\clearpage
\section{Appendix A: BNL E-910, Low-Momentum Pion Production}
Inclusive pion cross sections in proton nucleus interactions are quite hard to
calculate due to the contribution of many different processes and are best
determined experimentally. Various event-generator codes used by the heavy-ion-%
physics community \cite{arc,mars,dpmjet} to simulate the cascade inside the
nucleus
indicate a pronounced peak in pion production at low momenta. Unfortunately,
there is very limited data in the literature for pion production at the low
end of the spectrum (below 200~MeV/$c$). These data also are essential for
calibrating the event generators for use in a realistic simulation of the
muon-collider front end.
Since many aspects of the targetry and pion capture/phase rotation depend on
the shape and magnitude of these spectra, the Muon Collider Collaboration has
allocated some resources to obtain critical results on pion production by
joining BNL experiment 910, which was capable of the necessary acceptance and
statistics.
By combining large acceptance with particle identification and high statistics,
data from E910 have allowed a systematic study of proton-nucleus interactions
as a function of the number of slow protons and pions
produced, rapidity loss of the leading particle, total transverse-energy
content, \etc
\begin{figure}[ht]
\begin{center}
\includegraphics[width=5in,height=2.5in]{E910detconf.eps}
\caption{Major detectors in E910. The MPS magnet around the TPC has been
omitted. The beam comes in from the left toward the target located
in front of the TPC, which is followed by the \v Cerenkov and
time-of-flight counters. The rectangular frames are wire chambers.}
\label{E910detconf}
\end{center}
\end{figure}
A simplified GEANT depiction of the E910 detector setup can be seen in
Fig.~\ref{E910detconf}. The main tracking detector was the EOS
time projection chamber (TPC) placed
inside the MPS magnet, downstream of the target to achieve almost full forward
acceptance for charged tracks, an accurate determination of the vertex position
using these tracks, and particle identification using ionization energy loss in
the P-10 gas volume. The TPC
was supplemented by proportional chambers placed upstream
for incoming beam track reconstruction, as well as by
drift chambers, a \v Cerenkov
counter, and a time of flight wall located downstream for improved momentum
resolution and particle id. A scintillating-fiber detector behind the target
was used as a multiplicity trigger for central collisions, and a scintillator
beam veto behind the TPC defined minimum-bias events, including interactions
that occur in the TPC gas.
Experiment 910 ran for 14 weeks in the A1 beamline at the AGS during
Spring~1996 using a proton beam on a target placed in the MPS spectrometer, and
collected over 20 million events, of which about a quarter are minimum bias
triggers for inclusive cross section measurements. The targets were varied in
material (Be, Cu, Au, U) and thickness (2-100\% interaction length)
and three different beam energies were used (6, 12.5 and 18~GeV/$c$).
This was the first and only run of this experiment so far. Since then,
the efforts of
the E910 collaboration have focused on careful analysis of the large
data sample obtained.
%Detailed breakdown of the data is shown in Table~\ref{E910data}.
A typical event in the TPC is shown in
Fig.~\ref{E910event}, and Fig.~\ref{E910chmult} shows the charged
multiplicity distribution in the TPC.
Figure~\ref{E910dedxpid} shows the $dE/dx$ energy loss \vs\
momentum for reconstructed tracks in the TPC, with clear separation of different
particle species \cite{Hiro}.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=3in]{E910event.eps}
\caption{Downstream view of an interaction in the Au target located
upstream of the TPC, showing hits reconstructed in the TPC.}
\label{E910event}
\end{center}
\end{figure}
\begin{figure}[ht]
\begin{center}
\includegraphics[width=3in]{E910chmult.eps}
\caption{Charged-track multiplicity in the TPC from the 2-mm-thick Au target
with a soft interaction trigger.}
\label{E910chmult}
\end{center}
\end{figure}
\begin{figure}[ht]
\begin{center}
\includegraphics[width=3in]{E910dedxpid.eps}
\caption{Ionization energy loss for tracks with 30 or more hits in the TPC.
The beam momentum was 18~GeV/$c$.
}
\label{E910dedxpid}
\end{center}
\end{figure}
An early tracking pass over a fraction of the data for
preliminary physics insight has been performed in March-April~1997.
Reliable tracking of particles down to 50~MeV/$c$ has been
accomplished in offline analysis. Approximate
shapes for total and transverse momentum spectra for pions from this pass are
shown in Figs.~\ref{E910au18} and \ref{E910cu18}. A calibration pass was
completed through August-October~1997, and a tracking pass over all the data
using the calibration constants obtained. Many improvements in tracking are
underway and should be complete in Fall~1998.
The data processing effort is being
carried out in parallel at many sites including BNL, Columbia, FSU, Iowa State,
LLNL and ORNL.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=3in]{E910au18.eps}
\caption{Forward pion spectrum for Au at 18~GeV/$c$. Particles to the
left of the vertical line at 225 MeV/$c$ would be captured by a 20-T,
15-cm-bore solenoid.}
\label{E910au18}
\end{center}
\end{figure}
\begin{figure}[ht]
\begin{center}
\includegraphics[width=3in,]{E910cu18.eps}
\caption{Forward pion spectrum for Cu at 18 GeV/$c$.}
\label{E910cu18}
\end{center}
\end{figure}
An important aspect of the pion
measurement in E910 is that the $dE/dx$ sampling in the TPC is the only means
of identification for particles below about 500~MeV/$c$, since these particles
either don't
reach any detectors downstream of the TPC or their momentum is not high enough
for particle id using time of flight or \v Cerenkov light.
However, there is a large amount
of overlap between the electron and muon/pion $dE/dx$ bands around 100-200
MeV/$c$, as
can be seen in Fig.~\ref{E910dedxslow} \cite{Hiro}. The electrons are
produced mostly from photon conversions to \ee pairs in the target, which has
enough radiation lengths to make the electron/pion ratio about one in
this momentum region for the 2\%-interaction-length Au target. Electrons
can be identified in the TPC by reconstructing \ee pairs.
The current tracking pass will produce better $dE/dx$ resolution based on
accurate TPC calibration, and will allow better separation of electrons and
pions.
An important question in interpreting results and validating event generators
is the size of the very slow, large-angle/backward component of the pion
spectrum. This will be addressed with E910 events in which beam-gas
interactions occurred in the TPC, allowing full $4\pi$
coverage for tracks produced in proton-Ar interactions.
A typical beam-gas event is shown in Fig.~\ref{E910beamgas}.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=4in]{E910beamgas.eps}
\caption{Side view of a beam-gas interaction in the TPC with complete
coverage for backward tracks.}
\label{E910beamgas}
\end{center}
\end{figure}
A publication on inclusive pion production based on E910 data is in preparation
and will come out later this year. Comparison with event generators also is
underway.
\clearpage
\section{Appendix B: High Intensity Performance and Upgrades at the AGS}
[This Appendix has been published separately as ref.~\cite{Roser98}.]
%%%%%%%%%
%\def\mco{\multicolumn}
%%%%%%%%
\subsection{Recent AGS High Intensity Performance}
Figure \ref{agscomplex} shows the present layout of the AGS-RHIC accelerator
complex. The high intensity proton beam of the AGS is used both for the
slow-extracted-beam (SEB) area (with many target stations to produce secondary
beams) and for the fast-extracted-beam (FEB) line (used for the production
of muons for the $g-2$ experiment and for high intensity target testing
for the spallation neutron sources and muon production targets for the muon
collider). The same FEB line also will be used for the transfer of beam
to RHIC.
\begin{figure}[htb]
\begin{center}
\includegraphics [width=5in,clip]{agscomplex.eps}
\caption{The AGS-RHIC accelerator complex.}
\label{agscomplex}
\end{center}
\end{figure}
The proton-beam intensity in the AGS has increased steadily over the
35-year existence of the AGS, but the most dramatic increase occurred over
the last
couple of years with the addition of the new AGS Booster
\cite{agsint95,Ahrens97}.
In Fig.~\ref{agsint} the history of the AGS intensity improvements is
shown, and
the major upgrades are indicated. The AGS Booster has one quarter the
circumference of the AGS and therefore allows four Booster beam pulses
to be stacked in the AGS at an injection energy of 1.5-1.9~GeV.
At this increased
energy, space-charge forces are much reduced, and this in turn allows
for the dramatic increase in the AGS beam intensity.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=3in,clip]{agsint97.eps}
\caption{The evolution of the proton beam intensity
in the Brookhaven AGS.}
\label{agsint}
\end{center}
\end{figure}
The 200-MeV LINAC is being used both as the injector into the Booster
and as an isotope production facility. A recent upgrade of the LINAC
rf system made it possible to operate at an average H$^{-}$ current of
150~$\mu$A and a maximum of $12\times 10^{13}$ H$^{-}$ per 500-$\mu$s
LINAC pulse for the isotope production target. Typical beam currents during
the 500-$\mu$s pulse are about
80~mA at the source, 60~mA after the 750-keV RFQ, 38~mA after the
first LINAC tank (10~MeV), and 37~mA at the end of the LINAC at 200~MeV.
The normalized beam emittance is about $2 \pi$ mm-mrad for 95\%
of the beam, and the beam energy spread is about $\pm 1.2$~MeV. A magnetic
fast chopper installed at 750~keV allows the shaping of the beam
injected into the Booster to avoid excessive beam loss.
The beam intensity achieved in the Booster surpassed the design goal
of $1.5\times 10^{13}$ protons per pulse and reached a peak value of
$2.3\times
10^{13}$ protons per pulse. This was achieved by very carefully correcting
all the important nonlinear orbit resonances, especially at the injection
energy of 200~MeV,
and by using the extra set of rf cavities that was installed for heavy-ion
operation as a second-harmonic rf system. The latter
allows for the creation of a flattened rf bucket, which gives longer
bunches
with lower space-charge forces. The fundamental rf system operated
with 90~kV, and the second-harmonic with 30~kV. The typical bunch
area was about 1.5~eV-s.
Even with the second-harmonic rf system
the incoherent space-charge tune shift can
reach one unit right at injection ($3\times 10^{13}$ protons,
norm.\ 95\% emittance: $50 \pi$ mm-mrad, bunching factor: 0.5).
Of course, such a large tune shift is not
sustainable, but the beam emittance growth and beam loss can be minimized
by accelerating rapidly during and after injection. Best conditions
are achieved by ramping the main field during injection with 3~T/s
increasing to 9~T/s after about 10~ms.
The quite-large nonlinear fields from eddy currents in the
Iconel vacuum chamber of the Booster are passively corrected
using correction windings on the vacuum
chamber that are driven by backleg windings \cite{Danby90}.
The AGS itself also had to be upgraded to be able to cope with the higher
beam intensity. During beam injection from the Booster, which cycles
with a
repetition rate of 7.5~Hz, the AGS needs to store the already transferred
beam bunches for about 0.4~s. During this time the beam is exposed to
the strong image forces from the vacuum chamber, which cause beam loss
from resistive-wall-coupled bunch-beam instabilities within
as short a time as a few-hundred
revolutions. A very powerful feedback system was installed that senses
any transverse movement of the beam and compensates with a correcting kick.
This transverse damper can deliver $\pm 160$~V to a pair of 50-$\Omega$,
1-m-long striplines. A recursive digital notch filter is used
in the feedback circuit to allow for accurate determination of the
average beam position and increased sensitivity to the unstable coherent
beam motion. This filter design is particularly important for the betatron
tune setting
of about 8.9, which is required to avoid the nonlinear octupole stopband
resonance at 8.75.
With an incoherent tune shift at the AGS injection energy of 0.1 to
0.2 it is still necessary, however, to correct the octupole stopband
resonances to avoid excessive beam loss.
To reduce the space-charge forces
further, the beam bunches in the AGS are lengthened by purposely mismatching
the bunch-to-bucket transfer from the Booster and then smoothing the bunch
distribution using a high-frequency 100-MHz dilution cavity. The
resulting reduction of the peak current helps both with coupled bunch
instabilities and stopband beam losses.
During acceleration, the AGS beam has to pass through the transition
energy after which the revolution time of higher-energy protons becomes longer
than for the lower-energy protons. This potentially unstable point during
the acceleration cycle was crossed very quickly with a new powerful transition-%
energy-jump system with only minimal losses even at the highest intensities.
The large lattice distortions introduced by the jump system prior to the
transition crossing severely limits the available aperture of the AGS,
in particular for momentum spread. Efforts to correct the distortions
using sextupoles have been partially successful \cite{vanAsselt95}.
After the transition energy, a very rapid, high-frequency
instability developed which could be avoided only by purposely further
increasing the bunch length using again the high-frequency dilution
cavity.
The peak beam intensity reached at the AGS extraction energy of 24~GeV
was $6.3\times 10^{13}$ protons per pulse, also exceeding the design
goal for this latest round of intensity upgrades. It also represents a world
record beam intensity for a proton synchrotron.
With a 1.6-s slow-extracted-beam spill, the average extracted beam
current was about 3~$\mu$A. This level of performance was reached quite
consistently over the last few years, and during
a typical 20 week run a total of $1 \times 10^{20}$ protons
is accelerated in the AGS to the extraction energy of 24~GeV.
At maximum beam intensity, about 30\% of the beam is lost at Booster
injection (200~MeV), 25\% during the transfer from Booster to AGS
(1.5~GeV), which includes losses during the 0.4-s storage time in the
AGS, and about 3\% is lost at transition (8~GeV). Although
activation levels are quite high, all machines still can be manually
maintained and repaired in a safe manner.
\begin{figure}[htb]
\begin{center}
\includegraphics[height=4in,clip]{barrier.eps}
\caption{Time-domain-stacking scheme using a barrier-bucket cavity.
The evolution of the longitudinal beam structure during the stacking process
is shown from top to bottom.}
\label{barrier}
\end{center}
\end{figure}
\subsection{Possible Future AGS Intensity Upgrades}
Currently the number of Booster beam pulses that can be accumulated
in the AGS is limited to four by the fact that the circumference of the AGS
is four times the circumference of the Booster. This limits the maximum beam
intensity in the AGS to four times the maximum Booster intensity, which
itself is limited to $2.5\times 10^{13}$ protons per pulse by the
space-charge forces at Booster injection. To overcome this limitation,
some sort of stacking will have to be used in the AGS. The most promising
scheme is stacking in the time domain.
To accomplish this, a cavity that produces
isolated rf buckets can be used to maintain a partially debunched beam
in the AGS and still leave an empty gap for filling in additional Booster
beam pulses. The stacking scheme is illustrated in Fig.~\ref{barrier}. It
makes
use of two isolated rf buckets to control the width of this gap. Isolated
bucket cavities, also called Barrier Bucket cavities, have been used
elsewhere \cite{fnal-barrier}. However, for this stacking scheme, a
high rf voltage will be needed to contain the large bunch area
of the high-intensity beam. An additional important advantage of this
scheme is that while the beam is partially debunched in the AGS, the
beam density and therefore space-charge forces are reduced by up to a factor
of two. A successful test of this scheme has recently been completed
\cite{ags-barrier}, and two 40-kV Barrier cavities are being installed in
the AGS with the aim of accumulating six Booster beam pulses in the
AGS to reach an intensity of about $1\times 10^{14}$ protons per pulse.
For further increases in the intensity, the space-charge forces at
Booster injection represent the main limitation. This could be overcome
by an energy upgrade of the LINAC to about 600~MeV, replacing
some of the present 200-MHz cavities with higher-gradient 400-MHz
cavities driven by klystrons. At 600 MeV, the space-charge limit at
Booster injection would be $5\times 10^{13}$ protons per pulse or
$2\times 10^{14}$ protons in the AGS for 4~cycles per AGS cycle.
As more Booster beam pulses are accumulated in the AGS, the reduction in the
overall duty cycle becomes more significant. For fast-extracted-beam
operation (FEB) the accumulation of four Booster pulses already contributes
significantly to the overall cycle time. With the addition of a 2-GeV
accumulator ring in the AGS tunnel, this
overhead time could be completely avoided. Such a ring could be built
rather inexpensively using low-field magnets.
The maximum repetition rate of the Linac and Booster is 10~Hz. Since
the circumference of the AGS is four times that of the Booster, a repetition
rate of 2.5~Hz would maintain a throughput of 80~$\mu$A through the whole
accelerator chain. Such an increase of the AGS repetition rate by a
factor of 2.5 could be achieved by an upgrade of the AGS main magnet power
supply only. The resulting beam power of 2~MW at 25~GeV corresponds to the
required proton driver performance needed for a demonstration muon-collider
project. The upgrades to the AGS complex are summarized in
Fig.~\ref{agscomplex_upgrade}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=5in,clip]{agscomplex_upgrades.eps}
\caption{Summary of intensity upgrades for the AGS.}
\label{agscomplex_upgrade}
\end{center}
\end{figure}