\section{Fringe Fields}
\subsection*{Introduction}
Understanding to a high accuracy the focusing effects of dipoles and
quadrupoles pays dividends in tuning time saved. If the elements are
quite long compared with aperture, accuracy is easily obtained. On the
other hand, when the fringe field is relatively long, its effect must be
well-understood. This applies both to linear effects and aberrations.
%\subsection*{Timeline}
%This is ongoing.
New beamlines are now designed knowing the effect of
fringe fields, so they are relatively more easily commissioned than has
been the case in the past. Older beamlines that have always been tuned
empirically are, one-by-one becoming treated more scientifically.
\subsection*{Results \& Progress}
It is of course possible to use the element field map in a ray-tracing
code. But this makes simple optics calculations very cumbersome. If only
the linear and lowest order aberration are important, one can ask ``How
much of the detail of the field map is needed?''. It turns out very
little. For example, the linear effect of the quadrupole can be
summarized exactly using only 3 parameters: effective length, effective
strength, and a fringe field parameter. And the lowest order (cubic force)
aberration depends not at all on the fringe field shape.
\begin{itemize}\footnotesize
\item R.\ Baartman, D.\ Kaltchev,
{\it Short Quadrupole Parametrization\/},
\href{http://lin12.triumf.ca/text/2007PAC/ShortQuads/THPAN005.html}
{Proc.\ 2007 Particle Accelerator Conference}.
\end{itemize}
These results are used to distill the field maps into a simple and
efficient form. For example, of the 100's of electrostatic quadrupoles
used in both ISAC and ISIS (the cyclotron injection line), almost all
are set to their theoretical values. This is in spite of the fact that
many are short compared with their aperture. Magnetic quadrupoles are
also being treated in this way. This has made the beam optics
calculations sufficiently efficient that beam envelopes can be
calculated continuously in a Graphical User Interface (GUI) as the
operator tunes the elements.