# SPECTRUM FROM THE PROPOSED BNL VERY lONG bASELINE nEUTRINO FACILITY\*

S.A. Kahn and M.V. Diwan, Brookhaven National Laboratory, Upton, NY,
11973, USA

Abstract

This paper calculates the neutrino flux that would be seen at the far
detector location for the proposed BNL Very Long Baseline Neutrino
Facility. The far detector is assumed to be located at an underground
facility in South Dakota 2540 km from BNL. The neutrino beam facility
uses a 1 MW upgraded AGS to provide an intense proton beam on the target
and a magnetic horn to focus the secondary pion beam. The paper will
examine the sensitivity of the neutrino flux at the far detector to the
positioning of the horn and target so as to establish alignment
tolerances for the neutrino system.

## INtroduction

A bold proposal to send a neutrino beam from Brookhaven National
Laboratory to the Homestake Mine in South Dakota, a distance of 2540 km,
could provide sensitivity to the mixing angles, mass splittings and CP
violating phase that describe the neutrino oscillation matrix. The
physics potential of this proposed long baseline experiment is described
elsewhere \[1, 2\]. To provide a sufficient event rate at the far
detector, an upgrade to the existing AGS facility would be required to
provide the necessary proton intensity. The AGS upgrade would increase
the machine repetition rate from the current 0.5 Hz to 2.5 Hz with
8.9×10^13^ protons per beam fill which would yield an average beam power
of 1MW. The integrated intensity for a typical year of operation (10^7^
sec) is expected to be 2.2×10^21^ protons on target. A description of
the accelerator upgrades, neutrino beam line and target system design
are given in the neutrino facility draft conceptual design report \[3\].
The target chosen must be able to handle this intense proton beam. The
choice was to use a solid target with a low Z material. A woven
carbon-carbon composite that has a very small coefficient of thermal
expansion up to 1000º C was chosen to extend the life of the target by
reducing thermo-mechanical stresses induced by the beam. The target is
surrounded by a horn magnet which it is mounted in. A description of the
target and horn system is discussed in another paper submitted to this
conference \[4\].

## NEutrino Beamline

In order to reach the detector at Homestake the neutrino beam at BNL
must be directed into the ground with an incline of 11.3º with respect
to the surface. The beam line is mounted on a 42 m high hill to
accommodate the need for a 200 m decay tunnel and to avoid the
possibility of contaminating the local ground water. The proton beam at
BNL is transported to the U-line spur using the RHIC transport line. The
beam is bent by 68º and then up the hill to a targeting station near the
top. In order to obtain a broad band neutrino spectrum a two parabolic
horn scheme similar to that which was employed for previous AGS neutrino
beams. Each of the horns selects a different pion momentum range. In
order to have a two interaction length, the carbon-carbon target must be
80 cm long. The long length makes the design of the horn system
difficult because the target does not act as a point source for pion
secondaries. The horn geometry must be modified to account for the
finite length of the target. Consequently the horn system cannot be
viewed as a series of simple thin lenses. The upstream part of the first
horn which surrounds the target captures the 1 to 3 GeV/c secondary
particles produced from the target. The downstream part of the first
horn has an approximately parabolic shape to collect particles in the
3-4 GeV/c momentum range from that part of the target. The second horn
is placed 8.3 m from the upstream end of the first horn to collect
particles with momentum greater than 3-4 GeV/c. The shape of the horn
has been studied using the GEANT simulation program \[5\]. The important
issues for the optimization of the first horn include (1) the opening
angle after the target, (2) the thickness of the conductor on the inner
wall of the horn, (3) the horn length, and (4) the shape of the
parabolic lens at the downstream end.

![](media/image1.png){width="3.2534722222222223in"
height="2.9611111111111112in"}

Figure 1: Wide band horn focused muon neutrino spectrum for 28 GeV
protons on a carbon target.

Figure 1 and 2 show the neutrino and antineutrino flux, respectively,
for 28 GeV protons using the carbon-carbon target, two horn system and
200 m long 4 m diameter decay tunnel. The figures also show the ν~e~
(ˉν~e~ ) contamination in the beam from K and μ decays.

The decay tunnel diameter was chosen to permit the option of operating
the beam line so as to produce a 1º off-axis neutrino beam. Figure 3
shows a comparison of the off-axis beam with the on-axis beam. The
off-axis beam suppresses the flux in the 3 to 8 GeV range of neutrino
energy. This provides a narrow band neutrino beam which is advantageous
for observing the appearance oscillations into ν~e~ since the beam
contamination in the narrow band range is greatly reduced.

![](media/image2.png){width="3.2534722222222223in"
height="3.0215277777777776in"}

Figure 2: Wide band horn focused muon antineutrino spectrum for 28 GeV
protons on a carbon target.

![](media/image3.png){width="3.1875in" height="3.125in"}

Figure 3: Comparison of the 1º off-axis muon neutrino spectrum with the
on-axis neutrino beam for 28 GeV protons on a carbon target.

## Alignment Requirements

In order to have confidence that the flux of neutrinos is known at the
far detector site the beam, target and horns must be positioned and
oriented within certain tolerances. The criterion that is being used for
determining the tolerances is that the worst acceptable flux variation
of the far detector should be less than 5% from alignment uncertainties.
There are approximately twenty parameters that can be varied in
positioning the beam, the target relative to the horn, and each of the
horns. Since any of these variables can be randomly misaligned any
single variable should have a 1.25% variation. We can allow some of the
variables to exceed this 1.25% variation since other parameters would
come under this variation. We have set a maximum tolerance of 2.5%
variation for each of the positioning parameters. This criterion is less
stringent than that which has been used for the NuMI beam line at
Fermilab. The NuMI criteria accepted a worst flux variation of 2% in any
1 GeV bin from 1-80 GeV of neutrino energy. The effective error of
positioning the beam, target and horns for the NuMI beam line was
approximately 0.5 mm. The necessity for precise knowledge of the
neutrino flux at the far detector is to measure ∆m~23~^2^ by the
decrease in the number of neutrino events seen at the far detector from
those expected if there were no oscillations of neutrino states. The
BNL-Homestake wideband oscillation experiment expects to see more than
one oscillation peak in the disappearance spectrum seen at the far
detector. The ∆m~23~^2^ measurement can be determined from the spacing
of the peaks on the E~ν~ spectrum distribution, thus it is less
sensitive to as precise knowledge of the neutrino flux as the NuMI
experiments are.

The PBEAM program \[6\] program that was used for the NuMI alignment
study was used to evaluate the flux at our far and near detector
locations for slightly misaligned configurations of the beam, target and
horn positions and orientations. The program produces π^±^, K^±^ and
K^0^ from the target and tracks these particles through the horn
focusing system and decay tunnel. A weight is assigned to neutrinos
produced from the meson decays corresponding to the branching ratio for
that decay mode and the probability that the corresponding neutrino
reaches the detector. The weighting process permits the generation of
significantly larger statistics than can be reasonably obtained with
GEANT. The PBEAM program does not handle cascading decays such as the
π→μ→ν~e~ decay, which is an important source of the ν~e~ background for
the lower energy BNL spectrum. The meson production spectrum that is
observed off the target with the PBEAM program is not consistent with
that observed with GEANT. PBEAM does not produce as many high energy
mesons as GEANT does, however this may not be critical in this study
since the analysis looks at ratios of perturbed to unperturbed
distributions. Table 1 shows the parameters that were used to describe
the target-horn system for this study. These parameters vary slightly
from the current baseline values.

  ----------------------------------- -----------------------------------
  Parameter                           Value

  Beam Momentum                       28 GeV/c

  Beam RMS Radial Size                1.0 mm

  Target Material                     Carbon

  Target Density                      1.7 g/cm^3^

  Target Length                       80 cm

  Target Radius                       3 mm

  Horn 1 Length                       2.17 m

  Horn 1 Inner Radius                 7 mm

  Horn 1 Upstream Position            0 m

  Horn 2 Length                       1.5 m

  Horn 2 Inner Radius                 32-44 cm

  Horn 2 Upstream Position            8.5 m

  Horn Current                        250 kA
  ----------------------------------- -----------------------------------

Table 1: Parameters used to describe the beam, target and horn for the
alignment analysis.

In the analysis each of the following variables was varied one at a time
and the flux was calculated at the detector positions:

-   x, y, θ~x~, and θ~y~ of the beam position on the target.

-   x, y, θ~x,~ and θ~y~ of the target relative to horn 1.

-   x, y, θ~x,~ and θ~y~ of the position of the horn 1 plus target
    ensemble.

-   x, y, θ~x,~ and θ~y~ of horn 2.

-   the horn current.

    The ratio of the perturbed distribution to the unperturbed is
    calculated and fitted to a polynomial to smooth out the
    distribution. The largest variation in the distribution is used to
    determine the tolerance of that variable. Table 2 shows the
    allowable tolerances for the positioning and orientation of the
    beam, target and horns.

  ----------------------------------- -----------------------------------
  Variable                            Proposed Tolerance

  Beam Position                       1.5 mm

  Beam Angle                          3 mr

  Target Position                     1 mm

  Target Angle                        3.7 mr

  Horn 1 Position                     1.7 mm

  Horn 1 Angle                        3.5 mr

  Horn 2 Position                     3.5 mm

  Horn 2 Angle                        7.0 mr
  ----------------------------------- -----------------------------------

Table 2: Proposed positioning tolerances for the neutrino beam elements.

The target position and angle tolerances are given with respect to the
position and angle of horn 1 which surrounds it. They can be stated as
tolerances of the relative positions of the downstream part with respect
to the upstream part. The listed angular tolerances would be achieved if
each end of the element were positioned with this respective positioning
tolerance.

These tolerances should be achievable initially. There is concern as to
whether the neutrino beam elements will stay within these tolerances
over time since the hill on which the beam line is built might settle
after the alignment is made. If the positioning of the beam elements is
monitored during a running period, corrections to the determination of
the flux at the far detector can be made. Active repositioning of the
beam elements need not be made during a run. They can be repositioned
during long shutdown periods. An optical system of measuring fiducial
markers on both ends of the neutrino beam line elements during the run
will be necessary.

## acknowledgements

This work was performed with the support of the US DOE under Contract
No. DE-AC02-98CH10886.

## References

\[1\] *Report of the BNL Neutrino Working Group: Very Long Baseline
Neutrino Oscillation Experiment for Precise Determination of Oscillation
Parameters and Search for ν~μ~→ν~e~ Appearance and CP Violation,* BNL
Report 69395(2002)

\[2\] M.V. Diwan et al., *Very Long Baseline Neutrino Oscillation
Experiment for Precise Measurements of Mixing Parameters and CP
Violation Effects*, Physical Review D 68, 01002 (2003)

\[3\] .*The AGS-Based Super Neutrino Beam Facility*, CDR, BNL Report
73210-IR (2004)

\[4\] S. Bellavia et al., *Target and Horn Cooling for the Very Long
Baseline Neutrino Experiment*, submitted to this conference.

\[5\] *GEANT, Detector Description and Simulation Tool*, CERN Program
Write-up W5013.

\[6\] The *PBEAM* program was written by Noel Stanton and modified by
Wesley Smart.