\contentsline {title}{Muon g-2 storage ring beam and spin dynamics}{1}{section*.2}% 
\contentsline {abstract}{Abstract}{2}{section*.1}% 
\tocdepth@munge 
\contentsline {section}{\numberline {}Contents}{2}{section*.3}% 
\tocdepth@restore 
\contentsline {section}{\numberline {I} Introduction}{3}{section*.4}% 
\contentsline {section}{\numberline {II}Pitch}{4}{section*.5}% 
\contentsline {subsection}{\numberline {A}Pitch Correction}{4}{section*.6}% 
\contentsline {section}{\numberline {III} Electric Field}{6}{section*.7}% 
\contentsline {subsection}{\numberline {A} E-field Correction}{6}{section*.8}% 
\contentsline {section}{\numberline {IV}Fast Rotation}{7}{section*.9}% 
\contentsline {subsection}{\numberline {A}Fourier method}{8}{section*.10}% 
\contentsline {subsubsection}{\numberline {1}Start time}{9}{section*.11}% 
\contentsline {subsection}{\numberline {B}9 parameter fit}{11}{section*.12}% 
\contentsline {subsection}{\numberline {C}Momentum time correlation}{11}{section*.13}% 
\contentsline {section}{\numberline {V} Betatron Oscillations and E-field Systematic}{16}{section*.14}% 
\contentsline {subsection}{\numberline {}Electrostatic quadrupole nonlinearity}{16}{section*.15}% 
\contentsline {subsection}{\numberline {}Path length}{18}{section*.16}% 
\contentsline {subsection}{\numberline {}E-field correction}{19}{section*.17}% 
\contentsline {subsection}{\numberline {}Quadrupole Nonlinearity}{19}{section*.18}% 
\contentsline {section}{\numberline {}Efield and pitch and Quadrupole Nonlinearity}{21}{section*.19}% 
\contentsline {subsection}{\numberline {}Electric field contribution}{22}{section*.20}% 
\contentsline {subsection}{\numberline {}Pitch}{22}{section*.21}% 
\contentsline {section}{\numberline {}Simulation of Efield and pitch contributions to $\omega _a$}{24}{section*.22}% 
\contentsline {section}{\numberline {}References}{30}{section*.23}%