\section{The AGS as a Proton Driver}
\label{Proton:sec1}

After more than 40~years of operation, the AGS is still at the
heart of the Brookhaven hadron accelerator complex. This system
of accelerators presently comprises a 200~MeV linac for the
pre-acceleration of high intensity and polarized protons, two
Tandem Van de Graaff for the pre-acceleration of heavy ion
beams, a versatile Booster that allows for efficient injection of
all three types of beams into the AGS and, most recently, the two
RHIC collider rings that produce high luminosity heavy ion and
polarized proton collisions. For several years now, the AGS has
held  the world intensity record with more than $7\times 10^{13}$
protons accelerated in a single pulse.

We describe here possible upgrades to the AGS complex that would
meet the requirements for the proton beam driver for Neutrino Factory
operation. Those requirements are summarized in
Table~\ref{Proton:tb1} and a layout of the upgraded AGS is shown in
Fig.~\ref{Proton:fg1}. Since the present number of protons per
fill is already close to the required number, the upgrade focuses
on increasing the repetition rate and reducing beam losses (to
avoid excessive shielding requirements and to maintain the ability to service machine components by hand). It is also important to preserve
all the present capabilities of the AGS, in particular its role as
injector to RHIC.

The AGS Booster was built not only to allow the injection of any
species of heavy ion into the AGS, but to allow a fourfold
increase of the AGS intensity. It is one-quarter the
circumference  of the AGS with the same aperture. However, the
accumulation of four Booster loads in the AGS takes time, and is
therefore not well suited for high average beam power operation.
We are proposing here to build a superconducting upgrade to the
existing 200~MeV linac to reach an energy of 1.2~GeV for direct
$\textrm{H}^-$ injection into the AGS. This will be discussed in
Section~\ref{Proton:secSCL}. The minimum ramp time to full energy
is presently 0.5~s; this must be upgraded to reach the required
repetition rate of 2.5~Hz. Since the six bunches are extracted one
bunch at a time, as is presently done for the operation of the g-2
experiment, a 100~ms flattop is included, which leaves only 150~ms
for the ramp up or ramp down cycle. The required upgrade of the
AGS power supply will be described in Section~\ref{Proton:sec3}.
Finally, the increased ramp rate and the final bunch compression
require a substantial upgrade to the AGS rf system and improvements in the vacuum chamber as well. The rf upgrade will be
discussed in Section~\ref{Proton:sec4}.
%The final section describes possible upgrade paths toward a 4~MW operation.
\begin{table}[!thb]
\begin{center}
\caption{AGS proton driver parameters.}
\label{Proton:tb1}
\begin{tabular}{|lc|}
\hline
Total beam power (MW) &1 \\
Beam energy (GeV)     &24 \\
Average beam current $(\mu A)$  &42\\
Cycle time (ms)& 400 \\
Number of protons per fill &$1\times 10^{14}$\\
Average circulating current (A) & 6 \\
No. of bunches per fill &6\\
No. of protons per bunch & $1.7\times 10^{13}$\\
Time between extracted bunches (ms)& 20\\
Bunch length at extraction, rms (ns)&3\\
Peak bunch current (A)&400 \\
Total bunch area (eVs)&5\\
Bunch emittance, rms (eV-s)& 0.3\\
Momentum spread, rms & 0.005 \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{figure}
\begin{center}
\includegraphics[width=5.5in]{../template/report/ps-and-eps/Proton_driver_fg1.eps}  % TROUBLE
\caption{AGS proton driver layout.}
\label{Proton:fg1}
\end{center}
\end{figure}

The front end consists of a high intensity negative ion source,
followed by a 750~keV RFQ, and the first five tanks of the
existing room temperature Drift Tube Linac (DTL).  The
superconducting linac (SCL) is made of three sections, each with
its own energy range and cavity cryostat arrangement.

The front end ion source operates with a 1\% duty cycle at the
repetition rate of 2.5~Hz. The beam current within a pulse is
37.5~mA of $\textrm{H}^-.$ The ion source sits on a platform at
35~kV. The beam is prechopped by a chopper located between the
ion source and the RFQ. The chopping extends over 65\% of the
beam length, at a frequency matching the accelerating rf at
injection into the AGS. Transmission efficiency through the RFQ
is taken conservatively to be 80\%, so that the average current
of the beam pulse in the linac, where we assume no further beam
loss, is 20~mA, with a peak value of 30~mA. The combination of the
chopper and the RFQ pre�bunches the beam with a sufficiently
small bunch length that each beam bunch fits into an 
accelerating rf bucket of the downstream DTL, which operates at
201.25~MHz. The DTL is a room-temperature conventional linac that
accelerates to 116~MeV.

The proposed new injector for the AGS adds a 1.2~GeV SCL with an
average output beam power of about 50~kW. The injection energy is
still low enough to control beam losses due to stripping of the
negative ions that are used for multi�turn injection into the
the AGS. The duty cycle is about 0.5\%. Injection into the AGS is
modeled after the SNS scheme~\cite{Proton:SNS}. However, the
repetition rate, and consequently the average beam power, is much
lower here. The larger circumference of the AGS also reduces the
number of foil traversals. Beam losses at injection into the AGS are
estimated to be about 3\% controlled losses and 0.3\%
uncontrolled losses. This is based on a comparison with the
actual experience in the AGS Booster and the LANL PSR and the
predicted losses at the SNS, using the quantity N$_{\rm{}P}$
/$\beta^2\gamma^3$ A), which is proportional to the Laslett tune
shift, as a scaling factor. This is summarized in
Table~\ref{Proton:tb2}. As can be seen, the predicted 3\% beam loss
is consistent with the AGS Booster and the PSR experience and
also with the SNS prediction.
\begin{table}[!htb]
\begin{center}
\caption[Comparison of H minus injection parameters] {Comparison of $\textrm{H}^-$ injection parameters.}
\label{Proton:tb2}
\begin{tabular}{|lcccc|}
\hline
&AGS Booster & SNS & PSR &1 MW AGS\\
Beam power, linac exit (kW) & 3 & 1000 & 80 &54\\
Kinetic energy (MeV) & 200 & 1000 & 800 & 1200\\
No. of protons $N_{\rm{}P}$ $(10^{12})$&15&100&31&100\\
Vertical acceptance, $A~(\pi~\textrm{mm mrad})$ &89 &480 & 140 &55\\
$\beta^{2} \gamma^{3}$ &0.57 &6.75  &4.50 & 9.56\\
$N_{P}/(\beta^{2}\gamma^{3} A)$ $(10^{12}/\pi~\textrm{mm mrad})$&0.296&0.031&0.049&0.190\\
Total beam losses (\%)  & 5 &0.1 &0.3& 3\\
Total lost beam power (W)  & 150 &1000 & 240 & 1440\\
Circumference (m)  & 202 &248 & 90& 807\\
Lost beam power per meter (W/m)  & 0.8 &4.0 & 2.7 & 1.8\\
\hline
\end{tabular}
\end{center}
\end{table}

With the AGS rf harmonic number of 24, the Linac beam will be
injected into 18 buckets, as discussed in Section~\ref{Proton:sec4}. A bunch merge
of 3 to 1 will take place later in the cycle to produce 6 bunches
in the AGS.

The AGS injection parameters are summarized in
Table~\ref{Proton:tb3}. A relatively low rf voltage of 450~kV at 
injection energy is necessary to limit the beam momentum spread during the
multi-turn injection process to about 0.48\%, and the longitudinal
emittance to be about 1.2~eV-s per bunch. Such a small emittance
is important to limit beam losses during transition crossing and
to allow for effective bunch compression before extraction from
the AGS.

A preliminary simulation of the 360-turn injection process is
shown in Fig.~\ref{Proton:fg2}. Without the second harmonic rf,
some dilution in phase space of the injected particles  is
inevitable. The bunch shape is similar to that at the PSR in
Los Alamos, with a noticeable sharp peak. A possible
Linac beam momentum ramping could improve this if necessary.


\begin{table}[!bth]
\begin{center}
\caption{AGS injection parameters.}
\label{Proton:tb3}
\begin{tabular}{|lc|}
\hline
Injection turns &360\\
Repetition rate (Hz) &2.5 \\
Pulse length (ms)&1.08 \\
Chopping rate (\%)&65\\
Linac average/peak current (mA)& 20/30 \\
Momentum spread & $\pm 0.0015$ \\
Norm. 95\% emittance $(\pi \mu \rm{m}\cdot \rm{rad})$& 12\\
RF voltage (kV)& 450 \\
Bunch length (ns) &85\\
Longitudinal emittance (eV-s) &1.2 \\
Momentum spread &$\pm 0.0048$\\
Norm. 95\% emittance $(\pi \mu \rm{m}\cdot \rm{rad})$ & 100\\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{figure}
\begin{center}
\includegraphics[width=5.5in]{../template/report/ps-and-eps/Proton_driver_fg2.eps}
\caption{AGS injection simulation. The abscissa is phase.}
\label{Proton:fg2}
\end{center}
\end{figure}


Beam instability consideration are focused on two aspects.
These are, for the AGS, the longitudinal instability
around transition energy, and the transverse instability  above 
transition, at high energy.

The fractional beam momentum spread at transition must be 
less than 0.0075 because of the limited momentum aperture during
the transition-energy jump. With the transition jump, the slippage
factor can be controlled to be greater than 0.002. With a bunch
rms length of 4.25~ns and a peak current of 85~A at transition,
the longitudinal impedance must be less than $11~\Omega$ to
avoid longitudinal microwave instability. An upgraded vacuum chamber to accomplish this is included in the baseline design.

The measured AGS broadband impedance is about $30~\Omega$. The
broadband impedance mainly comes from the unshielded bellows, the
vacuum chamber connections and steps, and cavities, and also has 
possible contributions from the BPMs and ferrite kickers. With a
modest effort, this impedance can be reduced to be less than
$10~\Omega$, which is consistent with newly designed proton
machines.

In fact, if only the longitudinal microwave instability were of
concern, a larger broadband impedance could be tolerated, since
the longitudinal space-charge impedance of about $10~\Omega$ at
transition, which is capacitive, has the effect of canceling the
inductive broadband impedance. However, the transverse instability
at high energy is more serious, even with a broadband
impedance of $10~\Omega$.

At 24~GeV, and with bunches compressed to 3 ns rms, each with an
intensity of $1.7\times10^{13}$ protons, the beam peak current
reaches almost 400~A, which is about 7 times higher than the
present running condition. With a transverse broadband impedance
of $2.1~\rm{M}\Omega/\rm{m}$, scaled from the longitudinal impedance of
$10~\Omega$, the coherent tune shift is then about 0.04, which
implies an instability growth rate of $10~\mu \rm{s}$.

The space-charge incoherent tune spread, which is the main
transverse microwave instability damping force at low energy,
is reduced at high energy to a value comparable to 0.04. This is
not sufficient to stabilize the beam. Other possible damping
forces are discussed as follows. The slippage factor
$\eta=0.013$  at 24~GeV, together with the beam momentum spread of 0.01
for a bunch with 3~ns rms length, gives rise to a tune
spread of 0.001, which is negligible. The chromatic tune spread
with the chromaticity of 0.25 is 0.02, contributing only marginally
to beam stability. Possibly the tune spread from octupoles or rf
quadrupoles could stabilize the beam, but the choice of an improved vacuum chamber seems prudent.

Other issues are not as significant. For example, the space charge
is not significant even for the compressed bunches and the
beam momentum spread of $\pm 0.01$ is well within the AGS momentum
aperture at high energy.

In summary, since the intensity of $1\times10^{14}$ is only
marginally higher than the present intensity of $7\times10^{13}$,
the beam instability during acceleration and transition crossing
can be avoided. Transverse instability is likely to be the most
dangerous during the bunch compression in the AGS ring, even with
a reduced broadband impedance.


\section{Superconducting Linac (SCL)}
\label{Proton:secSCL}

The SCLs accelerate the proton beam from 116~MeV to 1.2~GeV. The
configuration we use follows a design similar to that described
in Ref.~\cite{Proton:ref1}. All three linacs are built up from a sequence
of identical periods, as shown in Fig.~\ref{Proton:fg2}. Each period
comprises a cryo�module and a room-temperature insertion that is
needed for the placement of focusing quadrupoles, vacuum pumps,
steering magnets, beam diagnostic devices, bellows and flanges. Each
cryo�module includes four identical cavities, each with four or eight identical
cells.

\begin{figure}
\begin{center}
%\vskip 2cm
\includegraphics[width=4in]{../template/report/ps-and-eps/Proton_driver_fg3.eps}
\caption{Configuration of the cavities within the cryo-modules (cryostats).}
\label{Proton:fg3}
\end{center}
\end{figure}

The choice of cryo�modules with identical geometry, and with the
same cavity/cell configuration, is economical and convenient for
construction. Still, there is a penalty due to the reduced
transit--time factors when a particle crosses cavity cells with
lengths adjusted to a common central value $\beta_o$ that does not
correspond to the particle's instantaneous velocity. This is the
main reason to divide the superconducting linac into three
sections, each designed around a different central value
$\beta_o,$ and, therefore, having different cavity/cell
configurations. The cell length in a section is fixed to be
${l\frac{\beta_o} {2}}$ where $l$ is the rf wavelength.

The major parameters of the three sections of the SCL are given in
Table~\ref{Proton:tb4}. The low-energy section operates at 805~MHz
and accelerates from 116 to 400~MeV. The following two sections,
accelerating to 800~MeV and 1.2~GeV, respectively, operate at
1.62~GHz. A higher frequency is desirable for obtaining a larger
accelerating gradient with a more compact structure and reduced
cost. Transverse focusing is done with a sequence of FODO cells
with half�length equal to that of a period. The phase advance per
cell is $90^{\circ}.$ The rms normalized betatron emittance is
$\approx 0.3~\pi~\textrm{mm mrad}$. The rms bunch area is
$0.5\pi~\textrm{MeV-deg.}$ The rf phase angle is $30^{\circ}.$
\begin{table}
\begin{center}
\caption{Parameters of the superconducting linacs.}
\label{Proton:tb4}
\begin{tabular}{|lccc|}
\hline
&Low energy&Medium energy&High\\
Beam power, linac exit (kW) &16&32&48\\
Kinetic energy range (MeV) &116 - 400&400 - 800&800 - 1200\\
Velocity range, $\beta$
&0.4560 - 0.7131
&0.7131 - 0.8418
&0.8418 - 0.8986\\
Frequency (MHz)
&805
&1610
&1610\\
Protons per bunch $(10^{8})$
&9.32
&9.32
&9.32\\
Temperature (K)
&2.0
&2.0
&2.0\\
Cells per cavity
&4
&8
&8\\
Cavities per cryo-module
&4
&4
&4\\
Cell length (cm)
&9.68
&6.98
&8.05\\
Cell reference velocity, $\beta_o$
&0.520 &0.750  &0.865\\
Cavity internal diameter (cm)
&10&5&5\\
Cavity separation (cm)
&32
&16
&16\\
Cold-to-warm transition (cm)
&30&30&30\\
Accelerating gradient (MV/m)
&11.9&22.0&21.5\\
Cavities per klystron
&4&4&4\\
No. of klystrons (or periods)
&18&10&9\\
Klystron power (kW)
&720&1920&2160\\
Energy gain per period (MeV)
&16.0&42.7&48.0\\
Length of period (m)
&4.2&4.4&4.7\\
Total length (m)
&75.4&43.9&42.6\\
\hline
\end{tabular}
\end{center}
\end{table}
The length of the linac depends on the average accelerating
gradient, which has a maximum value that is limited by
three causes: 
\begin{enumerate}
\item The surface-field limit at the frequency of
805~MHz, taken to be 26~MV/m. For a realistic cavity shape, we set
a limit of 13~MV/m on the axial electric field. For the following
two sections, the surface-field limit at 1.61~GHz is 40~MV/m and,
correspondingly, we adopt a limit of 20~MV/m on the axial
electric field.
\item The rf coupler power limit, which we take
here not to exceed 400~kW (including a contingency of 50\% to
avoid saturation effects).
\item The need to make  the
longitudinal motion stable, which limits the energy gain per
cryo�module to a small fraction of the beam
energy~\cite{Proton:ref1}.
\end{enumerate}

The proposed mode of operation is to run each section of the
SCL with the same rf input power per cryo�module. This will
result in some variation of the actual axial field from one
cryo�module to the next. A constant value of the axial field, if
needed, could be obtained by locally adjusting the value of the
rf phase.

For a pulsed mode of operation of the superconducting cavities, the
Lorentz forces could deform the cavity cells enough to tune them off
resonance. This is controlled with a thick cavity wall and
additional supports. Also, a significant time to fill the cavities
with rf power is required before the maximum gradient is reached and
beam can be injected. The expected filling time is short compared with the
beam pulse length of 1~ms.

\section{AGS Main Power Supply Upgrade}
\label{Proton:sec3}
\subsection{Present Mode of Operation}
%\label{Proton:sec2.3.1}
The present AGS Main Magnet Power Supply (MMPS) is a fully
programmable 6000~A, $\pm$9000 V SCR power supply. A 9~MW Motor
Generator (MG), made by Siemens, is a part of the main magnet power supply
of the accelerator. The MG permits pulsing the main magnets up to 50~MW
peak power, while the input power of the MG itself
 remains constant. The highest power into the MG ever utilized is 7~MW,
that is, the maximum average power dissipated in the AGS magnets
has never exceeded 5~MW.

The AGS ring comprises 240~magnets connected in series. The total
resistance, $R,$ is $0.27~\Omega$ and the total inductance, $L,$ is
0.75~H. There are 12 superperiods, designated $A$ through
$L,$ of 20 magnets each, divided in two identical sets of
10~magnets per superperiod.

Two stations of power supplies are each capable of delivering up
to 4500~V and 6000~A. Every station consists of two power supplies
connected in parallel. One power supply is a 12-pulse SCR unit (P type)  rated
at $\pm 5000$~V, 6000~A, that is typically used for fast
ramping during acceleration and energy recovery. The other is a
lower voltage 24~pulse unit (F type), rated at $\pm 1000$~V, 6000~A,
that is used for flattop or slow ramping operation.  The two
stations are connected in series, with the magnet coils arranged
to have a total resistance $R/2$ and a total inductance of $L/2.$ The
grounding of the power supply is done only in one place, in the
middle of station 1 or 2, through a resistive network. With this
grounding configuration, the maximum voltage to ground in the
magnets does not exceed 2500~V. The magnets are tested at 3~kV to
ground prior to each startup of the AGS MMPS after long
maintenance periods.
\subsection{Neutrino Factory Mode of Operation}
To cycle the AGS ring to 24~GeV at 2.5~Hz and with a ramp time of
150~ms, the magnet peak current is 4300~A and the peak voltage is
25~kV.  Figure~\ref{Proton:fg4} displays the magnet current and
voltage of a 2.5~Hz cycle.  The cycle includes a 100~ms flat-top
for the six single-bunch extractions.  The total average power
dissipated in the AGS magnets is estimated to be 3.7~MW. To limit
the AGS coil voltage to ground to 2.5~kV, the AGS magnets must be
divided into three identical sections, each powered similarly to
the present AGS except that now the magnet loads represent only
 1/6 of the total resistance and inductance. Every section will
 be powered separately with its own feed to the ring magnets and an
identical system of power supplies, as shown in
Fig.~\ref{Proton:fg5}. Bypass SCRs will be used across the four
new P-type stations, to bypass these units during the flat-top,
and ensure minimum ripple.  Note that only station 1 will be
grounded, as done presently.
\begin{figure}[!hbt]
\begin{center}
\includegraphics[width=6in]{../template/report/ps-and-eps/Proton_driver_fg4.eps}
\caption[Current and voltage cycle for 2.5~Hz operation
]{Current and voltage cycle for 2.5~Hz operation. Also shown are
the AGS dipole field and average power.} \label{Proton:fg4}
\end{center}
\end{figure}
 Although the average power will not be higher than now, the peak
power required is approximately 110~MW, exceeding the 50~MW rating
of the existing MG. A new MG, capable of providing 100~MW, would 
operate with 12~phases to limit, or even eliminate, the need for
phase-shifting transformers, so that every power supply system
would generate 24~pulses. The generator voltage will be about
15~kV line-to-line, to limit the generator current to less than
6000~A during pulsing. The generator will be rated at a slip
frequency of 2.5~Hz.
\begin{figure}[!htb]
\begin{center}
%\includegraphics[width=6in]{proton-fg51.eps}
\includegraphics[width=4in]{../template/report/ps-and-eps/Proton_driver_fg5.eps}
\caption[Schematic of power supply connections to the AGS
magnets]{Schematic of power supply connections to the AGS magnets
for 2.5-Hz operation.} \label{Proton:fg5}
\end{center}
\end{figure}

Running the AGS at 2.5~Hz requires that the acceleration ramp
period decreases from 0.5~s to 0.15~s. That is, the magnet
current variation \textsl{dI/dt} is about 3.3 times larger than
at present. Eddy current losses in the vacuum chamber are
proportional to the square of \textsl{(dI/dt)}, that is, they are
10~times larger. However, this is still significantly below the
present ramp rate of the AGS Booster which does not require
active cooling. The increased eddy currents give rise to increased
sextupole fields during the ramp, and will add about 20 units of
chromaticity. The present chromaticity sextupoles will be
upgraded to correct this and the upgraded vacuum chamber will also mitigate the effects of the faster cycle.

\section{AGS rf System Upgrade}
\label{Proton:sec4}

At 2.5~Hz, the peak acceleration rate is three times the present
value for the AGS. With 10 accelerating stations, each station will
need to supply 270~kW peak power to the beam. The present power
amplifier design, employing a 300~kW power tetrode will be
suitable to drive the cavities and supply power to the beam. The
number of power amplifiers will be doubled, so that each station
will be driven by two amplifiers of the present design. This
follows not so much from power considerations but from the
necessity to supply 2.5 times the rf voltage.

An AGS rf station comprises four acceleration gaps surrounded by
0.35~m of ferrite stacks. The maximum voltage capability of a gap
is not limited by the sparking threshold of the gap, but by the
ability of the ferrite to supply the magnetic induction. When the
AGS operates at 0.5~Hz, the gap voltage is 10~kV. At 2.5~Hz, we
will need up to 25~kV per gap (roughly equal to the voltage from
the same gap design used at the Booster, 22.5~kV) and this taxes
the properties of the ferrite. Above a certain threshold value of
$B_{rf}$ (20~mT for AGS ferrite 4L2) a ferrite becomes unstable
and excessively lossy. The gap voltage at this $B_{rf,max}$ is
simply given by


\begin{equation}
  V=-\frac{d}{dt}\int \omega B_{rf} dA = \omega a l B_{rf,max} \ln\frac{b}{a}
\end{equation}

\noindent where $\omega$ is the rf angular frequency and the
variables $a$, $b$, and $l$ are the inner and outer radius and
length of the ferrite stack, respectively.

The only free variable is $\omega$. If we operate the rf system at
the 24th harmonic of the revolution frequency (9~MHz) then the
required voltage of 25~kV can be achieved with a safe value for
$B_{rf,max}$ of 18~mT.

The next issue is the power dissipation in the ferrite and the
thermal stress that is created by differential heating due to rf
losses in the bulk of the material. We know from experience that
below 300~mW/cm$^3$ the ferrites can be adequately cooled. The
power density is also proportional to $B^2_{rf}$ and is given by

\begin{equation}
  \frac{P}{V}=\frac{\omega B^2_{rf}}{2 \mu_0(\mu Q)}
\end{equation}

\noindent where $\mu Q$ is the quality factor of the ferrite.

The $\mu Q$ product is a characteristic of the ferrite material
and depends on frequency and $B_{rf}$. We have data on ferrite 4M2
(used in the Booster and SNS) at 9~MHz and 20~mT where the power
dissipation is 900~mW/cm$^3$. The details of the acceleration
cycle determine the rf voltage program that is needed. For the
cycle shown in Fig.~\ref{Proton:fg4}, a peak voltage of 1~MV (40
gaps each with 25~kV) is needed but for only 20~ms during
acceleration. An additional 100~ms operation at 1~MV is required
for the bunch compression. Together, this is a duty factor of less
than 0.3, giving an average power dissipation below our limit. We do not yet have data on the present AGS ferrite, 4L2 at
9~MHz. Characterizing 4L2 in this parameter regime is identified
as an R\&D issue, but we know that retrofitting the AGS
cavities with 4M2 is a viable fallback option.

\begin{figure}[!hbt]
\begin{center}
\includegraphics[width=4in]{../template/report/ps-and-eps/Proton_driver_fg6.eps}
\caption[Bunch pattern for using harmonic 24 to create 6 bunches
]{Bunch pattern for using harmonic 24 to create 6 bunches.}
\label{Proton:fg6}
\end{center}
\end{figure}


With the rf system operating on harmonic 24, there will be 24 rf
buckets. However, we need all the beam in 6 bunches to extract to the
production target. This can be arranged by filling 18 of the 24
buckets with 6 triplets of bunches, as shown in
Fig.~\ref{Proton:fg6}. The fast chopper in front of the linac can
prepare this bunch pattern during the multi-turn injection as
described in Section~\ref{Proton:sec1}. The fast chopper fills
the buckets to a longitudinal emittance of 1.2~eV-s which can be
accelerated with 1~MV/turn of rf voltage, allowing some blowup
during the acceleration cycle. At the end of the acceleration
cycle, the triplets will be merged adiabatically into 6 single
bunches~\cite{Proton:ref2} using separate 100~kV/turn harmonic 6
rf cavities. The final bunch emittance would be at least 5~eV-s
per bunch after the 3:1 bunch merge.

With 100~kV/turn of the harmonic 6 rf system, the total bunch
length will be 80~ns for a 5~eV-s bunch. The rf system will then be
switched back to harmonic 24 and 1~MV/turn, where the bunch is now
mismatched. By strongly modulating the rf voltage with a frequency
close to twice the synchrotron frequency of 512~Hz, the tumbling
bunch can be kept from decohering. Also, the quadrupole
oscillation frequency of the bunch can be controlled so that the
bunch length is minimal at the times of the 6 bunch
extractions~\cite{Proton:ref3}. The minimal total bunch length is
about 15~ns, or 3~ns rms. This is about half of the matched total
bunch length of 32~ns.

\section{Conclusions}
The scheme for a 1-MW proton driver based on the AGS with upgraded
injection is feasible. Indeed, the AGS beam intensity is only
modestly higher than during the present high-intensity proton
operation and, therefore, beam instability is not expected to be a
problem during acceleration. Beam stability during the bunch
compression is marginal, and requires some care to reach the 3~ns bunch length specification.

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\bibitem{Proton:ref1}A. Ruggiero, \textsl{Design Considerations on a Proton Superconducting Linac}, BNL Internal Report 62312, 1995.
\bibitem{Proton:ref2}R. Garoby, \textsl{Bunch Merging and Splitting Techniques in the Injectors for High Energy Hadron Colliders}, CERN/PS 98-048.
\bibitem{Proton:ref3}M. Bai {\it et al.}, \textsl{Adiabatic excitation of longitudinal bunch shape oscillations}, Phys. Rev. ST Accel. Beams 3, 064001, 2000.

\end{thebibliography}
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