\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\gdef \tocmax@section{22.27782pt}
\gdef \tocmax@subsection{14.91669pt}
\gdef \tocmax@subsubsection{12.2778pt}
\gdef \tocmax@paragraph{5.0pt}
\gdef \tocmax@appendix{5.0pt}
\gdef \tocmax@pagenum{10.00003pt}
\citation{Charpak:1962zz,Bailey:1978mn,Bennett:2006fi,Bennett:2008dy}
\citation{Grange:2015fou}
\citation{Grange:2015fou}
\citation{Mohr:2015ccw}
\newlabel{FirstPage}{{}{1}{}{section*.1}{}}
\@writefile{toc}{\contentsline {title}{Muon g-2 storage ring beam and spin dynamics}{1}{section*.2}\protected@file@percent }
\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}\protected@file@percent }
\@writefile{toc}{\tocdepth@munge}
\@writefile{toc}{\contentsline {section}{\numberline {}Contents}{1}{section*.3}\protected@file@percent }
\@writefile{toc}{\tocdepth@restore}
\newlabel{sec:intro}{{I}{1}{}{section*.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {I} Introduction}{1}{section*.4}\protected@file@percent }
\newlabel{eq:a_mu_formula}{{1}{1}{}{equation.1.1}{}}
\citation{Tanabashi:2018oca}
\citation{Tanabashi:2018oca}
\citation{fermimuondept}
\citation{Stratakis:2017uci}
\citation{Stratakis:2019sun}
\citation{Hubbard:1973ur}
\citation{Brown:2013idd}
\citation{Morgan:2003zza}
\citation{Jackson:1998nia}
\newlabel{sec:exp_method}{{II}{2}{}{section*.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {II} Experimental Method}{2}{section*.5}\protected@file@percent }
\newlabel{sec:muon_campus}{{II\tmspace  +\thinmuskip {.1667em}A}{2}{}{section*.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A} Polarized Muon Production}{2}{section*.6}\protected@file@percent }
\newlabel{sec:spin}{{II\tmspace  +\thinmuskip {.1667em}B}{2}{}{section*.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B} Spin Precession}{2}{section*.8}\protected@file@percent }
\newlabel{eq:mdip_mom}{{2}{2}{}{equation.2.2}{}}
\newlabel{eq:spinpress}{{2}{2}{}{equation.2.2}{}}
\citation{Stratakis:2017uci}
\citation{Fienberg:2014kka,Kaspar:2016ofv}
\citation{Grange:2015fou}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces \leavevmode {\color {orange}Diktys} A diagram of the Muon Campus accelerator complex that is used by the Muon \ensuremath  {g\tmspace  -\thinmuskip {.1667em}-\tmspace  -\thinmuskip {.1667em}2}\nobreakspace  {}Experiment. \leavevmode {\color {red}\textit  {Trying to get a less pixelated image from Brian Drendel or Lee.}}\relax }}{3}{figure.caption.7}\protected@file@percent }
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:muon-campus}{{1}{3}{\textcolor {orange}{Diktys} A diagram of the Muon Campus accelerator complex that is used by the Muon \gmtwo ~Experiment. \textcolor {red}{\textit {Trying to get a less pixelated image from Brian Drendel or Lee.}}\relax }{figure.caption.7}{}}
\newlabel{eq:wiggle_func}{{3}{3}{}{equation.2.3}{}}
\citation{Mohr:2015ccw}
\citation{Bennett:2006fi,Grange:2015fou,Prigl:1996fpk}
\citation{Grange:2015fou}
\citation{Grange:2015fou}
\citation{Bennett:2006fi}
\citation{Bennett:2006fi}
\newlabel{eq:au}{{4}{4}{}{equation.2.4}{}}
\newlabel{sec:bfield}{{II\tmspace  +\thinmuskip {.1667em}C}{4}{}{section*.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C} Magnetic Field}{4}{section*.9}\protected@file@percent }
\newlabel{eq:omega_p}{{5}{4}{}{equation.2.5}{}}
\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces  \leavevmode {\color {orange}Jason} Muon \ensuremath  {g\tmspace  -\thinmuskip {.1667em}-\tmspace  -\thinmuskip {.1667em}2}\nobreakspace  {}storage ring magnet parameters\nobreakspace  {}\cite  {Bennett:2006fi} \leavevmode {\color {red}\textit  {[Do any of these values need updating???]}}.\relax }}{4}{table.caption.10}\protected@file@percent }
\newlabel{tab:ringparams}{{I}{4}{\textcolor {orange}{Jason} Muon \gmtwo ~storage ring magnet parameters~\cite {Bennett:2006fi} \textcolor {red}{\textit {[Do any of these values need updating???]}}.\relax }{table.caption.10}{}}
\citation{Grange:2015fou,Danby:2001eh}
\citation{Grange:2015fou,Semertzidis:2003zs,Crnkovic:IPAC2018-WEPAF015}
\citation{Grange:2015fou,Yamamoto:2002bb,Froemming:IPAC2018-WEPAF014}
\citation{Grange:2015fou,Schreckenberger:IPAC2018-THPML093}
\citation{Grange:2015fou,Fienberg:2014kka,Kaspar:2016ofv}
\citation{Grange:2015fou}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \leavevmode {\color {orange}Mike} Preliminary storage ring magnetic field measurement data. Deviations from the main dipole field component in the vertical ($b_{0}$) and radial ($a_{0}$) directions in parts per million are indicated, as well as the normal quadrupole gradient ($b_{1}$) in parts per million at a displacement of 45 mm from the central orbit. \leavevmode {\color {red}\textit  {Harmonize notation; check with field \& tracker experts.}}\relax }}{5}{figure.caption.11}\protected@file@percent }
\newlabel{fig:bfield}{{2}{5}{\textcolor {orange}{Mike} Preliminary storage ring magnetic field measurement data. Deviations from the main dipole field component in the vertical ($b_{0}$) and radial ($a_{0}$) directions in parts per million are indicated, as well as the normal quadrupole gradient ($b_{1}$) in parts per million at a displacement of 45 mm from the central orbit. \textcolor {red}{\textit {Harmonize notation; check with field \& tracker experts.}}\relax }{figure.caption.11}{}}
\newlabel{eq:b_field}{{6}{5}{}{equation.2.6}{}}
\newlabel{sec:ring}{{III}{5}{}{section*.12}{}}
\@writefile{toc}{\contentsline {section}{\numberline {III} Storage Ring}{5}{section*.12}\protected@file@percent }
\citation{T0}
\citation{IBMS}
\citation{Bennett:2006fi,Grange:2015fou}
\citation{g4beamline}
\citation{Agostinelli:2002hh}
\citation{Stratakis:2019sun}
\newlabel{fig:picture}{{3a}{6}{\textcolor {orange}{Jason} Picture of the storage ring. \textcolor {red}{\textit {Make a final decision on which picture to use.}}\relax }{figure.caption.13}{}}
\newlabel{sub@fig:picture}{{a}{6}{\textcolor {orange}{Jason} Picture of the storage ring. \textcolor {red}{\textit {Make a final decision on which picture to use.}}\relax }{figure.caption.13}{}}
\newlabel{fig:diagram}{{3b}{6}{\textcolor {orange}{David T.} Diagram of the storage ring. \textcolor {red}{\textit {Finalize diagram with David T. and Leah.}}\relax }{figure.caption.13}{}}
\newlabel{sub@fig:diagram}{{b}{6}{\textcolor {orange}{David T.} Diagram of the storage ring. \textcolor {red}{\textit {Finalize diagram with David T. and Leah.}}\relax }{figure.caption.13}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The muon storage ring used by the Muon \ensuremath  {g\tmspace  -\thinmuskip {.1667em}-\tmspace  -\thinmuskip {.1667em}2}\nobreakspace  {}Experiment.\relax }}{6}{figure.caption.13}\protected@file@percent }
\newlabel{fig:schematic}{{3}{6}{The muon storage ring used by the Muon \gmtwo ~Experiment.\relax }{figure.caption.13}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces \leavevmode {\color {orange}Dat} 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. \leavevmode {\color {red}\textit  {Check with fiber harp experts.}}\relax }}{6}{figure.caption.14}\protected@file@percent }
\newlabel{fig:fibercentroid}{{4}{6}{\textcolor {orange}{Dat} 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. \textcolor {red}{\textit {Check with fiber harp experts.}}\relax }{figure.caption.14}{}}
\citation{Sagan:2006sy}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces \leavevmode {\color {orange}Dat} Horizontal width at \SI {180}{\degree } harp (blue) and \SI {270}{\degree } harp (red) over the first \SI {30}{\micro \second } of the fill. The deep modulation is a combination of $\beta $ and $D$ mismatch. \leavevmode {\color {red}\textit  {Check with fiber harp experts.}}\relax }}{7}{figure.caption.15}\protected@file@percent }
\newlabel{fig:fiberwidth}{{5}{7}{\textcolor {orange}{Dat} Horizontal width at \SI {180}{\degree } harp (blue) and \SI {270}{\degree } harp (red) over the first \SI {30}{\micro \second } of the fill. The deep modulation is a combination of $\beta $ and $D$ mismatch. \textcolor {red}{\textit {Check with fiber harp experts.}}\relax }{figure.caption.15}{}}
\newlabel{sec:sim_tools}{{IV}{7}{}{section*.17}{}}
\@writefile{toc}{\contentsline {section}{\numberline {IV} Simulation Tools}{7}{section*.17}\protected@file@percent }
\newlabel{sec:g4beamline}{{IV\tmspace  +\thinmuskip {.1667em}A}{7}{}{section*.18}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A} G4beamline}{7}{section*.18}\protected@file@percent }
\newlabel{sec:phase_space}{{IV\tmspace  +\thinmuskip {.1667em}B}{7}{}{section*.19}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B} Phase Space Models}{7}{section*.19}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \leavevmode {\color {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. \leavevmode {\color {red}\textit  {Check with tracker experts.}}\relax }}{7}{figure.caption.16}\protected@file@percent }
\newlabel{fig:trackercentroid}{{6}{7}{\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. \textcolor {red}{\textit {Check with tracker experts.}}\relax }{figure.caption.16}{}}
\newlabel{sec:bmad}{{IV\tmspace  +\thinmuskip {.1667em}C}{7}{}{section*.20}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C} Bmad}{7}{section*.20}\protected@file@percent }
\citation{Agostinelli:2002hh}
\newlabel{sec:bmad_quads}{{IV\tmspace  +\thinmuskip {.1667em}C\tmspace  +\thinmuskip {.1667em}1}{8}{}{section*.21}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1} Quadrupoles}{8}{section*.21}\protected@file@percent }
\newlabel{sec:bmad_mainmag}{{IV\tmspace  +\thinmuskip {.1667em}C\tmspace  +\thinmuskip {.1667em}2}{8}{}{section*.22}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2} Main Magnet}{8}{section*.22}\protected@file@percent }
\newlabel{sec:bmad_inj}{{IV\tmspace  +\thinmuskip {.1667em}C\tmspace  +\thinmuskip {.1667em}3}{8}{}{section*.23}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3} Injection Channel}{8}{section*.23}\protected@file@percent }
\newlabel{sec:cosy}{{IV\tmspace  +\thinmuskip {.1667em}D}{8}{}{section*.24}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {D} COSY INFINITY}{8}{section*.24}\protected@file@percent }
\citation{Poole:2011aaa,Poole:2012aaa}
\newlabel{sec:gm2ringsim}{{IV\tmspace  +\thinmuskip {.1667em}E}{9}{}{section*.25}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {E} gm2ringsim}{9}{section*.25}\protected@file@percent }
\newlabel{sec:optics}{{V}{9}{}{section*.26}{}}
\@writefile{toc}{\contentsline {section}{\numberline {V} Storage Ring Optics}{9}{section*.26}\protected@file@percent }
\newlabel{eq:delta_def}{{7}{9}{}{equation.5.7}{}}
\newlabel{eq:delta_def}{{8}{9}{}{equation.5.8}{}}
\newlabel{eq:x_equil}{{9}{9}{}{equation.5.9}{}}
\newlabel{eq:x_and_xp_def}{{10}{9}{}{equation.5.10}{}}
\newlabel{eq:y_and_yp_def}{{11}{9}{}{equation.5.11}{}}
\citation{Semertzidis:2003zs}
\citation{Grange:2015fou}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces \leavevmode {\color {orange}David R.} Dependence of tune on quadrupole voltage computed with a Bmad based model of the guide field. Resonance lines are shown. Typical operating point is \SI {20.4}{\kilo \volt } (red dot). \leavevmode {\color {red}\textit  {Change red point to \SI {18.3}{\kilo \volt }; update black points with Run-2\nobreakspace  {}fiber harp data; remove timestamp and directory info.}}\relax }}{10}{figure.caption.27}\protected@file@percent }
\newlabel{fig:tuneplane}{{7}{10}{\textcolor {orange}{David R.} Dependence of tune on quadrupole voltage computed with a Bmad based model of the guide field. Resonance lines are shown. Typical operating point is \SI {20.4}{\kilo \volt } (red dot). \textcolor {red}{\textit {Change red point to \SI {18.3}{\kilo \volt }; update black points with \runtwo ~fiber harp data; remove timestamp and directory info.}}\relax }{figure.caption.27}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces \leavevmode {\color {orange}David R. and David T.} Twiss parameters in the closed storage ring. \leavevmode {\color {red}\textit  {Harmonize notation; remove timestamp and directory info.}}\relax }}{10}{figure.caption.28}\protected@file@percent }
\newlabel{fig:twissplot}{{8}{10}{\textcolor {orange}{David R. and David T.} Twiss parameters in the closed storage ring. \textcolor {red}{\textit {Harmonize notation; remove timestamp and directory info.}}\relax }{figure.caption.28}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces \leavevmode {\color {orange}Mike and David T.} Dependence of horizontal and vertical amplitude functions and horizontal dispersion function on the electrostatic quadrupole system high voltage. The values are for one point in the ring, namely at the entrance to the ring at the end of the inflector.\relax }}{10}{figure.caption.29}\protected@file@percent }
\newlabel{fig:twissvsv}{{9}{10}{\textcolor {orange}{Mike and David T.} Dependence of horizontal and vertical amplitude functions and horizontal dispersion function on the electrostatic quadrupole system high voltage. The values are for one point in the ring, namely at the entrance to the ring at the end of the inflector.\relax }{figure.caption.29}{}}
\citation{Grange:2015fou,Schreckenberger:IPAC2018-THPML093}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces \leavevmode {\color {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. \leavevmode {\color {red}\textit  {Harmonize notation; remove timestamp and directory info.}}\relax }}{11}{figure.caption.30}\protected@file@percent }
\newlabel{fig:tuneshift}{{10}{11}{\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. \textcolor {red}{\textit {Harmonize notation; remove timestamp and directory info.}}\relax }{figure.caption.30}{}}
\newlabel{sec:inject}{{V\tmspace  +\thinmuskip {.1667em}A}{11}{}{section*.36}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A} Injection}{11}{section*.36}\protected@file@percent }
\newlabel{sec:tunes}{{V\tmspace  +\thinmuskip {.1667em}B}{11}{}{section*.41}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B}Average Tune \& Chromaticity Measurements}{11}{section*.41}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces \leavevmode {\color {orange}David T.} Amplitude-dependent tune shifts ($\delta =\left .p_{x}\middle /\ensuremath  {p_{0}}\right .=\left .p_{y}\middle /\ensuremath  {p_{0}}\right .=0$) within the storage region ($r\leq \SI {45}{\milli \meter }$) for an ideal magnetic field. \leavevmode {\color {red}\textit  {Harmonize notation.}}\relax }}{12}{figure.caption.31}\protected@file@percent }
\newlabel{fig:2dtuneshift}{{11}{12}{\textcolor {orange}{David T.} Amplitude-dependent tune shifts ($\delta =\left .p_{x}\middle /\pmagic \right .=\left .p_{y}\middle /\pmagic \right .=0$) within the storage region ($r\leq \SI {45}{\milli \meter }$) for an ideal magnetic field. \textcolor {red}{\textit {Harmonize notation.}}\relax }{figure.caption.31}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces \leavevmode {\color {orange}Mike and David T.} Dependence of zero-amplitude horizontal and vertical betatron tunes from their design values as functions of relative momentum deviation, for a quadrupole system high voltage of 18.3 kV. \leavevmode {\color {red}\textit  {Define the dashed lines.}}\relax }}{12}{figure.caption.32}\protected@file@percent }
\newlabel{fig:tunedepp}{{12}{12}{\textcolor {orange}{Mike and David T.} Dependence of zero-amplitude horizontal and vertical betatron tunes from their design values as functions of relative momentum deviation, for a quadrupole system high voltage of 18.3 kV. \textcolor {red}{\textit {Define the dashed lines.}}\relax }{figure.caption.32}{}}
\newlabel{eq:tunedef}{{12}{12}{}{equation.5.12}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces \leavevmode {\color {orange}David T.} Chromaticity dependence on quadrupole voltage. \leavevmode {\color {red}\textit  {Harmonize notation; is this chromaticity or relative chromaticity; needs legend; readable font size.}}\relax }}{12}{figure.caption.33}\protected@file@percent }
\newlabel{fig:chromat}{{13}{12}{\textcolor {orange}{David T.} Chromaticity dependence on quadrupole voltage. \textcolor {red}{\textit {Harmonize notation; is this chromaticity or relative chromaticity; needs legend; readable font size.}}\relax }{figure.caption.33}{}}
\citation{Semertzidis:2003zs}
\newlabel{fig:20180210quadscan}{{14a}{13}{\relax }{figure.caption.34}{}}
\newlabel{sub@fig:20180210quadscan}{{a}{13}{\relax }{figure.caption.34}{}}
\newlabel{fig:20180324quadscan}{{14b}{13}{\relax }{figure.caption.34}{}}
\newlabel{sub@fig:20180324quadscan}{{b}{13}{\relax }{figure.caption.34}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces \leavevmode {\color {orange}Sudeshna} Relative number of decay positrons in a fill as a function of quadrupole voltage. Storage efficiency is degraded by betatron resonances at 18.8 and \SI {21.2}{\kilo \volt }. \leavevmode {\color {red}\textit  {Harmonize notation; update with Run-2\nobreakspace  {}calo data; do we need to compare to Run-1\nobreakspace  {}data.}}\relax }}{13}{figure.caption.34}\protected@file@percent }
\newlabel{fig:quadscan}{{14}{13}{\textcolor {orange}{Sudeshna} Relative number of decay positrons in a fill as a function of quadrupole voltage. Storage efficiency is degraded by betatron resonances at 18.8 and \SI {21.2}{\kilo \volt }. \textcolor {red}{\textit {Harmonize notation; update with \runtwo ~calo data; do we need to compare to \runone ~data.}}\relax }{figure.caption.34}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\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. \leavevmode {\color {red}\textit  {Remake with the ideal magnetic field; add a z-axis that defines the color range.}}\relax }}{13}{figure.caption.35}\protected@file@percent }
\newlabel{fig:tunefootprint}{{15}{13}{\textcolor {orange}{David T.} Tune footprint of a beam distribution at \SI {149}{\micro \second } after injection and for a magnetic field measurement. \textcolor {red}{\textit {Remake with the ideal magnetic field; add a z-axis that defines the color range.}}\relax }{figure.caption.35}{}}
\newlabel{eq:n_0_deff}{{13}{13}{}{equation.5.13}{}}
\newlabel{eq:n_deff}{{14}{13}{}{equation.5.14}{}}
\citation{Semertzidis:2003zs}
\citation{Semertzidis:2003zs}
\@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces  \leavevmode {\color {orange}Dat} Measured $\left <f_{c}\right >$, $\left <f_{\textnormal  {cbo}}\right >$, and $\left <f_{y}\right >$ (only statistical errors are given) along with the corresponding $\left <\nu _{x}\right >$ and $\left <\nu _{y}\right >$ calculated via Eq.\nobreakspace  {}(\ref  {eq:tunedef}). This data was collected during Run-1\nobreakspace  {}with the \SI {180}{\degree } horizontal and vertical fiber harp central (no. 4) fibers, where the first \SI {3}{\micro \second } of data are not used for these measurements. The $\left <f_{c}^{x}\right >$ is the $\left <f_{c}\right >$ measured by the horizontal fiber harp and used to calculate $\left <\nu _{x}\right >$, while the $\left <f_{c}^{y}\right >$ is the $\left <f_{c}\right >$ measured by the vertical fiber harp and used to calculate $\left <\nu _{y}\right >$. \leavevmode {\color {red}\textit  {Update with Run-2\nobreakspace  {}fiber harp data; do we need to compare to Run-1\nobreakspace  {}data.}}\relax }}{14}{table.caption.43}\protected@file@percent }
\newlabel{tab:tune_data}{{II}{14}{\textcolor {orange}{Dat} Measured $\left <f_{c}\right >$, $\left <f_{\textnormal {cbo}}\right >$, and $\left <f_{y}\right >$ (only statistical errors are given) along with the corresponding $\left <\nu _{x}\right >$ and $\left <\nu _{y}\right >$ calculated via Eq.~(\ref {eq:tunedef}). This data was collected during \runone ~with the \SI {180}{\degree } horizontal and vertical fiber harp central (no. 4) fibers, where the first \SI {3}{\micro \second } of data are not used for these measurements. The $\left <f_{c}^{x}\right >$ is the $\left <f_{c}\right >$ measured by the horizontal fiber harp and used to calculate $\left <\nu _{x}\right >$, while the $\left <f_{c}^{y}\right >$ is the $\left <f_{c}\right >$ measured by the vertical fiber harp and used to calculate $\left <\nu _{y}\right >$. \textcolor {red}{\textit {Update with \runtwo ~fiber harp data; do we need to compare to \runone ~data.}}\relax }{table.caption.43}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces \leavevmode {\color {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. \leavevmode {\color {red}\textit  {What are $a_{x}\left (\beta _{x}\right )^{\left .1\middle /2\right .}$ and $\sigma _{\delta }$; is the y-axis label really right; remove timestamp and directory info.}}\relax }}{14}{figure.caption.37}\protected@file@percent }
\newlabel{fig:mismatchap}{{16}{14}{\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. \textcolor {red}{\textit {What are $a_{x}\left (\beta _{x}\right )^{\left .1\middle /2\right .}$ and $\sigma _{\delta }$; is the y-axis label really right; remove timestamp and directory info.}}\relax }{figure.caption.37}{}}
\newlabel{eq:tunes_smooth}{{15}{14}{}{equation.5.15}{}}
\newlabel{eq:tunes_discrete}{{16}{14}{}{equation.5.16}{}}
\newlabel{eq:volt_to_index}{{17}{14}{}{equation.5.17}{}}
\newlabel{eq:tunes_xydiff}{{18}{14}{}{equation.5.18}{}}
\newlabel{fig:xbeamphasespace}{{17a}{15}{Horizontal phase space at the exit of the inflector.\relax }{figure.caption.38}{}}
\newlabel{sub@fig:xbeamphasespace}{{a}{15}{Horizontal phase space at the exit of the inflector.\relax }{figure.caption.38}{}}
\newlabel{fig:ybeamphasespace}{{17b}{15}{Vertical phase space at the exit of the inflector.\relax }{figure.caption.38}{}}
\newlabel{sub@fig:ybeamphasespace}{{b}{15}{Vertical phase space at the exit of the inflector.\relax }{figure.caption.38}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces \leavevmode {\color {orange}David R.} Simulated muon beam phase space at the downstream end of the inflector. \leavevmode {\color {red}\textit  {Harmonize notation; show full coordinate ranges; change from scatter plot to 2D histogram; remove timestamp and directory info.}}\relax }}{15}{figure.caption.38}\protected@file@percent }
\newlabel{fig:beamphasespace}{{17}{15}{\textcolor {orange}{David R.} Simulated muon beam phase space at the downstream end of the inflector. \textcolor {red}{\textit {Harmonize notation; show full coordinate ranges; change from scatter plot to 2D histogram; remove timestamp and directory info.}}\relax }{figure.caption.38}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\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. \leavevmode {\color {red}\textit  {Harmonize notation; should we change \SI {80}{\percent } nominal kick to \SI {90}{\percent } nominal kick as $\left .\SI {149}{\kilo \volt }\middle /\SI {165}{\kilo \volt }\right .=0.9$; remove timestamp and directory info.}}\relax }}{15}{figure.caption.39}\protected@file@percent }
\newlabel{fig:EnergyAcceptance1}{{18}{15}{\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. \textcolor {red}{\textit {Harmonize notation; should we change \SI {80}{\percent } nominal kick to \SI {90}{\percent } nominal kick as $\left .\SI {149}{\kilo \volt }\middle /\SI {165}{\kilo \volt }\right .=0.9$; remove timestamp and directory info.}}\relax }{figure.caption.39}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces \leavevmode {\color {orange}David R.} Horizontal betatron amplitude vs. average equilibrium position for stored muons. \leavevmode {\color {red}\textit  {Harmonize notation; check units used for calculations; change scatter plot to 2D histogram; remove timestamp and directory info.}}\relax }}{15}{figure.caption.40}\protected@file@percent }
\newlabel{fig:amplvsequpos}{{19}{15}{\textcolor {orange}{David R.} Horizontal betatron amplitude vs. average equilibrium position for stored muons. \textcolor {red}{\textit {Harmonize notation; check units used for calculations; change scatter plot to 2D histogram; remove timestamp and directory info.}}\relax }{figure.caption.40}{}}
\citation{Semertzidis:2003zs}
\citation{Semertzidis:2003zs}
\newlabel{fig:freq_ext_low_f}{{20a}{16}{\relax }{figure.caption.42}{}}
\newlabel{sub@fig:freq_ext_low_f}{{a}{16}{\relax }{figure.caption.42}{}}
\newlabel{fig:freq_ext_high_f}{{20b}{16}{\relax }{figure.caption.42}{}}
\newlabel{sub@fig:freq_ext_high_f}{{b}{16}{\relax }{figure.caption.42}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces \leavevmode {\color {orange}Dat} A sum of Gaussian functions is fitted to the FFT of the fiber harp signals to extract the $\left <f_{\textnormal  {cbo}}\right >$, $\left <f_{y}\right >$, $\left <f_{\textnormal  {vw}}\right >$, $\left <f_{x}\right >$, and $\left <f_{c}\right >$ values for a given $V_{Q}$ setting. \leavevmode {\color {red}\textit  {What do we really want to show?}}\relax }}{16}{figure.caption.42}\protected@file@percent }
\newlabel{fig:freq_ext}{{20}{16}{\textcolor {orange}{Dat} A sum of Gaussian functions is fitted to the FFT of the fiber harp signals to extract the $\left <f_{\textnormal {cbo}}\right >$, $\left <f_{y}\right >$, $\left <f_{\textnormal {vw}}\right >$, $\left <f_{x}\right >$, and $\left <f_{c}\right >$ values for a given $V_{Q}$ setting. \textcolor {red}{\textit {What do we really want to show?}}\relax }{figure.caption.42}{}}
\newlabel{eq:nvspconv}{{19}{16}{}{equation.5.19}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces \leavevmode {\color {orange}Dat} A measurement of $\left <\nu _{x}\right >$ versus $\left <\delta \right >$ for $V_{Q}=\SI {18.3}{\kilo \volt }$, where the slope of the fit line gives an estimate of $\left .d\nu _{x}\middle /d\delta \right .$. This data was collected during Run-2\nobreakspace  {}with the \SI {180}{\degree } horizontal fiber harp. \leavevmode {\color {red}\textit  {What do we really want to show?}}\relax }}{16}{figure.caption.44}\protected@file@percent }
\newlabel{fig:tune_vs_p}{{21}{16}{\textcolor {orange}{Dat} A measurement of $\left <\nu _{x}\right >$ versus $\left <\delta \right >$ for $V_{Q}=\SI {18.3}{\kilo \volt }$, where the slope of the fit line gives an estimate of $\left .d\nu _{x}\middle /d\delta \right .$. This data was collected during \runtwo ~with the \SI {180}{\degree } horizontal fiber harp. \textcolor {red}{\textit {What do we really want to show?}}\relax }{figure.caption.44}{}}
\@writefile{lot}{\contentsline {table}{\numberline {III}{\ignorespaces  \leavevmode {\color {orange}Dat} 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}. \leavevmode {\color {red}\textit  {Should the field indices also be calculated using the discrete model?}}\relax }}{16}{table.caption.47}\protected@file@percent }
\newlabel{tab:n_nu_estim}{{III}{16}{\textcolor {orange}{Dat} 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}. \textcolor {red}{\textit {Should the field indices also be calculated using the discrete model?}}\relax }{table.caption.47}{}}
\newlabel{sec:closedorbit}{{V\tmspace  +\thinmuskip {.1667em}C}{16}{}{section*.48}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C}Closed Orbit \& Quadrupole Distortions}{16}{section*.48}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces \leavevmode {\color {orange}Dat} An estimate of $\left .d\nu _{x}\middle /d\delta \right .$ versus $V_{Q}$ that is based on fiber harp data. This data was collected during Run-2\nobreakspace  {}with the \SI {180}{\degree } horizontal fiber harp. \leavevmode {\color {red}\textit  {What do we really want to show?}}\relax }}{17}{figure.caption.45}\protected@file@percent }
\newlabel{fig:chromat_vs_vq}{{22}{17}{\textcolor {orange}{Dat} An estimate of $\left .d\nu _{x}\middle /d\delta \right .$ versus $V_{Q}$ that is based on fiber harp data. This data was collected during \runtwo ~with the \SI {180}{\degree } horizontal fiber harp. \textcolor {red}{\textit {What do we really want to show?}}\relax }{figure.caption.45}{}}
\newlabel{sec:system}{{VI}{17}{}{section*.52}{}}
\@writefile{toc}{\contentsline {section}{\numberline {VI} Systematics}{17}{section*.52}\protected@file@percent }
\newlabel{fig:nu_x_vs_v}{{23a}{17}{$\left <\nu _{x}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.46}{}}
\newlabel{sub@fig:nu_x_vs_v}{{a}{17}{$\left <\nu _{x}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.46}{}}
\newlabel{fig:nu_y_vs_v}{{23b}{17}{$\left <\nu _{y}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.46}{}}
\newlabel{sub@fig:nu_y_vs_v}{{b}{17}{$\left <\nu _{y}\right >$ vs. $V_{\textnormal {quad}}$\relax }{figure.caption.46}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces \leavevmode {\color {orange}Dat} Average tune data (blue circular points), see Table\nobreakspace  {}\ref  {tab: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 {red}\textit  {Harmonize notation; update with Run-2\nobreakspace  {}fiber harp data; do we need to compare to Run-1\nobreakspace  {}data; should we add gm2ringsim tune curves.}}\relax }}{17}{figure.caption.46}\protected@file@percent }
\newlabel{fig:nu_vs_v}{{23}{17}{\textcolor {orange}{Dat} Average tune data (blue circular points), see Table~\ref {tab: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 {red}{\textit {Harmonize notation; update with \runtwo ~fiber harp data; do we need to compare to \runone ~data; should we add gm2ringsim tune curves.}}\relax }{figure.caption.46}{}}
\citation{Yamamoto:2002bb,Froemming:IPAC2018-WEPAF014}
\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces \leavevmode {\color {orange}Mike and David T.} Computed horizontal (solid) and vertical (dashed) closed orbit distortions due to quadrupole plate alignment errors (red) and main dipole field errors (blue); the heavy black curves are the sum of the effects from the quadrupole and dipole errors. \leavevmode {\color {red}\textit  {Check with field, tracker, \& quad experts.}}\relax }}{18}{figure.caption.50}\protected@file@percent }
\newlabel{fig:orbitdistort}{{24}{18}{\textcolor {orange}{Mike and David T.} Computed horizontal (solid) and vertical (dashed) closed orbit distortions due to quadrupole plate alignment errors (red) and main dipole field errors (blue); the heavy black curves are the sum of the effects from the quadrupole and dipole errors. \textcolor {red}{\textit {Check with field, tracker, \& quad experts.}}\relax }{figure.caption.50}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces \leavevmode {\color {orange}Mike and David T.} Computed horizontal (solid) and vertical (dashed) amplitude function distortions due to quadrupole plate alignment errors (red) and main dipole field gradient errors (blue); the heavy black curves are the sum of the effects from the quadrupole and dipole errors. \leavevmode {\color {red}\textit  {Harmonize notation; check with field, tracker, \& quad experts.}}\relax }}{18}{figure.caption.51}\protected@file@percent }
\newlabel{fig:betadistort}{{25}{18}{\textcolor {orange}{Mike and David T.} Computed horizontal (solid) and vertical (dashed) amplitude function distortions due to quadrupole plate alignment errors (red) and main dipole field gradient errors (blue); the heavy black curves are the sum of the effects from the quadrupole and dipole errors. \textcolor {red}{\textit {Harmonize notation; check with field, tracker, \& quad experts.}}\relax }{figure.caption.51}{}}
\@writefile{lot}{\contentsline {table}{\numberline {IV}{\ignorespaces \leavevmode {\color {orange}Mike} Quadrupole in situ alignment data; $dx$ and $dy$ indicate the displacement of the center of quadrupole plate pairs which will generate steering, while $dax$ and $day$ are the deviations in plate pair separation which will affect the focusing strength of the quadrupoles.\relax }}{18}{table.caption.49}\protected@file@percent }
\newlabel{tab:tmp_quad_align}{{IV}{18}{\textcolor {orange}{Mike} Quadrupole in situ alignment data; $dx$ and $dy$ indicate the displacement of the center of quadrupole plate pairs which will generate steering, while $dax$ and $day$ are the deviations in plate pair separation which will affect the focusing strength of the quadrupoles.\relax }{table.caption.49}{}}
\newlabel{sec:fit_model}{{VI\tmspace  +\thinmuskip {.1667em}A}{18}{}{section*.53}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A} Coherent Beam Motion \& Detector Acceptance}{18}{section*.53}\protected@file@percent }
\citation{Bennett:2006fi}
\newlabel{fig:radialdist}{{26a}{19}{Horizontal (radial) distribution.\relax }{figure.caption.54}{}}
\newlabel{sub@fig:radialdist}{{a}{19}{Horizontal (radial) distribution.\relax }{figure.caption.54}{}}
\newlabel{fig:verticaldist}{{26b}{19}{Vertical distribution.\relax }{figure.caption.54}{}}
\newlabel{sub@fig:verticaldist}{{b}{19}{Vertical distribution.\relax }{figure.caption.54}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces \leavevmode {\color {orange}David R.} Decay muon distributions measured by the\nobreakspace  {}\leavevmode {\color {red}\textit  {??}} straw tracker station for a subset of preliminary Run-1\nobreakspace  {}data. The data is not corrected for acceptance or resolution. \leavevmode {\color {red}\textit  {Should the y-axis label read $\left .dN\middle /dy\right .$ or counts; remove timestamp and directory information; check with tracker experts.}}\relax }}{19}{figure.caption.54}\protected@file@percent }
\newlabel{fig:positiondist}{{26}{19}{\textcolor {orange}{David R.} Decay muon distributions measured by the~\textcolor {red}{\textit {??}} straw tracker station for a subset of preliminary \runone ~data. The data is not corrected for acceptance or resolution. \textcolor {red}{\textit {Should the y-axis label read $\left .dN\middle /dy\right .$ or counts; remove timestamp and directory information; check with tracker experts.}}\relax }{figure.caption.54}{}}
\@writefile{lot}{\contentsline {table}{\numberline {V}{\ignorespaces  \leavevmode {\color {orange}Jason} Important beam frequencies that affect the Run-1\nobreakspace  {}decay positron spectra for the \SI {18.3}{\kilo \volt } EQS storage set-point \leavevmode {\color {red}\textit  {[Update with Run-2\nobreakspace  {}based values]}}. The tune values used to calculate the frequencies are taken from Table\nobreakspace  {}\ref  {tab:n_nu_estim}.\relax }}{20}{table.caption.55}\protected@file@percent }
\newlabel{tab:beamfreq}{{V}{20}{\textcolor {orange}{Jason} Important beam frequencies that affect the \runone ~decay positron spectra for the \SI {18.3}{\kilo \volt } EQS storage set-point \textcolor {red}{\textit {[Update with \runtwo ~based values]}}. The tune values used to calculate the frequencies are taken from Table~\ref {tab:n_nu_estim}.\relax }{table.caption.55}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {27}{\ignorespaces \leavevmode {\color {orange}Jason} The Fast Fourier transform (FFT) frequency spectrum for 5-parameter fit residuals from a decay positron time spectrum. Specifically, the magnitude of the FFT amplitude is shown. This subset of Run-1\nobreakspace  {}data was taken at $V_{Q}=\SI {18.3}{\kilo \volt }$. \leavevmode {\color {red}\textit  {Final unless David S. wants to make an updated version.}}\relax }}{20}{figure.caption.56}\protected@file@percent }
\newlabel{fig:residfft}{{27}{20}{\textcolor {orange}{Jason} The Fast Fourier transform (FFT) frequency spectrum for 5-parameter fit residuals from a decay positron time spectrum. Specifically, the magnitude of the FFT amplitude is shown. This subset of \runone ~data was taken at $V_{Q}=\SI {18.3}{\kilo \volt }$. \textcolor {red}{\textit {Final unless David S. wants to make an updated version.}}\relax }{figure.caption.56}{}}
\newlabel{eq:bnlfitfunc}{{20}{20}{}{equation.6.20}{}}
\citation{Bennett:2006fi}
\newlabel{eq:w_cbo_drift}{{21}{21}{}{equation.6.21}{}}
\newlabel{eq:inst_par_dep}{{22}{21}{}{equation.6.22}{}}
\newlabel{eq:moments}{{23}{21}{}{equation.6.23}{}}
\newlabel{eq:avg_par_dep}{{24}{21}{}{equation.6.24}{}}
\newlabel{eq:form_of_moments}{{25}{21}{}{equation.6.25}{}}
\newlabel{sec:pitch}{{VI\tmspace  +\thinmuskip {.1667em}B}{22}{}{section*.57}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B}Pitch Correction}{22}{section*.57}\protected@file@percent }
\newlabel{eq:betadots}{{26}{22}{}{equation.6.26}{}}
\newlabel{sec:efield}{{VI\tmspace  +\thinmuskip {.1667em}C}{22}{}{section*.58}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C} E-field Correction}{22}{section*.58}\protected@file@percent }
\citation{Orlov:2002ag}
\@writefile{lof}{\contentsline {figure}{\numberline {28}{\ignorespaces \leavevmode {\color {orange}David R.} Fourier analysis of the fast rotation signal and parameterized fit give the muon equilibrium radial (closed orbit) distribution revolution. \leavevmode {\color {red}\textit  {Harmonize notation; do we want lines connecting the points.}}\relax }}{23}{figure.caption.59}\protected@file@percent }
\newlabel{fig:fourierdebunching}{{28}{23}{\textcolor {orange}{David R.} Fourier analysis of the fast rotation signal and parameterized fit give the muon equilibrium radial (closed orbit) distribution revolution. \textcolor {red}{\textit {Harmonize notation; do we want lines connecting the points.}}\relax }{figure.caption.59}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {29}{\ignorespaces \leavevmode {\color {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. \leavevmode {\color {red}\textit  {Harmonize notation; should right-side y-axis label read $\left .dN\middle /dx_{e}\right .$ or counts; should x-axis range go from \SI {\pm 45}{\milli \meter }.}}\relax }}{23}{figure.caption.60}\protected@file@percent }
\newlabel{fig:efield_cor}{{29}{23}{\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. \textcolor {red}{\textit {Harmonize notation; should right-side y-axis label read $\left .dN\middle /dx_{e}\right .$ or counts; should x-axis range go from \SI {\pm 45}{\milli \meter }.}}\relax }{figure.caption.60}{}}
\newlabel{sec:early-to-late}{{VI\tmspace  +\thinmuskip {.1667em}D}{23}{}{section*.61}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {D} Spin Correlations \& Early-to-late Effects}{23}{section*.61}\protected@file@percent }
\newlabel{eq:cos_phase}{{28}{23}{}{equation.6.28}{}}
\newlabel{eq:phase_series}{{29}{23}{}{equation.6.29}{}}
\newlabel{eq:spin_corr_def}{{29}{24}{}{equation.6.29}{}}
\newlabel{eq:early_to_late_def}{{29}{24}{}{equation.6.29}{}}
\newlabel{eq:spin_mom_corr_def}{{30}{24}{}{equation.6.30}{}}
\newlabel{eq:precess_bend_mag}{{30}{24}{}{equation.6.30}{}}
\newlabel{eq:lorentz_factor}{{31}{24}{}{equation.6.31}{}}
\newlabel{eq:spin_tune}{{31}{24}{}{equation.6.31}{}}
\citation{lostmuons}
\newlabel{eq:precess_ring}{{32}{25}{}{equation.6.32}{}}
\newlabel{eq:mom_early_to_late_def_a}{{33}{25}{}{equation.6.33}{}}
\newlabel{eq:mom_early_to_late_def_a}{{33}{25}{}{equation.6.33}{}}
\newlabel{sec:spin_res}{{VI\tmspace  +\thinmuskip {.1667em}E}{25}{}{section*.63}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {E} Spin Resonances}{25}{section*.63}\protected@file@percent }
\newlabel{sec:lost_muons}{{VI\tmspace  +\thinmuskip {.1667em}F}{25}{}{section*.64}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {F} Lost Muons}{25}{section*.64}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {30}{\ignorespaces \leavevmode {\color {orange}Mike} Horizontal and vertical muon spin component distributions near the entrance to the Storage Ring for \SI {\sim e5}{} muons born in the Muon Campus M2-line, M3-line, and Delivery Ring (DR). These distributions have been generated using the G4beamline model of the Muon Campus lattice. \leavevmode {\color {red}\textit  {Harmonize notation; do the spin units make sense.}}\relax }}{26}{figure.caption.62}\protected@file@percent }
\newlabel{fig:beamline_spin_distr}{{30}{26}{\textcolor {orange}{Mike} Horizontal and vertical muon spin component distributions near the entrance to the Storage Ring for \SI {\sim e5}{} muons born in the Muon Campus M2-line, M3-line, and Delivery Ring (DR). These distributions have been generated using the G4beamline model of the Muon Campus lattice. \textcolor {red}{\textit {Harmonize notation; do the spin units make sense.}}\relax }{figure.caption.62}{}}
\newlabel{sec:conc}{{VII}{26}{}{section*.67}{}}
\@writefile{toc}{\contentsline {section}{\numberline {VII} Conclusion}{26}{section*.67}\protected@file@percent }
\bibdata{g-2-srbdNotes,g-2-srbd}
\bibcite{Charpak:1962zz}{{1}{1962}{{Charpak\ \emph  {et~al.}}}{{Charpak \emph  {et~al.}}}}
\bibcite{Bailey:1978mn}{{2}{1979}{{Bailey\ \emph  {et~al.}}}{{Bailey \emph  {et~al.}}}}
\@writefile{lof}{\contentsline {figure}{\numberline {31}{\ignorespaces \leavevmode {\color {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. \leavevmode {\color {red}\textit  {Harmonize notation; update with Run-2\nobreakspace  {}calo data; do we need to compare to Run-1\nobreakspace  {}data; add COSY curve.}}\relax }}{27}{figure.caption.65}\protected@file@percent }
\newlabel{fig:lostmuonsscan}{{31}{27}{\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. \textcolor {red}{\textit {Harmonize notation; update with \runtwo ~calo data; do we need to compare to \runone ~data; add COSY curve.}}\relax }{figure.caption.65}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {32}{\ignorespaces \leavevmode {\color {orange}David R.} Vertical displacement of the centroid at the \SI {180}{\degree } tracker during the scraping cycle. \leavevmode {\color {red}\textit  {Check with tracker experts.}}\relax }}{27}{figure.caption.66}\protected@file@percent }
\newlabel{fig:injvert}{{32}{27}{\textcolor {orange}{David R.} Vertical displacement of the centroid at the \SI {180}{\degree } tracker during the scraping cycle. \textcolor {red}{\textit {Check with tracker experts.}}\relax }{figure.caption.66}{}}
\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{27}{section*.68}\protected@file@percent }
\@writefile{toc}{\appendix }
\@writefile{toc}{\contentsline {section}{\numberline {A}An Appendix}{27}{section*.69}\protected@file@percent }
\newlabel{app:subsec}{{A\tmspace  +\thinmuskip {.1667em}1}{27}{}{section*.70}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1}An Appendix Subsection}{27}{section*.70}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {}References}{27}{section*.71}\protected@file@percent }
\bibcite{Bennett:2006fi}{{3}{2006}{{Bennett\ \emph  {et~al.}}}{{Bennett \emph  {et~al.}}}}
\bibcite{Bennett:2008dy}{{4}{2009}{{Bennett\ \emph  {et~al.}}}{{Bennett \emph  {et~al.}}}}
\bibcite{Grange:2015fou}{{5}{2015}{{Grange\ \emph  {et~al.}}}{{Grange \emph  {et~al.}}}}
\bibcite{Mohr:2015ccw}{{6}{2016}{{Mohr\ \emph  {et~al.}}}{{Mohr \emph  {et~al.}}}}
\bibcite{Tanabashi:2018oca}{{7}{2018}{{Tanabashi\ \emph  {et~al.}}}{{Tanabashi \emph  {et~al.}}}}
\bibcite{fermimuondept}{{8}{}{{fer}}{{}}}
\bibcite{Stratakis:2017uci}{{9}{2017}{{Stratakis\ \emph  {et~al.}}}{{Stratakis \emph  {et~al.}}}}
\bibcite{Stratakis:2019sun}{{10}{2019}{{Stratakis\ \emph  {et~al.}}}{{Stratakis \emph  {et~al.}}}}
\bibcite{Hubbard:1973ur}{{11}{1973}{{Hubbard\ \emph  {et~al.}}}{{Hubbard \emph  {et~al.}}}}
\bibcite{Brown:2013idd}{{12}{2013}{{Brown\ \emph  {et~al.}}}{{Brown \emph  {et~al.}}}}
\bibcite{Morgan:2003zza}{{13}{2003}{{Morgan}}{{}}}
\bibcite{Fienberg:2014kka}{{14}{2015}{{Fienberg\ \emph  {et~al.}}}{{Fienberg \emph  {et~al.}}}}
\bibcite{Kaspar:2016ofv}{{15}{2017}{{Kaspar\ \emph  {et~al.}}}{{Kaspar \emph  {et~al.}}}}
\bibcite{Prigl:1996fpk}{{16}{1996}{{Prigl\ \emph  {et~al.}}}{{Prigl \emph  {et~al.}}}}
\bibcite{Danby:2001eh}{{17}{2001}{{Danby\ \emph  {et~al.}}}{{Danby \emph  {et~al.}}}}
\bibcite{Semertzidis:2003zs}{{18}{2003}{{Semertzidis\ \emph  {et~al.}}}{{Semertzidis \emph  {et~al.}}}}
\bibcite{Crnkovic:IPAC2018-WEPAF015}{{19}{2018}{{Crnkovic\ \emph  {et~al.}}}{{Crnkovic \emph  {et~al.}}}}
\bibcite{Yamamoto:2002bb}{{20}{2002}{{Yamamoto\ \emph  {et~al.}}}{{Yamamoto \emph  {et~al.}}}}
\bibcite{Froemming:IPAC2018-WEPAF014}{{21}{2018}{{Froemming\ \emph  {et~al.}}}{{Froemming \emph  {et~al.}}}}
\bibcite{Schreckenberger:IPAC2018-THPML093}{{22}{2018}{{Schreckenberger\ \emph  {et~al.}}}{{Schreckenberger \emph  {et~al.}}}}
\bibcite{g4beamline}{{23}{}{{g4b}}{{}}}
\bibcite{Agostinelli:2002hh}{{24}{2003}{{Agostinelli\ \emph  {et~al.}}}{{Agostinelli \emph  {et~al.}}}}
\bibcite{Sagan:2006sy}{{25}{2006}{{Sagan}}{{}}}
\bibcite{Poole:2011aaa}{{26}{2011}{{Poole\ \emph  {et~al.}}}{{Poole \emph  {et~al.}}}}
\bibcite{Poole:2012aaa}{{27}{2012}{{Poole\ \emph  {et~al.}}}{{Poole \emph  {et~al.}}}}
\bibcite{Orlov:2002ag}{{28}{2002}{{Orlov\ \emph  {et~al.}}}{{Orlov \emph  {et~al.}}}}
\bibstyle{apsrev4-2}
\citation{REVTEX42Control}
\citation{apsrev42Control}
\xwm@secstopagerange{{I}{1},{II}{2},{II}{2},{II}{2},{II}{4},{III}{5},{IV}{6},{IV}{6},{IV}{7},{IV}{7},{IV}{8},{IV}{8},{IV}{8},{IV}{8},{IV}{8},{V}{9},{V}{11},{V}{11},{V}{16},{VI}{17},{VI}{18},{VI}{22},{VI}{22},{VI}{23},{VI}{25},{VI}{25},{VII}{26},{A}{27},{10000}{28}}
\newlabel{LastBibItem}{{28}{28}{}{section*.71}{}}
\newlabel{xwmlastpage}{{A\protect \leavevmode@ifvmode \kern +.1667em\relax 1}{28}{\relax }{section*.71}{}}
\newlabel{LastPage}{{}{28}{}{}{}}