Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
Computational Design Optimizations for Aerogel Kaon
Cherenkov Detector for JLab Hall C.
Nathaniel Hlavin
Catholic University of America
Advisor: Dr. Tanja Horn
Abstract: The purpose of the project is to design a silica aerogel Cherenkov
detector to install in Hall C at the Jefferson Laboratory. This detector will be used to identify
kaons. The detector is designed for use in the detection of particles with momenta ranging
from 2 GeV to 8 GeV. If the particles are moving faster than the speed of light through aerogel,
they will create Cherenkov radiation as they pass through it. This light will be collected by
efficiently placed Photo Multiplier Tubes (PMTs). Via the photoelectric effect, the PMTs will
emit photoelectrons and amplify their signal to be a discernable and analyzable electric pulse.
Desirable properties for our detector are high Cherenkov light output for kaons, good efficiency
in the collecting and converting of the light, and light emission that can be converted by existing
and cost-efficient PMTs. Among the chief tasks is the distinguishing of kaons from protons. The
index of refraction of the aerogel will need to be chosen so that the protons do not emit a
signal when they pass through but the kaons still emit a desirable signal. Testing and optimizing
of the design of the detector will be done using a Monte Carlo computer simulator.
1
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
1. Introduction
Generalized Parton Distributions (GPD) are used to understand the internal structure of
nucleons. By observing and analyzing data taken from particles produced in hard
scattering meson electroproduction (diagram below), we can construct the GPD of the
proton.1 Pictured below are some examples of GPDs generated by models. We are
looking for experimental data to generate actual GPDs for the proton. The x variable is
the fraction of the momentum of the quark over the momentum of the proton.
Different x values result in different distributions.
Generalized Parton Distributions
Meson Electroproduction
2
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
However, for the data to have this desired effect, it must conform to the hard, or
perturbative, quantum chromodynamic (QCD) form factorization.
Meson Form Factors
T
.
Unfortunately, as can be seen in the plot2 pictured above, current form factors for the
pion do not match up with the QCD model. Some data on the kaon has been produced,
but further experiments could determine if the kaon’s form factors match up with hard
QCD and could be used to construct the GPD. To that end, a new detector is being
developed to detect kaons in the Super High Momentum Spectrometer (SHMS) in JLab
Hall C.3
2. Theory
The proposed detector would be an Aerogel Cherenkov detector. As charged particles,
in our case kaons, pass through a material faster than the speed of light through that
material, light is emitted in a process that is analogous to a sonic boom. This is called
Cherenkov radiation and can be utilized to detect high energy sub-atomic particles.
Aerogel, even though it is a delicate substance, has a very low index of refraction and so
is ideal for good light output from these very small high energy particles.4 The light from
this process goes into a lightbox where it is collected by Photomultiplier Tubes (PMT)
and turned into electric signal via the photoelectric effect. This signal is then amplified
so that it can be analyzed.
3
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
2.1 Varied Indices
The detector would be used to detect particles with momenta from 2-8 GeV/c.
However, since no one refractive index of the aerogel produces a kaon signal only for
this range, multiple refractive indices would be needed. A pion signal always occurs for
all momentum values, but since this is already distinguished from the kaon signal by
another detector, we do not have to take this into account. However, for many
momentum values and indices, a proton signal is emitted and would introduce error
into our kaon values. This proton signal needs to be minimized, while still maximizing
the desired kaon signal. This presents one major challenge for detector design.
2.2 Other Design Constraints
Other design constraints include geometric constraints due to the placement of our
detector within the SHMS detector stack. We have been left approximately 45 cm of
space for our entire detector. Also, being financially efficient with our materials is a high
priority, which is why we are building an Aerogel Cherenkov detector rather than the
pricier RICH detector.
2.3 Preliminary Calculations
Before any experimental testing we chose several likely values of efficient refractive
indices using an equation5 that gives the number of emitted photoelectrons for
standard Cherenkov radiation and photoelectric collection.
𝛼2 𝑧 2
𝑁𝑝.𝑒. = L 𝑟 𝑚
𝑒
𝑒𝑐
2
∫ 𝜖 𝑑(𝐸) sin2 𝜃𝑐 (𝐸)𝑑𝐸
(1)
𝛼2
where L is the thickness of the aerogel and z = 1 and 𝑟 𝑚
𝑒
𝑒𝑐
2
= 370 𝑐𝑚−1 𝑒𝑉 −1 . ∫ 𝜖 𝑑(𝐸)
is the efficiency percentage, which is our case multiplies out to be 11.2%. This
percentage includes the reflectivity of the aerogel, the absorption percentage of the
PMTs, the quantum efficiency of the PMTs, and the reflectivity of the Millipore paper
that lines the lightbox.6 To find some of these likely values, equation (1) is used to
calculate the number of photoelectrons for a range of refractive indices (1.007-1.127)
and momentum values (2-8 GeV). From these 7 plots (Graphs 1-7 in appendix) several
candidates can be discerned. We chose 1.01, 1.015, 1.02, and 1.03. Graphs 8-11 show
the plots of number of photoelectrons across the range of momentum for each of these
refractive indices. From these graphs it is evident different indices are more ideal for
different parts of the momentum range. 1.03 seems to be a good choice for 2-4 GeV
and 1.015 seems to be a be a good choice for 4-6 GeV. No refractive index seems to be
a good choice for the higher values of 6-8 GeV. For this part of the range we can use
kinematic separation to distinguish protons and kaons.
4
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
3. Experimental Simulation
With these four refractive index values in hand we move on to experimental testing. In
order to test the various parameters and characteristics of our detector to achieve the
optimal design, we used a Monte Carlo computer simulation for Aerogel Cherenkov
detectors called SimCherenkov, originally written by D.W. Higinbotham of Jefferson
Lab.7 It is written in the programming language FORTRAN, so this language was adopted
for any additional programming as well. In order to fully test all the characteristics of
the detector, some supplementary features were added to the program. The program
originally allowed for PMTs to be placed on the east and west walls of the lightbox.
Additional choices were added to put PMTs on the north and south walls, as well as a
three-walled and four-walled configuration option. To this end, we increased the total
number of PMTs able to be used from sixteen to thirty-two. We also provided an option
to have a mix of PMTs with different radii, with the larger PMTs in the center of the
walls. This option was available for the three-walled setup only. The program itself
already provided for the adjustment and testing of a number of other variables, such as
the thickness of the aerogel, the depth of the lightbox, the refractive index of the
aerogel, the size of the aerogel panel, and the efficiency percentages of the various
components of the detector. The detector’s design was optimized using this program to
test each design characteristic one at a time. For all the following optimization tests the
refractive index was held at 1.015
3.1 Length and Width of Aerogel Panel
The first design characteristic that was optimized was the length and width dimension of
the aerogel panel. In this investigation the density distribution of incident particles
must be considered. At our placement in the SHMS this distribution takes an hourglass
shape (pictured below) due to the focusing and defocusing magnets that bend the
particles into the SHMS. A 110x100 cm panel encloses the entire distribution, and a
90x60 cm panel encloses the area of greatest density.
5
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
8.00
7.00
Number of Photoelectrons
90x60 cm
Panel Size
110x80 cm
6.00
110x100 cm
5.00
4.00
3.00
2.00
1.00
0.00
0
2
4
6
Momentum (GeV)
8
10
The pictured plot shows the photoelectron output for 3 different sizes of panel. It is
clear that the optimal size is the one that encloses the area of greatest density in the
distribution, 90x60. The difference in size of these panels necessitates a different
number of PMTs as well but all setups have as many 5” radius PMTs as will fit.
3.2 Thickness of Aerogel
A further dimension of the aerogel that had to be optimized was the thickness. Here we
must remember that this is the dimension that is constrained by 45 cm slot allotted for
this detector in the SHMS. The aerogel thickness and the depth of the lightbox must not
sum to a number higher than ~45. The thicknesses that were tried were 5 cm, 8 cm, and
10 cm. Below is the graph of the photoelectron outputs for these thicknesses.
16.00
Aerogel Thickness
Number of Photoelectrons
14.00
10 cm
12.00
8 cm
10.00
5 cm
8.00
6.00
4.00
2.00
0.00
0
1
2
3
4
5
Momentum (GeV)
6
6
7
8
9
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
Clearly, the 10 cm thickness offers a significant boost in photoelectron output. It is a
large enough increase to justify the extra financial cost of the increased amount of
aerogel.
3.3 Photomultiplier Tube Placement
A more complicated challenge is the optimization of the PMT configuration. Here, the
dimensions of the box also play a role, so some of the optimization involved changing
the previously optimized aerogel panel size. Perhaps if the PMT configuration was
sufficiently optimized, the panel would actually be more efficient with a different size.
As it turns out, the same panel size remained optimal, with 5” PMTs on three sides.
Pictured below is the photoelectron output plot for the various configurations. Larger
panel dimensions, even with the addition of more PMTs, did not produce higher signals.
A one-sided configuration was very poor. The two-sided configuration, either N/S or
E/W did not improve very much. Mixing PMTs of different radii on three sides was only
a slight improvement on the two side setup. One four-sided setup was tried, but its
results do not matter because the SHMS does not allow for four sides of PMTs. Three
sided layouts were the best, and among them the optimized panel size emitted the
highest signal. For this panel size 6 5” PMTs were put on the E/W sides and 4 5” PMTs
on the smaller N side.
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Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
3.4 Lightbox depth/PMT coverage percentage.
A final design characteristic to investigate was the depth of the light box. This, like the
aerogel thickness, is constrained by the ~45cm amount of space in the SHMS. Here, the
values assessed were 22.5 cm, 24.5 cm, and 26.5 cm. The sum of any of these and the
optimized aerogel thickness does not exceed this constraint. When the simulations had
been run for these three depths, 22.5 was shown to be the optimal value. This is
because it decreased the total surface area of the lightbox, which in turn increased the
PMT coverage percentage. The higher the PMT coverage percentage, the more efficient
photon collection is. The gain in signal was very small, however, with only a 4% gain
when the curves are furthest apart. Graph below.
7.00
Lightbox Depth
Number of Photoelectrons
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
4
5
6
Momentum (GeV)
7
8
4. Results
The results gained from our computer simulation study are optimized design
characteristics for the Kaon Aerogel Cherenkov Detector. Several refractive indices of
aerogel must be used, with 1.03 for the lower momenta (2-4 GeV), 1.015 for the midrange momenta (4-6 GeV), and kinematic separation for the higher momenta (6-8 GeV).
The aerogel panel itself ought to enclose the area of highest density of the hourglass
distribution, 90x60 cm. The aerogel should be 10 cm thick to maximize photoelectron
output. The PMTs should be configured according to the optimal panel size, fitting a
6x6x4 5” PMT layout. The lightbox could be adjusted to be shallower to increase PMT
coverage slightly, but this was shown to not significantly change performance.
5. Conclusion
Using the tools of computational physics and computer programming, we were able to
find the optimum design for a Kaon Aerogel Cherenkov Detector. Further steps include
creating technical drawings to aide in communication of this design to those who will
construct the detector. Plans to test the components of the detector such as aerogel
8
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
and PMTs in a small scale experiment have also been made. Use of this detector could
provide us with data to find out whether the resulting form factor for the kaon will
match the current hard QCD model. Should this occur, the GPD of the proton would
perhaps be within reach.
Acknowledgements: The author would like to thank Dr. Tanja Horn for mentoring and advising
this work and the research behind it, and the Catholic University of America Physics Department
for providing the opportunity.
References:
1
T. Horn et al., Proposal to JLab PAC 34, Studies of L-T separated Kaon Electroproduction at 5-11 GeV, December
15, 2008
2
T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.; T. Horn et al., arXiv:0707.1794 (2007). ; A.P. Bakulev et al, Phys. Rev. D70
(2004)]
3
T. Horn et al., E12-09-011, L/T separated Kaon cross sections at JLab 11 GeV
Nuclear Instruments and Methods in Physics Research A 553 (2005) 364-369
5
Physics Review Letters, Volume 592, Issue 1-4 (2004)
6
R. Asaturyan et al., arXiv:physics/0411147v1 [physics.ins-det] 16 Nov 2004
7
Nuclear Instruments and Methods in Physics Research A 414 (1998) 332-339
4
Appendix:
1. (For Graphs 1-11, Blue = Kaon, Red = Proton)
80
Momentum = 2 GeV
70
Number of Photoelectrons
60
50
40
30
20
10
0
1.000
-10
1.020
1.040
1.060
1.080
1.100
Refractive Index
9
1.120
1.140
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
2.
90
Momentum = 3 GeV
80
Number of Photoelectrons
70
60
50
40
30
20
10
0
1.000
-10
1.020
1.040
1.060
1.080
1.100
1.120
1.140
Refractive Indices
3.
90
Momentum = 4 GeV
80
Number of Photoelectrons
70
60
50
40
30
20
10
0
1.000
-10
1.020
1.040
1.060
1.080
1.100
Refractive Index
10
1.120
1.140
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
4.
90
Momentum = 5 GeV
80
Number of Photoelectrons
70
60
50
40
30
20
10
0
1.000
-10
1.020
1.040
1.060
1.080
1.100
1.120
1.140
1.120
1.140
Refractive Index
5.
100
90
Momentum = 6 GeV
Number of Photoelectrons
80
70
60
50
40
30
20
10
0
1.000
-10
1.020
1.040
1.060
1.080
1.100
Refractive Index
11
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
6.
100
Momentum = 7 GeV
90
Number of Photoelectrons
80
70
60
50
40
30
20
10
0
1.000
1.020
1.040
1.060
1.080
1.100
1.120
1.140
Refractive Index
7.
100
90
Momentum = 8 GeV
Number of Photoelectrons
80
70
60
50
40
30
20
10
0
1.000
1.020
1.040
1.060
1.080
1.100
Refractive Index
12
1.120
1.140
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
8.
7
n = 1.01
Number of Photoelectrons
6
5
4
3
2
1
0
0.00
2.00
-1
4.00
6.00
8.00
10.00
8.00
10.00
Momentum (GeV)
9.
12
n = 1.015
Number of Photoelectrons
10
8
6
4
2
0
0.00
-2
2.00
4.00
6.00
Momentum (GeV)
13
Computational Design Optimizations for Aerogel Kaon Cherenkov Detector.
10.
16
n = 1.02
Number of Photoelectrons
14
12
10
8
6
4
2
0
-2
0.00
2.00
4.00
6.00
Momentum (GeV)
8.00
10.00
11.
Number of Photoelectrons
25
n = 1.03
20
15
10
5
0
0.00
-5
2.00
4.00
6.00
Momentum (GeV)
14
8.00
10.00