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\begin{document}
\begin{titlepage}
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\begin{center}
{\LARGE \bf
Research Plan for Spin Physics at RHIC}
\end{center}
\par \vspace{2mm}
\par \vspace{2mm}
\begin{center} {\large \bf Abstract}
\end{center}
\begin{quote}
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\section{Accelerator performance}
Polarized proton beams were accelerated, stored and collided in RHIC at a
proton energy of 100~GeV. The average store luminosity reached $4\times
10^{30}$cm$^{-2}$s$^{-1}$, and the average store polarization 40\% (see
Tab.~\ref{tab:rhic}). Over the next 4 years we aim to reach the Enhanced
Luminosity goal for polarized protons, consisting of an average store
luminosity of
\vspace*{-3mm}
\begin{itemize}
  \item {\bf \hspace*{1.5mm} 60$\times$10$^{30}$cm$^{-2}$s$^{-1}$ for 100 GeV}
  proton energy, and
  \vspace*{-3mm}
  \item {\bf 150$\times$10$^{30}$cm$^{-2}$s$^{-1}$ for 250 GeV} proton energy,
  \vspace*{-3mm}
\end{itemize}
\vspace*{-1mm}
both with an {\bf average store polarization of 70\%}. Tab.~\ref{tab:rhic}
gives a projection of the luminosity and polarization evolution through FY2008.
Luminosity numbers are given for 100~GeV proton energy and one interaction
point, with collisions at two interaction points. For operation with more
than two experiments, the luminosity per interaction point is reduced due
to an increased beam-beam interaction. For each year the maximum
achievable luminosity and polarization is projected. Projections over several
years are not very reliable and should only be seen as guidance for the average
annual machine improvements needed to reach the goal. 
%We do not give a minimum projection as we usually do in Ref.~\cite{RhicProj},
%since the minimum projection is based on proven performance, and no long 
%polarized proton run was done so far. 
We assume that 10 weeks of physics running are scheduled every year to 
allow for commissioning of the improvements and development of the machine 
performance.

\begin{table}[tbh]
\centering
\caption{Maximum projected RHIC polarized proton luminosities through FY2008.
Delivered luminosity numbers are given for 100~GeV proton energy and one 
interaction point, with collisions at two interaction points. 10~weeks of 
physics operation per year are assumed.}\label{tab:rhic}
\small
\begin{tabular}{lcccccccc}
\hline\hline
Fiscal year              &           & 2002A & 2003A & 2004A & 2005E & 2006E & 2007E & 2008E \\
\hline
No of bunches            & ...       & 55  & 55  & 56  & 79  & 79  & 100 & 112 \\
Protons/bunch, initial   & $10^{11}$ & 0.7 & 0.7 & 0.7 & 1.0 & 1.4 & 2.0 & 2.0 \\
$\beta^{*}$              & m         & 3   & 1   & 1   & 1   & 1   & 1   & 1   \\
Peak luminosity          & \hspace*{-9mm} $10^{30}$cm$^{-2}$s$^{-1}$ & 2   & 6 & 6 & 16 & 31 & 80 & 89 \\
Average luminosity       & \hspace*{-9mm} $10^{30}$cm$^{-2}$s$^{-1}$ & 1.5 & 3 & 4 &  9 & 21 & 53 & 60 \\
Time in store              & \%        & 30  & 41  & 41  & 50  & 53  & 56   & 60   \\
Max luminosity/week        & pb$^{-1}$ & 0.2 & 0.6 & 0.9 & 2.8 & 6.6 & 18.0 & 21.6 \\
Max integrated luminosity  & pb$^{-1}$ & 0.5 & 1.6 & 3   & 20  & 46  & 126  & 151  \\
Average store polarization & \%        & 15  & 30  & 40  & 45  & 65  & 70   & 70   \\
Max LP$^4$/week            & nb$^{-1}$ & 0.1 & 5   & 23  & 120 & 1180& 4330 & 5190 \\
\hline\hline
\end{tabular}
\normalsize
\end{table}

In Fig.~\ref{fig:Lumi} the integrated luminosity delivered to one experiment
is shown through FY2012 for two scenarios: 10 weeks of physics operation per
year, and 10 weeks of physics operation every other year. 
For every projected year shown in Fig.~\ref{fig:Lumi} the weekly luminosity 
starts at 25\% of the final value, and increases linearly in time to the 
final value in 8 weeks. During the remaining weeks the weekly luminosity is 
assumed to be constant. For the maximum projection the values in 
Tab.~\ref{tab:rhic} are used as final values until FY2008. For later years 
the FY2008 values are assumed with no further improvement. The minimum 
projection is one third of the maxium projection, based on past experience
in projecting heavy ion luminosities~\cite{RhicProj}.

For the scenario with 10 weeks of physics operation per year, the assumed 
proton energy is 100~GeV until FY2008, and 250~GeV thereafter. For the 
scenario with 10 weeks every other year, the assumed proton energy is 100~GeV 
throughout the entire period to reach the physics goal.

For the scenario with 10 weeks of physics operation every
other year, the final values are not increased in years without proton
operation, since no time is available to develop the machine performance. Thus
in our projections we reach the Enhanced Luminosity goal in FY2008 with 10 
week physics operation per year, but need until FY2011 with 10 weeks of 
physics operation every other year.
For operation at 250~GeV proton energy, the luminosity projections in 
Tab.~\ref{tab:rhic} need to be multiplied by 2.5. We expect no significant 
reduction in the averages store polarization after full commissioning of 
polarized proton ramps to 250~GeV.

\begin{figure}[tbh]
\begin{center}
\epsfig{figure=LumiProjection.eps,width=1.0\textwidth}
\end{center}
\vspace*{-7mm}
\caption{Minimum and Maximum projected integrated luminosity through FY2012.
Delivered luminosity numbers are given for one interaction point, with 
collisions at two interaction points. For the scenario with 10 weeks of 
physics operation per year, the assumed proton energy is 100~GeV until FY2008,
and 250~GeV thereafter. For the scenario with 10 weeks every other year, the
assumed proton energy is 100~GeV throughout the entire period.\label{fig:Lumi}}
\end{figure}

\subsection{Polarization limitations}
The RHIC beam polarization at 100~GeV is currently limited by the AGS beam
polarization transmission efficiency of about 70\%, and the source
polarization. With the installation of a new solenoid in FY2005, the source
polarization is expected to increase from 80\% to 85\%. The existing AGS
polarized proton setup includes a 5\% warm helical snake for overcoming
imperfection spin depolarizing resonances and an RF dipole for overcoming 4
strong intrinsic spin resonances. This setup has two drawbacks:
\vspace*{-5mm}
\begin{enumerate}
\item All the weak intrinsic spin resonances are crossed with no correction
 and result in a total depolarization of about 16\%.
 \vspace*{-3mm}
\item Operation with the RF dipole still leads to about 15\%
 depolarization.
 \vspace*{-3mm}
\end{enumerate}
\vspace*{-0mm}
In addition, the AGS has shown a dependence of the beam polarization
on the bunch intensity. These shortcomings can be overcome with the
installation of a new AGS cold snake, to be initially commissioned in 2005.
With a scheme that combines the AGS cold snake of 15\%, and the AGS warm snake
of 5\%, depolarizations at all imperfection and all intrinsic spin resonances
should be eliminated, making the AGS spin transparent with the exception of
some mismatch at injection and extraction~\cite{TwoSnk}.

Obtaining 70\% beam polarization in RHIC at 250~GeV is challenging because
of strong intrinsic and imperfection resonances beyond 100~GeV. Betatron tunes
and orbit distortions have to be controlled precisely to avoid depolarization
due to snake resonances. Simulations show that orbit distortions have to be
corrected to less than 0.3~mm rms. Orbit errors are introduced due to
misalignments and remain if the orbit cannot be corrected completely. A
realignment of the entire ring is scheduled for the 2005 summer shutdown.
Efforts continue to improve the existing beam position monitor system,
and the orbit correction techniques. A beam-based alignment technique is
under development. With the existing hardware and software, orbit distortions
of 1~mm rms were achieved, as measured by the beam position monitors.
Acceleration of polarized proton beams beyond 100~GeV is planned in 2005. The
result of this machine development effort will provide guidance for the
tolerable levels of machine misalignments and orbit errors.

\subsection{Luminosity limitations}
A number of effects limit the achievable luminosity. Currently the
bunch intensity is limited to about $1\times 10^{11}$ to maintain
maximum polarization in the AGS. This restriction should be removed with
the AGS cold snake. With intense bunches the beam-beam interaction
will limit the luminosity lifetime. With bunches of $2\times
10^{11}$ protons and 2 interaction points, the total beam-beam
induced tune spread will reach 0.015. Operation with more
than two collision will significantly reduce the luminosity
lifetime. High intensity beams also lead to a vacuum breakdown,
caused by electron clouds. In the warm sections, NEG coated beam
pipes are installed, that have a lower secondary electron yield,
and provide linear pumping. In the cold regions, additional pumps
are installed to improve the vacuum to an average value of
$10^{-5}$ Torr before the cool-down starts. With the PHENIX and
STAR detector upgrades, the vacuum system in the experimental
regions will also be improved.

Time in store can be gained through faster machine set-up, a reduction in
system failures, and the injection of multiple bunches in each AGS cycle.
We project that the time in store can be increased to about 100 hours per week,
or 60\% of calendar time.

\subsection{Polarimetry}
Beam polarization measurements in RHIC provide immediate information for 
performance monitoring, and absolute polarization to normalize the 
experimental asymmetry results. Two types of polarimeters are used. Both are 
based on small angle elastic scattering, where the sensitivity to the proton 
beam polarization comes from the interference between the electromagnetic 
spin-flip amplitude that generates the proton anomalous magnetic moment and 
the hadronic spin non-flip amplitude, and possibly a hadronic spin-flip term.  

One type of polarimeter uses a micro-ribbon carbon target, and provides
fast relative polarization measurements. The other type uses a polarized 
atomic hydrogen gas target, and provides slow absolute polarization 
measurements. In addition, both PHENIX and STAR have developed local 
polarimeters that measure the residual transverse polarization at their 
interaction points. These polarimeters are used to tune and monitor the spin 
rotators that provide longitudinal polarization for the experiments. They 
polarimeters are discussed in the Experiments section.

The fast proton-carbon polarimeter was first developed at the IUCF and the 
AGS~\cite{E950}. It measures the polarization in RHIC to 
$\Delta P=\pm$0.02 in 30 seconds. Measurements taken during a typical store in 
2004 are shown in Fig.~\ref{fig:pCPol}. A carbon ribbon target is introduced 
into the beam, and the left-right scattering asymmetry of recoil carbon ions 
is observed with silicon detectors inside the vacuum. The silicon detectors
observe the energy and time of flight of the recoil particles near 
90$^{\circ}$~\cite{polnote}. The detector selects carbon ions with a 
momentum transfer in the coulomb-nuclear interference (CNI) region, 
$-t=0.005-0.02$~(GeV/c)$^2$. In this region, the interference of the 
electromagnetic spin flip amplitude and the hadronic non-flip amplitude 
produces a calculable $t$-dependent asymmetry of 0.03 to 0.02. The cross 
section is large, so that the sensitivity to polarization is large.  A term 
from a hadronic spin flip amplitude is also possible and is reported in 
Ref.~\cite{E950}. This contribution is not calculable, so that this 
polarimeter must be calibrated using a beam of a known polarization.

\begin{figure}[tbh]
\begin{center}
\epsfig{figure=pCPol.eps,width=0.75\textwidth}
\end{center}
\vspace*{-7mm}
\caption{Measured polarization during one store of RHIC in 2004.
\label{fig:pCPol}}
\end{figure}

A polarized atomic hydrogen gas jet target was used for the first time in RHIC 
in 2004~\cite{jettgt}. The atoms are polarized with the Stern-Gehrlach process
to give electronic polarization, with rf transition to select proton 
polarization.  The atoms are focused in the RHIC beam region to 6 mm FWHM 
using the atomic hydrogen magnetic moment.  A Breit-Rabi polarimeter after the 
RHIC beam measures the polarization by cycling through rf transition states.  
The polarization was determined to be 0.92$\pm$0.02, including correction for 
the measured 2\% molecular fraction (4\% nuclear fraction) that is unpolarized.
Silicon detectors observe a left-right asymmetry for proton-proton elastic 
scattering in the CNI region, similar to the p-carbon polarimeters.  By 
measuring the asymmetry with respect to the target polarization sign, flipped 
every 8 minutes in 2004 by changing rf transitions, we measure the analyzing 
power for proton-proton elastic scattering.  This is shown in 
Fig.~\ref{fig:ppPol}. This
(preliminary) result from 2004 provides the most sensitive measurement of 
A$_N$, as can be seen in the figure.  By then measuring the left-right 
asymmetry with respect to the beam polarization sign, flipping each bunch 
(every 200 ns), we obtain the absolute beam polarization.  The absolute beam 
polarization was measured to about $\Delta P/P=7\%$ in 2004 (preliminary).

\begin{figure}[tbh]
\begin{center}
\epsfig{figure=ppPol.eps,width=0.75\textwidth}
\end{center}
\vspace*{-7mm}
\caption{A$_N$ for proton-proton elastic scattering in the CNI region, 
measured using the polarized atomic hydrogen jet target in RHIC~\cite{jettgt}. 
The open circles are data from E704 at Fermilab~\cite{E704CNI}.
\label{fig:ppPol}}
\end{figure}

A remaining issue is whether the carbon polarimeter calibration can be used 
for different detectors, from year to year, or whether it will be necessary to 
recalibrate each year using the jet target.  We can also choose to use the jet 
target as the RHIC polarimeter, with the carbon polarimeter used for 
corrections, for example for different polarization of the bunches and for
a polarization profile of the beams.

\subsection{Long-term perspective}
A number of ideas are pursued for long-term improvements of the
machine performance. RHIC II aims at increasing the heavy ion
luminosity by an order of magnitude through electron cooling. For
protons, cooling at store is not practical but pre-cooling at
injection might be beneficial. A further reduction of $\beta^*$,
especially at 250~GeV proton energy appears possible. Some benefits
may also come from stochastic cooling, currently developed for
heavy ions. We expect a luminosity improvement of a factor 2-5 for
polarized protons for RHIC II.

With a new interaction region design, the final focusing
quadrupoles can be moved closer to the interaction point, thus
allowing to squeeze $\beta^*$ further. This, however, makes some
space unavailable for the detectors. Additional increases in the
luminosity may come from a further increase in the number of
bunches, to close to 360, as is planned for eRHIC, or operation
with very long bunches. The latter requires a substantial R\&D
effort, as well as a new timing system for the detectors.

\section*{Acknowledgments}

\begin{thebibliography}{90}
\bibitem{RhicProj} T. Roser, W. Fischer, M. Bai, F. Pilat, ``RHIC Collider 
  Projections (FY2005-FY2008)'', 
  http://www.rhichome.bnl.gov/RHIC/Runs/RhicProjections/pdf
  (Last update on 16 August 2004).
\bibitem{TwoSnk} T. Roser et al., ``Acceleration of Polarized Beam Using Multiple Strong Partial Siberian Snakes.'', \it {Proceeding of European Particle Accelerator Conference}, Lucerne, Switzerland, 2004.
\bibitem{E950} J. Tojo et al., {\it Phys. Rev. Lett.} {\bf 89}, 052302 (2002).
\bibitem{polnote} O. Jinnouchi et al., RHIC/CAD Acc. Phys. Note 171 (2004),
\bibitem{jettgt} T. Wise et al., and H. Okada et al., Spin2004 Proceedings, 
Trieste, Italy, to be published; and talks in 
  http://www.ts.infn.it/events/SPIN2004/. 
\bibitem{E704CNI} N. Akchurin et al., {\it Phys. Rev.} {\bf D48}, 3026 (1993).
\end{thebibliography}
\end{document}