E614 Experiment Tech Notes Project Mail

From: Dan Rankin <drankin@triumf.ca>
Date: Mon, 28 Feb 2000 17:05:38 -0700
To: E614TN@relay.phys.ualberta.ca
Subject: TN-42: A Monte-Carlo Study of a Pion Based Calibration Experiment

The purpose of this study is to evaluate the viability of using a pi+
beam
from the M13 production target to produce either a polarized or an
unpolarized mu+ spectrum in the detector.  This mu+ spectrum could then
be
used to calibrate the detector.  This study was carried out using E614
GEANT V1.2.  The results of this study show that for a 65 MeV/c pi+
beam, only 1% of the incident pi's result in mu's that decay in the
target foil.
This figure drops to 0.59% when we only consider stopped pi's, and is
further reduced to 0.2% when we only look at pi's that stop in the
target
foil.


Dan Rankin
E614 Co-op Student

Filename: TN-42.ps

NOTE: Sorry, the pi and mu symbols did not convert over properly from Word97
(they appear as ?'s). Please refer to the postscript file if you get
confused, or email me (drankin@triumf.ca) and I'll try to get you either
an enriched text format that displays the characters in question or the
original word 97 file. Thank you.
Dan Rankin
February 25, 2000

TRIUMF Experiment E614

TN-42

A Monte-Carlo Study of a Pion Based Calibration
Experiment

D. Rankin, TRIUMF Co-op Student
Supervisor: D. Gill, TRIUMF

February 21, 2000

Abstract

The purpose of this study is to evaluate the viability of using a ?+ beam
from the M13 production target to produce either a polarized or an
unpolarized ?+ spectrum in the detector. This ?+ spectrum could then be
used to calibrate the detector. This study was carried out using E614
GEANT V1.2. The results of this study show that for a 65 MeV/c ?+
beam, only 1% of the incident ?'s result in ?'s that decay in the target foil.
This figure drops to 0.59% when we only consider stopped ?'s, and is
further reduced to 0.2% when we only look at ?'s that stop in the target
foil.

INTRODUCTION

The premise of this study is to discover whether or not it is possible to produce a
polarized or unpolarized spectrum of ?'s in the target foil from an incident beam of ?'s.
This study consists essentially of two major parts: characterizing the spin distribution of
daughter ?'s that decay in the target foil, and examining the resultant flux of ?'s that
would be available to perform the experiment. Originally an incident ?+ beam
momentum of 65 MeV/c was chosen because of a relatively high flux from the M13
production target (~4000 counts / uA sec) along with relatively low e+ and ?+
background[1].

Ideally, we would like to have the maximum number of ?'s stopping in the target in
order to maximize the ?+ flux in the target. The way that we achieved this is as follows.
The finished detector will use a volume of an He/Ar mixture to slow the incident ?'s in
order to stop the maximum amount of them in the target foil. In this study, we did not
alter the He/Ar mix, but instead we increased the thickness of the scintillators to 360
microns (from 160 microns) in order to obtain a maximum number of 30 MeV/c ? stops
in the target foil. Then in order to stop the more energetic ?'s in the target foil, we added
two plastic degraders, one upstream to absorb the ?'s energy, and one downstream for
symmetry. These degraders were varied in thickness depending on the momentum of the
incoming ?'s.

65 MeV/c ? Beam Results

The 65 MeV/c incident ?+ beam was created by E614 GEANT using the BEAM data
card found in the e614.ffcards user input file [2]. This input allows us to select the
initial beam momentum of 65 MeV/c, with a momentum spread of 0.5%. The detector
geometry is already included in the E614 GEANT V1.2 package, and the only parts of
the detector geometry that were modified are the scintillators and the added plastic
degraders.
At 65 MeV/c, the incident ?'s decay along a large section of the z axis, as shown in
figure 1.

The top graphic of figure 1 shows not only the stopping ?'s, but also the ?'s that decay in
flight in the detector. The bottom graphic shows only the ?'s that stop. The stopping ?'s
comprise about 31% of the incident ?'s. There is a noticeable baseline of in flight decays
of the ?'s on the top figure. This baseline extends off of the graph to the left, accounting
for the large fraction of the ? decays that are not accounted for on the top graphic of
figure one. It is also worthy to note that the stopping distribution does not appear to be
exactly optimized, as the peaks to the immediate right of the stopping target are slightly
larger than those peaks to the immediate left. This may be the cause of the slightly non-
zero mean spin distribution that we will encounter later in this note. Figure 1 is the result
of 500,000 incident ?'s.
Figure 2 shows a magnified view of the decay locations of ?'s in the scintillators
and degraders. Please note the differences in scale between the four graphics.
The graphics of figure 2 were created again using 500,000 incident ?'s. All of these
graphics total less than 1.6% of the incident beam, with the downstream scintillator
having the greatest proportion of the original beam at 0.67%. The detailed statistics are
available in Table 1.

The graphics of figure 3 were not created using the BEAM card as in the previous
graphics. In order to be able to "see" a meaningful distribution, we needed to run many
more events. To save CPU time, we stored the stopping locations of the ?'s that decayed
in the degraders and scintillators from a 500,000 event run in a data file, discarding all
other decay locations. We then generated stopped ?'s at the stored locations, so that we
had 500,000 stopped ?'s in only the scintillators and degraders. This is the statistical
equivalent of running ~33 million incident beam ?'s .

From the graphics of Figure 3, it seems that the flux of ?'s that reach the target from
the scintillators and degraders is very low, with the largest flux coming again from the
downstream scintillator. The statistics are available in Table 1.

Figure 4 shows the spin distribution of daughter ?'s versus the z location of the ?
decay that produced the ?. The top graphic shows that the likelihood of a ? stopping in
the target depends on its initial momentum (hence its spin) and initial z position. In the
following discussion, spin is often used to describe the direction of motion of the ?? For
example, a ? produced in a module at z = 10cm with a spin of 0.9 will not "see" enough
material in order to degrade the ?'s momentum enough to stop it in the target foil. On the
other hand, a ? produced at the same location with a spin of 0.1 leaves at a much larger
angle than the previous case, passes through much more degrading material, and loses
sufficient momentum to make stopping in the target much more probable.
The bottom graphic of figure 4 shows the projection of the top graph onto its Y-axis.
The significance of this graphic is that it shows the mean spin distribution of ?'s stopping
in the target that originate from all over the detector body. The mean spin is 2.6*10-2,
which is very close to being an unpolarized spectrum. It may be that the non-zero mean
spin is a result of the error seen in the optimization of the ? stopping distribution that was
seen in figure 1.
Figure 5 shows the same type of histograms as the top graphic of figure 4, but figure
5 displays only the ?'s that originate in the degraders. The ?'s that originate in the
degraders all need spins that are close to ń1, as the scintillators were optimized to stop
?'s in the target foil. As the ?'s come from deeper in the degraders, they need spins
closer to ń1 to reach the target foil, hence the slight curvature to the histogrammed
distribution.

Figure 6 is complementary to figures 4 and 5, but in this instance it is only the
scintillators that are histogrammed. In figure 6 it is even more apparent that the deeper
inside the scintillator the source of the ? is, the closer the spin must be to ń1.

Figure 7 is again the same type of histogram as figures 4-6, but figure 7 shows only the
?'s that stop in the target foil from parent ?'s that stopped in the target foil. The bottom
part of figure 7 shows the projection of the top graphic onto its Y-axis. This is to show
the spin distribution, along with its mean. The mean is 6.59*10-3, even closer to an
unpolarized spectrum than the spectrum that was observed from all of the ? sources.
Again, the non-zero value of the mean spin may be a result of error in optimizing
the???stopping distribution.

Figure 8 shows the wire number in PC plane #6 (closest to target foil on the upstream
side) where the incident ? and the daughter ? both create a hit in the same wire. It was
desirable to examine this potential problem to see if the rate at which the same wire is hit
creates a significant processing problem. As these results were created from a run of
500,000 incident 65 MeV/c ?'s, this process of same wire hits occurs in less than 0.5%
of the events tracked. This may present a significant problem.

Table 1 shows the majority of the statistical information gathered through the runs at
an incident ? momentum of 65 MeV/c. Generally, the important statistical numbers are
those found under the heading "% (or fraction) of original beam". Again, all of these
statistics were generated using the E614 GEANT V1.2 Monte Carlo software package,
along with slight modifications for histogramming and data collection.
40 MeV /c ? Beam Results

As the useful ? flux available from incoming ?'s at 65 MeV/c is somewhat low, the
next step was to test for the available flux for a ? beam at 40 MeV/c. The flux of ?'s
available from the M13 production target at 40 MeV/c is considerably lower (about a
factor of 30) than the flux available at 60 MeV/c [1]. However, the ? stopping
distribution curve was much steeper at 40 MeV/c, so it was hoped that there would also
be an increase in the flux of useful ?'s that were produced. The degraders needed to
optimize the stopping distribution were 530 microns thick.
From figure 9 it is seen that the majority of the ?'s that stop in the detector do so in
the target foil. The contribution of daughter ?'s from the degraders and scintillators is
negligible. The ?'s that stop in the target are the greatest source of useful ?'s. As seen in
figure 10, 2839 useful ?'s were produced in the target, a fraction of 0.57%. This is about
a factor of 3 higher than the 65 MeV/c case. However, the total ? flux is much less, so
the flux of useful ?'s is effectively reduced by a factor of 7 Ť. An advantage to using 40
MeV/c ?'s is that there are fewer background sources of ?'s (scintillators, degraders,
modules, etc.), so it is easier on the data acquisition system.

The bottom part of figure 10 shows that the mean spin distribution at 40 MeV/c is as
close to unpolarized as it is at 65 MeV/c.

52 MeV/c ? Beam Results

In an effort to find an even better ? beam momentum operating point, we tried an
incident ? momentum of 52 MeV/c. At this momentum, the required degrader thickness
was 3.468 mm. The flux of incident ?'s available from the M13 production target is
about a factor of four less than at 65 MeV/c [1].
In figure 11, the distribution of stopping ?'s is an intermediate of the two previous
cases that have been discussed. There will not be as many background ?'s as the 65
MeV/c case, but more than the 40 MeV/c example. The flux of incoming ?'s at 52
MeV/c is about a factor of 4 less than the flux at 65 MeV/c. As seen in figure 12, the flux
of useful ?'s available increases to 0.38% of the incident beam, just less than twice as
much as at 65 MeV/c. Thus 50 MeV/c provides half of the flux of useful ?'s that 65
MeV/c, but it also provides a reduction in background ??'s.

As in both the 65 MeV/c case and the 40 MeV/c case, the mean spin distribution is
close to zero, which is shown on the bottom part of figure 12.

CONCLUSIONS

If we set as a goal to have 5,000 target foil ? events/sec, it is interesting to examine
the needed flux of incident ?'s under different assumptions. If all of the ?'s that end up
stopped in the target are useful for this experiment, then at 65 MeV/c we need 500,000
incident ?'s/sec to have the required 5,000 target foil ?'s/sec. If only the ?'s that stop
create usable ?'s in the target, then we need about 850,000 ?'s/sec. If we can use only
the ?'s in the target that are created from ?'s that stop in the target, the number of ?'s
needed increases to 2.5 million ?'s/sec. Using a momentum of 40 or 52 MeV/c requires
fewer ?'s/sec, but the available flux from the M13 decreases by a greater amount, so the
net result is that it would take longer to accumulate 109 events at these lower momentums
than at 65 MeV/c. The lower momentums would provide a smaller background of ?
sources, as the ? sources become more concentrated around the target foil. It seems that
the scintillators and degraders are not significant contributors to ? production that results
in ?'s in the target. Even at 65 MeV/c, only 0.03% of the incident ?'s decay in the
scintillators and degraders to produce ?'s that end up in the target foil.
Another question to answer is can we use the ?'s from the surface of the scintillator
for a spin experiment. Using the configuration that was utilized in this study, it is not
possible. The available flux of ?'s from the scintillators is much too low at only 0.005%
of the incident ? beam. However, it may be possible to alter the scintillator and/or
degrader thicknesses along with optimizing the beam momentum in order to maximize ?
stops in the surface of the downstream scintillator in order to possibly perform an S? =
+1.0 experiment using the daughter ?'s.

References

1. TRIUMF Users Handbook, p. IV-18a

2. D. H. Wright, TN-29, "A Users Guide to E614 GEANT".

A total of 7591 ?'s stopped in the scintillators and degraders. That is 1.52% of the original 500,000
events. A further 500,000 events were generated ONLY from this 1.52%, so the statistical equivalent of
the original beam is 500,000/(1.52*10-2) = 32.89*106 events
The term "spin" as used in this document refers to the orthogonal spin component along the z-axis. That
is, ?'s with spin ń1 travel parallel the z-axis, whereas a spin of 0 means the ? is moving in the x-y plane.
As all ?'s have the same initial momentum (29.7 MeV/c) the spin can also be used as a measure of decay angle.
2468 same wire hits out of 500,000 ? events. 2468/500,000 = 0.494%
1