# Proton Driver 

## Introduction

The proton driver under design at Fermilab is a high intensity rapid
cycling proton synchrotron. Its function is to deliver intense short
proton bunches to the target for muon production. These muons will be
captured, phase rotated, bunched, cooled, accelerated and finally,
injected into a storage ring for neutrino experiments. In this sense,
the proton driver is *the front end* of a neutrino factory. In addition
to serving a neutrino factory, the proton driver may serve other needs.
For example, it would replace the present Fermilab Booster as a high
intensity new booster. As such it could be the platform for providing 6
times as high proton flux and 12 times as high beam power to
experiments. It could also increase the beam intensity in the Main
Injector by a factor of 4, where it may begin to have intensity
limitations. The antiproton production rate and Tevatron luminosity
could be enhanced accordingly, after comparatively modest upgrades in
other machines.

The first serious effort for designing a new proton driver at Fermilab
started around 1995 and was summarized in 1997 \[1\]. That work has
continued, and a complete design report for such a machine is being
prepared for the end of 2000. It is not appropriate to include the
details here, and in the following, we only discuss the interaction
between the Booster design parameters and those of the Neutrino source.

There are two primary requirements of the proton driver:

1.  High beam power: *P*~beam~ = 1.2 MW

> This requirement is similar to other high intensity proton machines
> that are presently under design or construction, e.g. the SNS at the
> ORNL, the ESS in Europe and the Joint Project (formerly known as the
> JHF) in Japan. This similarity makes it possible to establish a
> worldwide collaboration for tackling various technical design issues
> in a coherent manner.

2.  Short bunch length at exit: ~b~ = 3 ns.

> This requirement is particular to the proton driver. It brings up a
> number of interesting and challenging beam physics issues that must be
> solved. The bunch length is related to the longitudinal emittance ~L~
> and momentum spread *p* by:
>
> ~b~ $\frac{\varepsilon_{L}}{\Delta p}$
>
> In order to get short bunch length, it is essential to have:

-   small longitudinal emittance (emittance preservation during the
    cycle);

-   large momentum acceptance (in the rf and as well as in the lattice);

-   bunch compression at the end of the cycle.

3.  Low beam loss during acceleration to keep the activation of machine
    components low enough to allow maintenance. The above requirements
    on the machine design make this a major challenge.

## Choice of Major Design Parameters

The design goal of the neutrino factory at Fermilab is 210^20^ muons per
year to the neutrino experiments. This requires 4.510^14^ protons per
second (see chapter 2). At a repetition rate of 15 Hz, 310^13^ protons
per cycle are required. The average beam current is 72 A. At 16 GeV,
this provides a beam power of about 1.2 MW.

The beam power is the product of three parameters -- proton energy
*E~p~*, number of protons per cycle *N~p~* and the repetition rate
*f*~rep~:

*P~beam~ = E~p\ ~* *N~p~ f~rep~*

The rep rate is chosen to be 15 Hz for two reasons: (1) Fermilab has a
15 Hz linac. A repetition rate higher than 15 Hz would require a major
change in the present linac set-up. (2) A repetition rate lower than 15
Hz would mean more protons per cycle, which will be difficult in the
present linac.

A proton energy of 16 GeV was chosen for the proton driver study. The
choice of beam energy is a compromise resulting from the following
considerations:

1)  All other things being equal, higher energy synchrotrons most
    probably require higher investment cost.

2)  At the outset of this study, the calculations being made so far
    indicated that muon flux scales with beam power over a fairly wide
    range of proton energies. For a fixed repetition rate and a
    specified beam power, reducing the beam energy would require a
    proportional increase in beam intensity. Those changes in turn would
    cause the following undesirable parameter changes: higher
    longitudinal phase space density N~b~/~L~ (in which N~b~ is the
    number of protons per bunch), higher space charge tune shift Q at
    top energy (which would make bunch compression more difficult) and
    large momentum spread p/p.

3)  The present Fermilab linac should be able to deliver the intensity
    required for a 16 GeV synchrotron, 310^13^ particles per cycle at 15
    Hz, after upgrades of modest scope. More substantial upgrades would
    be necessary for higher intensities.

4)  Higher intensities will exacerbate space-charge effects at low
    energy in the synchrotron, and it would probably be necessary to
    raise the linac energy to alleviate these effects, perhaps to 1 GeV.

5)  For the present 400 MeV linac and a 16 GeV synchrotron, the ratio of
    input and output momenta for the synchrotron is about 18, which is a
    rather large but probably tolerable dynamic range for a rapid
    cycling synchrotron.

There are a number of open questions regarding the design energy for the
booster that can only be answered by looking at the overall service that
the Booster must provide in support of the laboratory physics programs.
These broader questions were not addressed at this time, and the
parameters shown in Table 1 below were determined to be adequate for the
purposes of this study.

The proton driver for the neutrino factory is called Phase I. Details of
Phase I design will be described in the following sections. A possible
future upgrade of the proton driver to serve a muon collider is called
Phase II. Table 1 lists the main parameters of the two phases. However,
Phase II design will not be discussed in this report. For comparison,
the present proton source parameters are also listed in Table 1.

## Technical Systems 

The central part of the proton driver is a new 16 GeV synchrotron that
would be installed in a new tunnel. There are eleven main technical
systems: a new linac front end, a chopper, 400 MeV line, 16 GeV lines,
16 GeV ring lattice, injection and extraction systems, RF systems,
magnets, power supplies, vacuum and collimators. The design of each
system has been worked out to some detail and will be briefly described
below.

### New Linac Front End

In order to use much of the present linac as an injector for the first
stage of the proton driver, the linac must provide H^-^ ions in excess
of 4800 mA-s (60 mA and 80 s). Although both the beam current and pulse
length are within the capability of the system, the beam loss and
induced radiation in the structure at high intensity operation would
become an issue. The front end of the linac will be changed to increase
the transverse brightness of the beam. The new front end consists of a
brighter source (either a modified magnetron or a DESY rf type volume
source), a short electrostatic focusing structure (LEBT) and a 201 MHz
RFQ from 30 keV to 1 MeV. In addition, an isochronous transport line
made of two 270 bending magnets (the -magnets) and five quads, a second
201 MHz RFQ from 1 MeV to 2.235 MeV and a modified Drift Tube Linac
(DTL) section, in which the first existing 18 drift tubes will be
eliminated, are required. The rest of the linac (*i.e.,* Tank 2 to 5 of
the DTL and the Coupled Cavity Linac) will remain the way it is now.
With these modifications the transverse beam emittance ~T~ at 400 MeV is
expected to decrease from 8 mm-mrad (present value) to 3 mm-mrad. This
would greatly reduce beam losses in the linac due to the aperture
limitations in the system.

+--------------------------------+---------+------------+-------------+
|                                | Present | (-factory) | Upgrade     |
|                                |         |            |             |
|                                |         | Phase I    | Phase II    |
+--------------------------------+---------+------------+-------------+
| **Linac** (operating at 15 Hz) |         |            |             |
+--------------------------------+---------+------------+-------------+
| Kinetic energy (MeV)           | 400     | 400        | 1000        |
+--------------------------------+---------+------------+-------------+
| Peak current (mA)              | 40      | 60         | 80          |
+--------------------------------+---------+------------+-------------+
| Pulse length (s)               | 25      | 80         | 200         |
+--------------------------------+---------+------------+-------------+
| H^-^ per pulse                 | 6.3     | 3 10^13^   | 1 10^14^    |
|                                | 10^12^  |            |             |
+--------------------------------+---------+------------+-------------+
| Average beam current (A)       | 15      | 72         | 240         |
+--------------------------------+---------+------------+-------------+
| Beam power (kW)                | 6       | 29         | 240         |
+--------------------------------+---------+------------+-------------+
| **Pre-booster** (operating at  |         |            |             |
| 15 Hz)                         |         |            |             |
+--------------------------------+---------+------------+-------------+
| Extraction kinetic energy      |         |            | 3           |
| (GeV)                          |         |            |             |
+--------------------------------+---------+------------+-------------+
| Protons per bunch              |         |            | 2.5 10^13^  |
+--------------------------------+---------+------------+-------------+
| Number of bunches              |         |            | 4           |
+--------------------------------+---------+------------+-------------+
| Total number of protons        |         |            | 1 10^14^    |
+--------------------------------+---------+------------+-------------+
| Norm. transverse emittance     |         |            | 200         |
| (mm-mrad)                      |         |            |             |
+--------------------------------+---------+------------+-------------+
| Longitudinal emittance (eV-s)  |         |            | 2           |
+--------------------------------+---------+------------+-------------+
| RF frequency (MHz)             |         |            | 7.5         |
+--------------------------------+---------+------------+-------------+
| Average beam current (A)       |         |            | 240         |
+--------------------------------+---------+------------+-------------+
| Beam power (kW)                |         |            | 720         |
+--------------------------------+---------+------------+-------------+
| **Booster** (operating at 15   |         |            |             |
| Hz)                            |         |            |             |
+--------------------------------+---------+------------+-------------+
| Extraction kinetic energy      | 8       | 16         | 16          |
| (GeV)                          |         |            |             |
+--------------------------------+---------+------------+-------------+
| Protons per bunch              | 6       | 7.5 10^12^ | 2.5 10^13^  |
|                                | 10^10^  |            |             |
+--------------------------------+---------+------------+-------------+
| Number of bunches              | 84      | 4          | 4           |
+--------------------------------+---------+------------+-------------+
| Total number of protons        | 5       | 3 10^13^   | 1 10^14^    |
|                                | 10^12^  |            |             |
+--------------------------------+---------+------------+-------------+
| Norm. transverse emittance     | 15      | 60         | 200         |
| (mm-mrad)                      |         |            |             |
+--------------------------------+---------+------------+-------------+
| Longitudinal emittance (eV-s)  | 0.1     | 2          | 2           |
+--------------------------------+---------+------------+-------------+
| RF frequency (MHz)             | 53      | 1.7        | 7.5         |
+--------------------------------+---------+------------+-------------+
| Extracted bunch length ~b~     | 0.2     | 3          | 1           |
| (ns)                           |         |            |             |
+--------------------------------+---------+------------+-------------+
| Average beam current (A)       | 12      | 72         | 240         |
+--------------------------------+---------+------------+-------------+
| Target beam power (kW)         | 100     | 1200       | 4000        |
+--------------------------------+---------+------------+-------------+

Table 1: Proton Driver Parameters of Present, Phase I and Phase II.

### Chopper

A new type of chopper has been designed and built in collaboration with
the KEK 2. This is a pulsed beam transformer made of three 1"-thick
Finemet cores. It is driven by two HTS 81-09 transistors for bipolar
operation. It is placed in front of the RFQ and modulates the injection
beam energy by 10%. The rise- and fall-time of the chopper is about 30
ns. A prototype has been installed and successfully tested with beam on
the linac at HIMAC, a medical center in Japan operating a high intensity
accelerator.

### 400 MeV Line

The 400 MeV line connects the linac to the 16 GeV ring. It could be made
of permanent magnets, similar to the present 8 GeV line used at
Fermilab.

### 16 GeV Line

In the present layout, the 16 GeV transport line is about 2 km long and
connects the driver to the target station. A major portion of it would
be in the Tevatron tunnel. A preliminary design using FODO lattice has
been worked out. One concern about transporting intense (N~b~ = 7.5 X
10^12^ ) short (~b~ = 3 ns) bunches in this long line is possible bunch
lengthening due to space charge and lack of longitudinal focusing.
However, simulation shows that the longitudinal emittance growth is
negligible in this line \[3\].

### 16 GeV Ring Lattice

In order to minimize longitudinal emittance dilution a lattice design
should be chosen which does not require to go through transition. This
excludes the traditional FODO lattice for a 16 GeV ring. Flexible
momentum compaction (FMC) type lattice have to be considered. Other
requirements include: B~max~ 1.5 T, large dynamic aperture (\> 100
mm-mrad), large momentum acceptance (p/p = 2.5%), and dispersion free
straight sections for rf. A collimation system is definitely required
and the collimator design must be coupled to the lattice design.
![](media/image1.png){width="2.9625984251968505in" height="4.2in"}

There are presently two FMC lattices under study. One with a triangular
shape is shown in Figure 1. The circumference is 711.3 m, which is 1.5
times the size of the present booster. Another lattice has a racetrack
shape. Both provide a large or imaginary ~t~ and use sextupoles to
increase the momentum acceptance. A choice will be made after more
careful comparisons between the two lattices.

### Injection and Extraction

In order to reduce space charge effects, the injected beam will be
painted in both transverse and longitudinal phase space. The horizontal
injection system consists of 4 orbit bumpers and 2 fast kickers. The
latter are used for painting and are located 90apart (in phase) on each
side of the foil. The foil temperature rise and beam emittance dilution
during multiple passes through the foil have been calculated and seem
tolerable.

Because this accelerator requires a resonant power supply, 1-turn fast
extraction is considered. So far only one extraction point has been
designed. A second extraction point is possible if placing the rf in
dispersive regions (*i.e.,* in the arcs) turns out to be feasible.

### The RF System

The required total rf voltage is about 1.4 MV. Due to the small
circumference of this machine, the cavities must have a high gradient
(30 kV/m). A study showed that Finemet cores (which is a new type of
magnetic alloy) can withstand higher rf B-field than regular ferrite and
thus provide higher gradient. The disadvantage is higher losses and
lower Q. This can be partially compensated by cutting the core to two
halves. In order to reduce eddy current heating, the sharp edges of the
cut core should be shaped in order to minimize the radial B-field. A
prototype 20 kV, 7.5 MHz Finemet cavity has been built at Fermilab in
collaboration with the KEK and is shown in Figure 2. It will be tested
in the Main Injector for 132 ns bunch spacing coalescing experiment.

In addition to this acceleration rf system, a second rf system for bunch
compression is considered 4. The main difference between the two systems
is the duty factor. The one for acceleration will be used throughout the
cycle. The second used for bunch compression is turned on for a few
hundred microseconds in the cycle. Therefore, the latter could work at
much higher gradient (0.5-1 MV/m).

### Magnets

The main requirements are a large aperture (dipole: 12.7 31.8 cm^2^,
quad: 8.56 cm pole tip radius) and a large good field region (dipole:
B/B \< 10^-3^ within 10 cm). The lamination uses 0.014" silicon steel
M17. The quadrupole design is similar to the large quadrupoles in the
Fermilab Accumulator, except that it will use 4-piece laminations
instead of 2-piece.![](media/image2.png){width="3.1006944444444446in"
height="2.954861111111111in"}

### Power Supplies 

A dual-resonance (15 Hz plus 12.5% 30 Hz component) is proposed. In
addition to the main power supply, a second power supply for correcting
the tracking error between dipole and quadrupole has also been designed.
It drives the correction coils in the quadrupoles and uses a bucking
choke in order to cancel the voltage and current induced by the main
coils.

### Vacuum System 

In a rapid cycling machine, the eddy current in the beam pipe is a major
problem. The ISIS solution, which is a ceramic pipe equipped with a
metallic cage inside, works well. However, it requires additional
vertical aperture within the magnet. The alternative is to use a thin
metallic pipe. Three designs are being pursued: a 0.05\" Inconel pipe
with cooling tubes, a 0.005\" Inconel pipe with ribs, and a composite
material pipe with a thin Inconel (or Ti-Al) sheet inside. The pipe size
is 5\" 9\". The vacuum system design would give a vacuum of 10^-8^ Torr
or lower. Such a vacuum would eliminate the concern about possible *e-p*
instability as observed in the PSR at LANL.

### Collimators

A 2-stage collimator system has been designed. Calculation shows that it
can dump 99% of the lost particles in a controlled manner. With such a
high efficiency, even for 10% loss at injection or 1% loss at ejection,
the activation level in most of the tunnel would be around 1 W/m.
Therefore, hands-on maintenance will be possible. The area near the
collimators will require special local shielding.

## Technical Design Issues

### High Longitudinal Brightness 

One of the most demanding issues in the proton driver design is the
required longitudinal brightness. Table 2 is a comparison of the
longitudinal brightness N~b~/~L~ in existing as well as planned proton
accelerators.

  -------------------- -------- ---------- ---------- -------- ---------------
  Machine              E~max~   N~tot~     N~b~       ~L~      N~b~/~L~

                       (GeV)    (10^12^)   (10^12^)   (eV-s)   (10^12^/eV-s)

  Existing:                                                    

  CERN SPS             450      46         0.012      0.5      0.024

  FNAL MR              150      20         0.03       0.2      0.15

  FNAL Booster         8        4          0.05       0.1      0.5

  PETRA II             40       5          0.08       0.12     0.7

  KEK PS               12       3.6        0.4        0.4      1

  DESY III             7.5      1.2        0.11       0.09     1.2

  FNAL Main Inj        150      60         0.12       0.1      1.2

  CERN PS              14       25         1.25       0.7      1.8

  BNL AGS              24       63         8          4        2

  LANL PSR             0.797    23         23         1.25     18

  RAL ISIS             0.8      25         12.5       0.6      21

  Planned:                                                     

  Proton Driver Phase  16       30         7.5        2        3.8
  I                                                            

  Proton Driver Phase  16       100        25         2        12.5
  II                                                           

  Japan JHF            50       200        12.5       5        2.5

  AGS for RHIC         25       0.4        0.4        0.3      1.3

  PS for LHC           26       14         0.9        1.0      0.9

  SPS for LHC          450      24         0.1        0.5      0.2
  -------------------- -------- ---------- ---------- -------- ---------------

Table 2: Longitudinal Brightness of Proton Machines

The first phase for the proton driver (see Table 1) requires 3.8x10^12^
particles per eV-s, which is higher than most of the existing proton
accelerators, with the exception of the PSR and ISIS. (The PSR is an 800
MeV accumulator ring. The ISIS, although an 800 MeV synchrotron, uses
low field magnets, a small rf system, and has no sextupoles.)

In order to achieve high longitudinal brightness, one has to preserve
~L~, which is in contrast to the controlled blow-up of ~L~ in many high
intensity machines for keeping beam stable. The following measures are
taken to preserve the longitudinal emittance ~L~:

1.  Avoiding transition crossing in the lattice design. This eliminates
    a major source of emittance dilution.

2.  Avoiding longitudinal microwave instability by keeping the beam
    below transition (The capacitive space charge impedance helps
    stabilize the beam below transition) and keeping the resistive
    impedance small (using a uniform metallic beam pipe).

3.  Avoiding coupled bunch instability by using low Q rf cavity.

4.  Applying inductive inserts for space charge compensation.

5.  Applying longitudinal feedback system.

### Bunch Compression

Bunch compression is required at the end of the cycle in order to
shorten the bunch length to 3 ns. There are at least three possible
methods to achieve this: (1) RF amplitude jump, (2) RF phase jump and,
(3) the so called t manipulation. The achieved compression ratio of
either of these methods is about 3-5. Method (1) is the most common one.
Although Fermilab has many years of experience with this operation, the
high bunch intensity imposes new challenges:

1\. During debunching, the beam momentum spread will decrease. This may
give rise to excitation of the microwave instability.

2\. During debunching, the rf voltage will decrease. This may exacerbate
beam-loading effects.

3\. In a regular bunch rotation simulation, the momentum compaction is
assumed to be a constant ~0~. However, the proton driver lattice is
nearly isochronous (~0~ 0). The higher order terms (~1~, ~2~,\...)
become important. Thus, particles with different p/p have different path
length L. This complicates the bunch rotation process.

4\. Due to short bunch length, the tune shift Q from direct space charge
and image charge remains large even at 16 GeV. This Q also gives
different path length L. In other words, the path length of each
particle depends not only on its longitudinal position but also on its
transverse amplitude. This effect couples the longitudinal and
transverse motion and is a new challenge to beam dynamics study.

Items 3 and 4 causes the so-called "-spread" ( is the slip factor),
which must be taken into account in theoretical modeling as well as in
numerical simulations.

Several laboratories (Fermilab, BNL, KEK, CERN, GSI and Indiana Univ.)
have decided to investigate methods to achieve the highest possible peak
current, longitudinal brightness and compression ratio. An experiment in
collaboration with BNL using the AGS has shown that bunches of ~b~ = 2
ns can be produced for a bunch intensity of 4 X 10^12^ protons. The
bunches were stable for the times measured during the experiment. \[5\]

### Transient Beamloading

Transient beamloading can impose severe limitations on intense short
bunch operation if not being compensated. A single bunch intensity of
7.5 X 10^12^ corresponds to a charge of q = 1.2 C. With a gap
capacitance of C = 300 pF, the single pass beamloading voltage q/C is 4
kV. Given the gap voltage of 20 kV the beamloading has to be
compensated. However, because the bunch is very short (~b~ = 3 ns), it
will be to difficult apply a short current pulse to perform direct
compensation. This subject is a high priority R&D item in the proton
driver study. RF feedforward systems for global compensation and an rf
feedback system to reduce the bunch to bunch and turn by turn variation
for a total reduction of 20-30 dB is required.

### Space Charge and Instabilities

Space charge is a main limitation to achieve high intensity proton
beams, in particular at injection. In order to reduce the Laslett tune
shift, a large transverse emittance (60 mm-mrad, normalized, 95%) is
used. Both the transverse and the longitudinal phase space will be
diluted (painted) for a uniform particle distribution. Inductive inserts
are foreseen to reduce the potential well distortion from space charge.
An experiment is going on at the PSR/LANL using inductive insert modules
provided by Fermilab. The results are encouraging. For a given rf
voltage, the achievable beam intensity is increased when the inserts are
in place. More measurements will be done to study the effects of the
inserts on the beam.

There are two categories of instabilities in the proton driver which
have been identified. One is the "conventional" type, for instance,
impedance budget, resistive wall, slow head-tail, Robinson, coupled
bunch, etc. These are by no means trivial. However, methods for
compensation are well understood. Another type is "non-conventional,"
which is not well understood but is important for the proton driver. For
example, the longitudinal microwave instability below transition, fast
head-tail instability (transverse mode coupling) in the presence of
strong space charge, and synchro-betatron coupling when rf is placed in
dispersive region. Both analytical and numerical studies are being
carried out on these effects. Machine experiments are also being
planned.

### Particle Loss, Collimation Shielding

Here the main concern is the residual activity, which requires the
residual dose to be below a certain level. Monte Carlo simulations using
the code MARS show that, assuming an average particle loss rate of 1
W/m, the residual dose after 30 days irradiation and 4 hours cool down
would be below 100 mrem/hr which is considered to be acceptable. This
result agrees with other simulations done at LANL and ORNL. To meet
these requirements, a collimation system has been designed with a
capture efficiency better than 99% and would allow 10% particle loss at
injection and 1% loss at extraction during normal operation. Shielding
calculations have been performed as well. The needed berm thickness for
shielding for a 1-hour accidental full beam loss is 29 feet.

## Summary

Significant progress has been made to achieve the Phase I design goals.
The proton driver consists of a modest improvement of the linac front
end, a new 16 GeV synchrotron in a new tunnel and two new beam lines
(400 MeV and 16 GeV). The synchrotron meets the needs of a neutrino
factory and can provide a 1.2 MW proton beam with 3 ns bunch length. It
also allows an upgrade path to a beam power of 4 MW and eventually a
bunch length of 1 ns. The proton driver would also serve as a complete
functional replacement for the Fermilab Booster, providing upgraded
capabilities for the ongoing programs.

REFERENCES

1.  S. Holmes, editor, "A Development Plan for the Fermilab Proton
    Source," FERMILAB-TM-2021 (1997).

2.  W. Chou et al., KEK Report 98-10 (September 1998), also see
    FERMILAB-Conf-99/102, which is published in the PAC'99 proceedings.

3.  M. Popovic, MUCOOL Note 106 (March, 2000).

4.  W. Chou and A. Van Ginneken, "Phase Rotation Using Low Frequency
    (Few MHz) RF," Fermilab MUCOOL Note 90 (February, 2000).

5.  C. Ankenbrandt *et al*., Phys. Rev. ST Accel. Beams 1, 030101
    (1998).