# Choice of proton driver parameters for a neutrino factory\*

![](media/image1.wmf){width="2.801388888888889in"
height="3.158333333333333in"}H.G. Kirk^\#^, J.S Berg, R.C. Fernow, J.C.
Gallardo, N. Simos, W.-T. Weng, Brookhaven National Laboratory, Upton,
NY 11973, U.S.A.; S. Brooks, Rutherford Appleton Laboratory, Chilton,
Didcot, Oxon, OX11 0QX

Abstract

We discuss criteria for designing an optimal "green field" proton driver
for a neutrino factory. The driver parameters are determined by
considerations of space charge, power capabilities of the target, beam
loading and available RF peak power.

## introduction

A neutrino factory may be the best experimental tool to unravel the
physics involved in neutrino oscillation and CP violation phenomena
\[1\]. To have sufficient neutrino flux for acceptable physics results
within 5 years requires about 10^22^ protons on target per year, which
corresponds to 1-4 MW of proton beam power from the proton driver
depending on the beam energy.

In the past, there were individual proposals from different laboratories
of a particular design of proton driver capable of delivering beam power
from 2 to 4 MW, without consistent attention paid to the needs or
requirements from the downstream systems. In this study, we try to
identify the requirements from those down stream systems first, then see
whether it is possible to design a proton driver to meet those needs.
Such a study will also assist site specific proposals to further improve
on their designs to better serve the need of a proton driver for
neutrino factory applications.

As shown in Fig.1, after the proton driver, there are several major
subsystems comprising the complete configuration of a neutrino factory
\[2\]. They are the target and capture system, the bunch rotation, the
cooling system, the acceleration system, and finally the decay ring.
Each of these systems requires the proton driver to have certain beam
qualities for optimal performance.

The beam power *P* of a proton driver depends on the energy *E*,
intensity *Ne* and repetition rate *f* of the proton beam, according to
the relation, *P* = *E N e f*. To achieve 4 MW, possible examples of
beam intensities required at given energies and rep rates are shown in
Table 1. It is important to realize that typically it requires a beam
intensity at the level of 5 10^13^ per pulse, which is at the current
limit of what can be reasonably achieved from our past experience, due
to the limitation from space charge and other coherent instabilities.

\*Work supported by the U.S. Department of Energy.

^\#^hkirk@bnl.gov

Figure 1: Schematic layout of a neutrino factory.

Therefore, special attention has to be paid to the choice of beam energy
and the number of bunches.

Table 1. Protons per pulse required for 4 MW. 1 Tp is 10^12^ protons.

  ----------------- ----------------- ----------------- -----------------
                    10 Hz             25 Hz             50 Hz

  10 GeV            250 Tp            100 Tp            50 Tp

  20 GeV            125 Tp            50 Tp             25 Tp
  ----------------- ----------------- ----------------- -----------------

## energy choice

We wish to determine the kinetic energy of the proton beam that is most
efficient for the production of the soft-pions, which will lead to the
maximal collection of muons in a pion decay channel. We process the
produced pions through the entire front end of the neutrino factory
front end using the Study 2a \[3\] configuration from the target module
to the conclusion of the cooling section. As a figure of merit, we
select those surviving muons which are fully contained within the
capture transverse acceptance (30 π mm-rad) and the longitudinal
acceptance (150 π mm-rad) of the assumed subsequent accelerating
section.

![](media/image2.wmf){width="3.252083333333333in"
height="2.6041666666666665in"}

Figure 2: Efficiency of muon collection at the exit of the Study 2a
front end versus proton driver energy.

The particle production model used was MARS V14 \[4\] and the
propagation of the particles though the neutrino factory front end was
done utilizing the ICOOL code \[5\]. The efficiency of the muon capture
was computed by evaluating the number of collected muons at the end of
the neutrino factory front end and normalizing the results to the power
of the proton beam such that a beam of e.g. 20 GeV kinetic energy is
assumed to contain twice the number of protons as an equivalent beam
with 40 GeV kinetic energy. Results of this analysis utilizing a mercury
based target is shown in Fig. 2. The target parameters such as radius,
tilt angle, and longitudinal placement have been previously optimized in
Study 2a.

We also investigated other candidate target types with elements of
various Z content with the result that the high-Z materials show the
highest proficiency for soft-pion production which will lead to the
greatest number of captured muons. In evaluating the most efficient
kinetic energy region we found that 6 to 38 GeV protons gave the sum of
positive and negative pions within 10% of the maximum efficiency.

## target issues

The challenge of delivering 4 MW of beam power on a target (solid or
liquid) is governed by two sets of parameters. The first set relates to
the production target and specifically the choice of material, as well
as its integrated design that allows it to operate as a functional unit.
The second set is linked with the proton pulse structure delivered to
the target and the parameter choices have a direct impact on the
survivability of the target. Whether liquid or solid, the target
feasibility issues stem from the inherent material limits that in turn
depend on the deposited energy density. This energy density is a
function of the proton energy, intensity and spatial structure, as well
as the material properties.

### Solid vs. Liquid Targets

The issues associated with each of these two target types are
distinctively different. On one hand, solid targets are vulnerable to
thermo-mechanical shock induced by high energy densities that can lead
to failure even with a single pulse on target. Fatigue due to the cyclic
nature of the problem can lead to premature failure of the target. Most
importantly, solid targets are susceptible to irradiation damage
manifesting itself in altering the key properties of the material, both
physical and mechanical, that are responsible for shock absorbance and
heat diffusion towards the heat sink. The onset of irradiation damage is
always expected to compromise the longevity and functionality of a solid
target. In addition, solid targets, even under the best of
circumstances, must enable the removal of the significant heat load
through a feasible and "smart" design. This is particularly challenging
because of the constraints brought onto the target by physics
requirements that limit the size of the target to avoid re-absorption of
secondary particles and thus limiting the available target surface area
for heat transfer to the heat sink. Solid targets seem capable of
reaching powers of 2 MW at best and only with low Z, high performance
materials.

Liquid targets, on the other hand, either in the form of jets or
contained volumes, do not suffer from thermal shock, fatigue or
irradiation damage. While these serious limitations are avoided
altogether, liquid targets face challenges of a different kind.
Specifically, interaction of the proton beams with a high Z liquid jet
target will lead to an explosive style destruction that, while of no
consequence to the secondary particle production, could have serious
consequences to the target container. The ability to replenish a liquid
jet to meet the repetition requirement of the high power proton driver
and the difficulties of adopting a feasible jet scheme to tight
geometrical constraints pose additional challenges. In the case of a
contained liquid, the generation of high cavitational pressures can
induce damage on the target infrastructure. Liquid targets seem capable
of supporting a 4 MW proton driver.

### Proton Energy

While the energy density distribution in a given solid target will vary
within the target depending on the energy of the incoming protons, an
important parameter in transferring deposited heat from the target, the
maximum energy density increases with increasing energy. Table 2 depicts
peak energy densities on a Cu target intercepting proton pulses with the
same intensity and pulse shape.

**Table 2: Energy Density in Cu Targets at Different Beam Energies
(MCNPX Code)**

  ---------------------------------- ------------- ----------- -----------
  proton energy (GeV)                8             16          24

  energy density (J/g)               234           351         377
  ---------------------------------- ------------- ----------- -----------

### Repetition Rate

The benefit of increased repetition rate of the proton driver is
two-fold. For a given proton driver power an increased rep-rate will
lower the demand on the target (especially the solid target) in that the
pulse intensity will be decreased. For the same pulse intensity and
increased repetition rate the proton driver power increases but the
demand on the target increases as well. Specifically, the thermal load
of each pulse on the target must, under the higher rep-rate, be removed
by the heat sink in a shorter time and the rep-rate limit will be
controlled by the ability to remove the dynamic stresses entirely
between pulses.

### Pulse length, intensity and structure

The survivability of the target depends on the above three parameters.
Specifically, the pulse intensity, combined with the beam spot size,
controls the quasi-static conditions of pressure and temperature
generated in the target upon beam interception. Energy densities of up
to 400 J/g, corresponding to \~ 24 10^12^ protons per pulse and σ~r~ =
1mm, may be tolerated by some high performance solid materials. The
pulse length controls the ensuing dynamic stresses and can play a
significant role in the way the solid target survives the induced shock.
Solid targets favor longer pulses because of the ability to relax during
deposition. On the other hand, liquid jet targets will perform best at
very short pulses (a few ns) where the onset of jet destruction has not
occurred. A pulse structured not as a Gaussian but as a uniform
distribution over the same (i.e., 3σ spot) and same intensity will
reduce the stress and temperature demand on the target by approximately
a factor of three.

## bunch length

The proton bunch length has a strong influence on the muon density
produced at the end of the front end. The accepted muon density at the
end of the cooling channel falls off with increasing proton driver bunch
length on the target. This behavior can be partially understood by a
simple theory that models the longitudinal dynamics of the muon beam
through the RF components of the front end. Longer proton bunches
produce initial longitudinal phase space areas that exceed the
longitudinal acceptance of the front end.

## repetition rate

The primary downside of a higher repetition rate is the average power
consumption for the RF systems. There are two sources of this: the first
is the energy to fill the RF cavities for each pulse (the unused portion
of which we have no good way of storing for the next pulse), and the
second is the cryogenic costs for cooling the dynamic heat load (the
heat from the absorption of the cavities' stored energy) in the
superconducting cavities.

In Study II \[6\], the average power required for these systems was 44
MW for a 15 Hz average repetition rate. This portion of the machine's
power consumption will be proportional to the repetition rate.

Higher repetition rates will reduce the amount of current per bunch
train, which will reduce the beam loading in the RF cavities. The
primary effect of beam loading is that the bunches toward the head of
the train will gain more energy than those at the tail of the train,
since the earlier bunches have extracted energy from the cavities. This
would be corrected, at least partially, if particles were undergoing
synchrotron oscillations, but they do not do so in scenarios involving
FFAGs, and they undergo a relatively small number of synchrotron
oscillations in the RLAs and initial linac. Furthermore, some schemes
for the storage ring require (superconducting) RF cavities to keep the
beam bunched, and higher currents might require more RF power (and
possibly more cavities) to compensate for beam loading there.

## References

\[1\] C. Albright et al., "Neutrino factory and beta beam experiments
and development", FNAL-TM-2259 (2004)

\[2\] M. Zisman, these proceedings.

\[3\] J.S. Berg et al., "Cost-effective design for a neutrino factory",
Phys. Rev. Spec. Top.-Acc. Beams 9 (2006) 011001.

\[4\] N.V.\~Mokhov et al., Fermilab-Conf-98/379LANL Report
LA-UR-98-5716(1998); <http://www-ap.fnal.gov/MARS>.

\[5\] R.C. Fernow, "Recent developments on the muon-facility design-code
ICOOL", PAC'05, Knoxville, TN, 2005, p. 2651,
[http://www.jacow.org](http://www.jacow.org/).

\[6\] M. Alsharo'a et al., "Recent progress in neutrino factory and muon
collider research within the Muon Collaboration", Phys. Rev. Spec.
Top.-Acc. Beams 6 (2003) 081001.