\relax \@writefile{toc}{\contentsline {section}{\numberline {6}Introduction to Ionization Cooling}{1}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Definitions}{1}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.1.1}WARNING}{1}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.1.2}emittance}{1}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.1.3}Partition Functions}{1}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.1.4}Heating Terms}{2}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.1.5}Emittance changes}{2}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Transverse Cooling}{2}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.1}Partition Functions}{2}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.2}Heating Terms}{3}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.3}Beam Divergence Angles}{5}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Focusing Systems}{6}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.1}Solenoid}{6}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.2}Current Carrying Rod}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.4}Longitudinal Cooling}{7}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.4.1}Energy Loss}{8}} \citation{perkins} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.4.2}Heating Terms}{9}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.4.3}rf and bunch length}{10}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.5}Energy Dependancies}{11}}