Eq.~(\ref {eq:tunedef}). This data was collected during \runone . The FBM measurements use the 6 o'clock horizontal FBM central fiber (no. 4), where the first \SI {3}{\micro \second } of data are not used for these measurements.\relax }{table.caption.40}{}}
\newlabel{eq:tunedef}{{2}{11}{}{equation.5.2}{}}
\newlabel{eq:n_0_deff}{{3}{11}{}{equation.5.3}{}}
\@writefile{lot}{\contentsline {table}{\numberline {III}{\ignorespaces  \leavevmode {\color {orange}Jason} Measured $\left <f_{c}\right >$ and $\left <f_{y}\right >$ (only statistical errors are given) and corresponding $\left <\nu _{y}\right >$ calculated via Eq.\nobreakspace  {}(\ref  {eq:tunedef}). This data was collected during Run-1. The FBM measurements use the 6 o'clock vertical FBM central fiber (no. 4), where the first \SI {3}{\micro \second } of data are not used for these measurements.\relax }}{11}{table.caption.41}}
\newlabel{tab:vert_tune_data}{{III}{11}{\textcolor {orange}{Jason} Measured $\left <f_{c}\right >$ and $\left <f_{y}\right >$ (only statistical errors are given) and corresponding $\left <\nu _{y}\right >$ calculated via Eq.~(\ref {eq:tunedef}). This data was collected during \runone . The FBM measurements use the 6 o'clock vertical FBM central fiber (no. 4), where the first \SI {3}{\micro \second } of data are not used for these measurements.\relax }{table.caption.41}{}}
\newlabel{eq:n_deff}{{4}{11}{}{equation.5.4}{}}
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\citation{Semertzidis:2003zs}
\citation{Semertzidis:2003zs}
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\newlabel{eq:nvspconv}{{9}{12}{}{equation.5.9}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {C}Closed Orbit Distortions}{12}{section*.44}}
\newlabel{fig:nu_x_vs_v}{{19a}{12}{$\left <\nu _{x}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.42}{}}
\newlabel{sub@fig:nu_x_vs_v}{{a}{12}{$\left <\nu _{x}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.42}{}}
\newlabel{fig:nu_y_vs_v}{{19b}{12}{$\left <\nu _{y}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.42}{}}
\newlabel{sub@fig:nu_y_vs_v}{{b}{12}{$\left <\nu _{y}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.42}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces \leavevmode {\color {orange}Jason} Average tune data (blue circular points), see Tables\nobreakspace  {}\ref  {tab:horz_tune_data} and\nobreakspace  {}\ref  {tab:vert_tune_data}, along with fits using the smoothed quadrupole model (solid black lines) and discrete quadrupole model (red dashed lines), see Eqs.\nobreakspace  {}(\ref  {eq:tunes_smooth}),\nobreakspace  {}(\ref  {eq:tunes_discrete}), and\nobreakspace  {}(\ref  {eq:volt_to_index}). The $\sigma _{x}^{s}$, $\sigma _{y}^{s}$, $\sigma _{x}^{d}$, and $\sigma _{y}^{d}$ fit parameters are for the smoothed model fit to $\left <\nu _{x}\right >$ data, smoothed model fit to $\left <\nu _{y}\right >$ data, discrete model fit to $\left <\nu _{x}\right >$ data, and discrete model fit to $\left <\nu _{y}\right >$ data respectively. \leavevmode {\color {orange}Mike and David T.} \leavevmode {\color {red}\textit  {: Add a set of simulation based tune curves, see DocDB15538 and DocDB16661.}}\relax }}{12}{figure.caption.42}}
\newlabel{fig:nu_vs_v}{{19}{12}{\textcolor {orange}{Jason} Average tune data (blue circular points), see Tables~\ref {tab:horz_tune_data} and~\ref {tab:vert_tune_data}, along with fits using the smoothed quadrupole model (solid black lines) and discrete quadrupole model (red dashed lines), see Eqs.~(\ref {eq:tunes_smooth}),~(\ref {eq:tunes_discrete}), and~(\ref {eq:volt_to_index}). The $\sigma _{x}^{s}$, $\sigma _{y}^{s}$, $\sigma _{x}^{d}$, and $\sigma _{y}^{d}$ fit parameters are for the smoothed model fit to $\left <\nu _{x}\right >$ data, smoothed model fit to $\left <\nu _{y}\right >$ data, discrete model fit to $\left <\nu _{x}\right >$ data, and discrete model fit to $\left <\nu _{y}\right >$ data respectively. \textcolor {orange}{Mike and David T.} \textcolor {red}{\textit {: Add a set of simulation based tune curves, see DocDB15538 and DocDB16661.}}\relax }{figure.caption.42}{}}
\@writefile{lot}{\contentsline {table}{\numberline {IV}{\ignorespaces  \leavevmode {\color {orange}Jason} Field index and tune values based on the smoothed model for different quadrupole storage voltages used in Run-1\nobreakspace  {}data collection, see Eqs.\nobreakspace  {}(\ref  {eq:tunes_smooth}),\nobreakspace  {}(\ref  {eq:volt_to_index}), and\nobreakspace  {}(\ref  {eq:nvspconv}), along with the numerical relation $n_{0}=\left .n\middle /0.43\right .$ obtained from\nobreakspace  {}\cite  {Semertzidis:2003zs}.\relax }}{13}{table.caption.43}}
\newlabel{tab:n_nu_estim}{{IV}{13}{\textcolor {orange}{Jason} Field index and tune values based on the smoothed model for different quadrupole storage voltages used in \runone ~data collection, see Eqs.~(\ref {eq:tunes_smooth}),~(\ref {eq:volt_to_index}), and~(\ref {eq:nvspconv}), along with the numerical relation $n_{0}=\left .n\middle /0.43\right .$ obtained from~\cite {Semertzidis:2003zs}.\relax }{table.caption.43}{}}
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\citation{Orlov:2002ag}
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\newlabel{tab:beamfreq}{{VII}{15}{\textcolor {orange}{Jason} Beam frequencies that can affect the decay positron spectra via detector acceptance for $n=0.137$ \textcolor {red}{\textit {[update with $V_{\textnormal {quad}}=\SI {18.3}{\kilo \volt }$ values]}}.\relax }{table.caption.51}{}}
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\newlabel{fig:verticaltracker}{{23}{15}{\textcolor {orange}{David R.} Vertical distribution measured by straw tracker for a subset of the data. The data is not corrected for acceptance or resolution.\relax }{figure.caption.54}{}}
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\citation{lostmuons}
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\newlabel{fig:efield_cor}{{25}{16}{\textcolor {orange}{David R.} The contribution to $\omega _a$ ($C_e$) due to the electric field is computed by spin tracking as a function of muon momentum and plotted in terms of the closed orbit. The measured radial distribution is superimposed. The average correction is the convolution of the two.\relax }{figure.caption.57}{}}
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\newlabel{fig:lostmuonsscan}{{27}{17}{\textcolor {orange}{Sudeshna} Fraction of lost muons as a function of EQS storage set-point voltage for calorimeter 1. An increased lost muon rate is observed from the betatron resonances centered near 18.8 and \SI {21.2}{\kilo \volt }. These resonances are due to the $3\nu _{y}=1$ and $\nu _{x}+2\nu _{y}=2$ lines in the tune plane.\relax }{figure.caption.62}{}}
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\newlabel{fig:injvert}{{28}{17}{\textcolor {orange}{David R.} Vertical displacement of the centroid at the \SI {180}{\degree } tracker during the scraping cycle.\relax }{figure.caption.63}{}}
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