\relax 
\providecommand\hyper@newdestlabel[2]{}
\@writefile{toc}{\contentsline {section}{\numberline {0.1}Betatron Oscillations and E-field Systematic}{2}{section.0.1}}
\newlabel{eq:laplaciansolution}{{3}{2}{Electrostatic quadrupole nonlinearity}{equation.0.1.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Curvilinear coordinate system. The integrated path length for the part of the trajectory at $\rho > \rho _0$ is greater than the length of the path for $\rho < \rho _0$.}}{3}{figure.0.1}}
\newlabel{fg:pathlength}{{1}{3}{Curvilinear coordinate system. The integrated path length for the part of the trajectory at $\rho > \rho _0$ is greater than the length of the path for $\rho < \rho _0$}{figure.0.1}{}}
\newlabel{eq:sextpluspath}{{4}{3}{Path length}{equation.0.1.4}{}}
\newlabel{eq:sextpluspath2}{{5}{3}{Path length}{equation.0.1.4}{}}
\newlabel{eq:opposite}{{6}{3}{Path length}{equation.0.1.4}{}}
\newlabel{eq:avgefield}{{7}{4}{Path length}{equation.0.1.7}{}}
\newlabel{eq:ce}{{8}{4}{E-field correction}{equation.0.1.8}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Equilibrium radial distribution}}{5}{figure.0.2}}
\newlabel{fg:equilibrium}{{2}{5}{Equilibrium radial distribution}{figure.0.2}{}}
\citation{wanwei}
\citation{bmad}
\citation{mcmillan}
\newlabel{eq:mpoleexpansion}{{9}{6}{Multipoles Fitted to 3-D Field Map}{equation.0.1.9}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces }}{6}{table.0.1}}
\newlabel{tab:multipoles}{{1}{6}{}{table.0.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Electric field along the x-axis in the midplane (y=0). The green points are computed from the multipole expansion using Equation \nobreakspace  {}\ref  {eq:mpoleexpansion} and the coefficients in Table \nobreakspace  {}\ref  {tab:multipoles}. The 'purple' curve (hidden by the green points) are the values from the field map.}}{7}{figure.0.3}}
\newlabel{fg:efield}{{0.1}{7}{Multipoles Fitted to 3-D Field Map}{figure.0.3}{}}
\@setckpt{EfieldSystematic-analytic}{
\setcounter{page}{8}
\setcounter{equation}{9}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{0}
\setcounter{section}{1}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{3}
\setcounter{table}{1}
\setcounter{parentequation}{0}
\setcounter{r@tfl@t}{0}
\setcounter{subfigure}{0}
\setcounter{lofdepth}{1}
\setcounter{subtable}{0}
\setcounter{lotdepth}{1}
\setcounter{LT@tables}{0}
\setcounter{LT@chunks}{0}
\setcounter{Item}{0}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{1}
\setcounter{AM@survey}{0}
\setcounter{section@level}{1}
}