Simulation and optimization of the
electric eld in a liquid xenon time
projection chamber
by Hrvoje Dujmovic
Supervised by Prof. Laura Baudis, Aaron Manalaysay
Bachelor thesis in physics at the University of Zürich
July 2012, Zürich
1
Contents
1 Introduction
1.1
1.2
5
Evidence for dark matter
. . . . . . . . . . . . . . . . . . . . . .
Velocity dispersion & rotation curves of galaxies
1.1.2
Gravitational lensing . . . . . . . . . . . . . . . . . . . . .
6
1.1.3
Cosmic microwave background radiation . . . . . . . . . .
8
1.1.4
Theoretical dark matter candidates . . . . . . . . . . . . .
9
Direct WIMP detection
. . . . .
2.2
6
. . . . . . . . . . . . . . . . . . . . . . .
9
1.2.1
Xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.2.2
Xürich . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2 Simulations
2.1
6
1.1.1
12
Introductory models
. . . . . . . . . . . . . . . . . . . . . . . . .
12
2.1.1
Xürich model . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.1.2
Field leakage through a wire grid . . . . . . . . . . . . . .
14
Xürich2 models . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.2.1
A simplied Xürich2 model
17
2.2.2
3D model
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2.2.1
Variation of the cathode voltage
. . . . . . . . .
22
2.2.2.2
Field at the liquid surface . . . . . . . . . . . . .
25
2.2.2.3
The nal design
26
. . . . . . . . . . . . . . . . . .
3 Measuring the properties of conducting PTFE
32
3.1
Resistivity distribution . . . . . . . . . . . . . . . . . . . . . . . .
32
3.2
Temperature dependance of the resistivity . . . . . . . . . . . . .
35
3.3
Outgassing
36
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Conclusion
39
2
List of Figures
1.1
The rotation curve of NGC 3198
1.2
Bullet Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
7
8
1.3
Early Xürich2 diagram . . . . . . . . . . . . . . . . . . . . . . . .
11
2.1
Xürich geometry used in electric eld simulations . . . . . . . . .
13
2.2
Electric eld density Xürich . . . . . . . . . . . . . . . . . . . . .
14
2.3
Electric eld density along the central line in Xürich
. . . . . . .
15
2.4
Field leakage geometry . . . . . . . . . . . . . . . . . . . . . . . .
16
2.5
Field leakage
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
2.6
Geometry of the simple Xürich2 model . . . . . . . . . . . . . . .
18
2.7
Xürich2 eld densities with dierent eld shaping setups . . . . .
19
2.8
Field with one resistor . . . . . . . . . . . . . . . . . . . . . . . .
20
2.9
Field with two resistors
. . . . . . . . . . . . . . . . . . . . . . .
21
2.10 Xürich2 3D geometry . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.11 3D model; basic eld . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.12 Field with cathode connection . . . . . . . . . . . . . . . . . . . .
23
2.13 Field variation comparison with a variable cathode voltage . . . .
24
2.14 Optimal voltage on PTFE top for a certain cathode voltage . . .
25
2.15 Circuit schematics
. . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Extraction eciency
. . . . . . . . . . . . . . . . . . . . . . . . .
26
27
2.17 Field density at the liquid surface; top view . . . . . . . . . . . .
27
2.18 Field density at the liquid surface; side view . . . . . . . . . . . .
28
2.19 Surface eld density at various radii
28
. . . . . . . . . . . . . . . .
2.20 Number of rings comparison . . . . . . . . . . . . . . . . . . . . .
29
2.21 Mean eld and deviation in the nal design
. . . . . . . . . . . .
30
. . . . . . . . . . . . . . . . . . . .
31
2.22 Field lines in the nal design
3.1
Resistance measurement circuit . . . . . . . . . . . . . . . . . . .
34
3.2
Temperature dependance of the conductivity
36
3.3
Conducting PTFE spectrum . . . . . . . . . . . . . . . . . . . . .
37
3.4
Conducting and normal PTFE spectra comparison
38
3
. . . . . . . . . . .
. . . . . . . .
List of Tables
2.1
Field densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
Current measurement results
. . . . . . . . . . . . . . . . . . . .
33
3.2
Current measurement results, no glue setup . . . . . . . . . . . .
34
3.3
Current vs. Temperature data . . . . . . . . . . . . . . . . . . . .
35
4
15
Chapter 1
Introduction
Overwhelming observational evidence indicates that all known particles from
the standard model contribute no more than 17% [1] of the total matter content
of the universe. The nature of the remaining 83%, which is referred to as dark
matter, is still unknown and is subject to intensive scientic research [2]. The
evidence for the existence of dark matter is presented in section 1.1. A popular
explanation for the dark matter is the existence of a so called weakly interacting
massive particle (WIMP) [11]. The nal section of this chapter (1.2) describes
a method for detecting WIMPs. This method is used by the XENON100 [18]
experiment in Laboratori Nazionali del Gran Sasso, Italy [3]. At the moment a
much smaller detector, Xürich, using a similar design, is operating at the University of Zürich. The purpose of this detector is the study of the properties
of liquid xenon detectors and the results gained from it can help interpret data
from larger liquid xenon detectors such as XENON100 [14]. Specically Xürich
is measuring the ionization and scintillation yield of the of electronic recoils.
The successor of Xürich, Xürich2, is at the moment being build in Zürich. Section 1.2 also describes the working principle of a liquid Xenon TPC in more
detail.
The main focus of this thesis is the development of several computer
simulations of the electric eld inside Xürich2 and the search for an optimal
design which would minimize the variation of the eld density inside the detector. Section 2.1 of chapter 2 describes several simple models that show some
interesting properties that are of great importance when trying to understand
the behavior of the Xürich2 models described in section 2.2. This chapter also
tests the practicability of a completely new approach to detector design, which
uses conducting polytetrauoroethylene (PTFE) for its hull (instead of the classically employed normal nonconducting PTFE). In order to test the feasibility
of this design several tests are done on the conducting PTFE available to us.
These are described in chapter 3.
5
1.1
Evidence for dark matter
Many dierent observations suggest that there exists a large amount of nonelectromagnetically interacting matter in the universe [1, 13].
This matter is
referred to as dark matter and its content is still unknown as it has not been
directly observed yet.
The reason why most people are condent that dark
matter does exists is the large amount of dierent observations on completely
dierent scales that are very dicult to explain without introducing the dark
matter. These observations also directly give us some information on the abundance and the distribution of dark matter. A selection of these observations is
given in the following sections.
1.1.1 Velocity dispersion & rotation curves of galaxies
If one looks at the spectrum of an elliptical galaxy
1 the spectral lines are broad-
ened [4]. The width of the lines is then related to the velocity dispersion of the
stars in the galaxy. One can then use the velocity dispersion to calculate the
total kinetic energy in the galaxy and using the virial theorem
hV i = −2 hT i one
can obtain an estimate for the total gravitational binding energy and thus the
total mass of the galaxy [5]. For every galaxy ever observed this virial mass is
much higher than the total mass of the visible matter, thus strongly indicating
to the existence of some kind of invisible matter.
A similar observation can be done with spiral galaxies.
If one looks at a
spiral galaxy sideways one can compare the position of the spectral lines from
the side that is rotating towards the observer to that of the other side of the
galaxy which is rotating away from us.
so called rotation curve of the galaxy.
By doing this one can measure the
A rotation curve describes the typical
rotation speed of an object in a galaxy in dependance on its distance from the
galactic center.
An example of such a curve can be seen in gure1.1 [12].
If
one accounts for only the luminous matter in a galaxy one expects the rotation
curve to drop constantly with increasing distance from the center.
However
observations suggest that the curve remains relatively at outside the central
bulge. This again indicates that there is a large amount of non luminous matter
[9].
1.1.2 Gravitational lensing
Large accumulations of matter create strong gravitational potential wells that
bend the light passing close to them. If the light of a distant object is bent in
this way the object appears distorted and by analyzing the distortion one can
than determine the strength of the gravitational potential in the region the light
passed through and the amount of matter present there. A beautiful example of
how one can use this method to show the existence of dark matter is the bullet
cluster [13].
It consists of two colliding galaxy clusters.
The hot intracluster
1 In contrast to spiral galaxies the movement direction of single stars in an elliptical galaxy
can be assumed to isotropically distributed.
6
Figure 1.1: The rotation curve of NGC 3198
The rotation velocity of objects versus distance from the galactic center is shown
here for the NGC 3198 galaxy. The points represent measurements with error
bars, the t is the best t from a dark matter model, the disk curve represents
the expected curve if one accounts only for the luminous matter, halo represents
the dierence of the two and thus the contribution due to the dark matter halo
[12].
7
Figure 1.2: Bullet Cluster
An image of the Bullet Cluster with overlays. Red represents the baryonic, blue
the total matter distribution. The scale bar corresponds to 1.5 arc minutes [13].
plasma from the two clusters interacts with each other electromagnetically and
thus lumps, while the dark matter halos of the two cluster pass through each
other. By directly observing the visible matter distribution and comparing it
with the total matter distribution obtained from lensing experiments one can
then get a clear evidence for the existence of dark matter as seen in gure1.2 [13].
The dark matter content of galaxy clusters obtained from these measurements
is ~80%[8].
1.1.3 Cosmic microwave background radiation
Roughly 0.38 My after the Big Bang the plasma that made up basically all of
baryonic matter in the universe cooled down enough to form neutral atoms. At
this point the photons became thermally decoupled from the baryonic matter
and created a homogenous background radiation [6]. This radiation is known as
the comic microwave background radiation (CMB) and by observing the temperature uctuations in it one can gain information about the state of the universe
at the moment where the radiation originates. Because baryons and dark matter
interact gravitationally with photons, but dark matter per denition does not
interact electromagnetically the two types of matter leave distinct signatures in
the CMB. Precise measurements of the CMB spectrum give indications that a
signicant part of the matter does not interact electromagnetically. The dark
matter content calculated from the CMB data is 83% of the total matter content
in the universe[1].
8
1.1.4 Theoretical dark matter candidates
Although we know a lot about dark matter abundance and distribution[1, 8, 9]
in the universe, we still have no idea what it is made of. We will not go into
too much detail about the nature of dierent proposed candidates, as most
extensions of the Standard Model have their own particle(s) that could make
up dark matter. An overview of some of the more popular theories can be for
example found in[11].
The most popular family of dark matter candidates is the so-called weakly
interacting massive particle (WIMP). They are predicted by many theories and
thus the details of their properties vary widely, but they all share some things
in common; they interact with ordinary matter only weakly with a typical cross
section for WIMP-baryon scattering on the order of
10−42 − 10−48
2
cm , their
mass is on the order of few GeV to few TeV[11].
1.2
Direct WIMP detection
From the study of star movement in our galaxy we can get an estimate for the
local dark matter density of around
0.4
3
GeV/cm [7]. If dark matter is indeed
made out of WIMPs this means that because the earth is moving with the sun
through the galaxy, a large number of WIMPs are passing through the earth
every second. In principle it should then be possible to make a detector that
looks for bypassing WIMPs scattering on and transferring some of their energy
2 in some detector material. In practice the biggest
and momentum to the nuclei
challenge is the fact that the very low cross section results in a very low event
rate and one thus needs a large detector mass and an excellent background
rejection in order to get a statistically signicant result. [19]
1.2.1 Xenon
Currently one of the most sensitive WIMP detectors in the world is XENON100
[17]. The detector consists of a time projection chamber, which is a PTFE bin
lled with xenon and an array of light detectors (PMTs) at the top and bottom.
It uses the liquid xenon in the detector as the target material.
An incoming
WIMP that interacts with a xenon nucleus produces primary photons (S1) and
ionization electrons.
Several arrays of wires creates a strong electric eld in
the detector. Due to this eld the ionization electrons drift upwards until they
reach the liquid surface and are extracted from the liquid into the gas phase by a
second, stronger, electric eld[17]. In the gas phase the electrons then generate
secondary scintillation photons (S2).
Both signals, S1 and S2, get detected
by the top and bottom PMT arrays. One can then use the timing dierence
and the relative signal strength of S1 and S2 in order to eciently discriminate
background events, especially particles scattering with electrons [14].
2 Because
of their large mass WIMP-electron scattering can be neglected.
9
1.2.2 Xürich
Xürich is a two phase xenon detector and works on a similar principle as
XENON100.
It is much smaller and has only one PMT at the top and bot-
tom for the light detection. The purpose of Xürich is to study and understand
the physical processes that are vital for the operation of the larger liquid xenon
detectors. Specically Xurich is measuring the scintillation and ionization yield
of the of electronic recoils at low energies. For a much more detailed description
of Xenon and Xürich experiments see [14]
Xürich2, the successor of Xürich, is developed and is currently being built.
Figure 1.3 shows an early draft of the Xürich2 geometry.
The cathode (the
bottom wire grid) and the gate (the middle wire grid) have the purpose of
creating an electric eld in the liquid phase so that the ionization electrons
can drift towards the liquid surface, which lies in the middle between the gate
and the anode (top wire grid).
The purpose of the anode and the gate is to
create a second, stronger electric eld at the liquid surface in order to extract
the electrons into the gaseous phase. One of the main design improvements of
Xürich2 over Xürich is the presence of a eld shaping device.
Its purpose is
to make the electric eld inside the detector as homogenous as possible, as the
processes of interest vary signicantly with the local eld density. Two dierent
methods are tested for the purpose of the eld shaping. One is using a series of
rings that are placed around the PTFE hull between the gate and the cathode.
The electrodes and the rings themselves are connected to each other by resistors.
A small current ows then through the resistors and creates a series of uniform,
discrete potential drops, eectively shaping the eld and compensating for edge
eects.
The second method uses a hull made out of conducting PTFE. The
resistivity of the PTFE is still very high so that only a small current ows
through it, which then creates a similar eect to the ring design, but with a
continuous potential drop along the walls, instead of discrete jumps between
the single rings.
10
Figure 1.3: Early Xürich2 diagram
The yellow and green parts are the frames for the PMTs. The blue PTFE hull
encloses the target LXe volume. The red frames and wires represent the cathode,
the gate and the anode respectively. Field shaping rings are not present in this
draft. Figure provided by A.James.
11
Chapter 2
Simulations
All the simulations described in this theses are preformed using the COMSOL
R
Multiphysics
software[15]. The main interest lies in the determination of the
electric eld in a certain setup.
This is done in COMSOL by specifying the
geometry and the boundary conditions (in most cases this will be the potential
on the surface). One then denes a meshing for the geometry, which COMSOL
uses to solve the Poisson equation for the given model. This gives us the potential distribution from which one can then easily compute the electric eld. The
size of the meshing varies strongly on the size of nearby geometrical features
(for example the mesh size close to a thin wire is much ner than further away
from it). In general the average size of the mesh is roughly between 0.03-0.3mm,
which can be considered as the spatial resolution of the models.
2.1
Introductory models
2.1.1 Xürich model
Several simulations of Xürich are done.
We are especially interested in the
single-phase mode of Xürich as this setup was used in 2011 and no eld simulations were done for it. In this mode the chamber is completely lled with liquid
xenon and charges thus can not be measured because no gas phase is present.
The model is done in two spatial dimensions
1 and consists of a PTFE structure,
anode, gate and cathode grids and two metal plates at top and bottom representing the PMTs. The detector is lled with liquid xenon and is surrounded by
a metal hull. The details are seen in gure 2.1.The potentials are set to -265V,
-530V and -2120V for the cathode, the gate and the anode respectively. The
PMTs and the hull are set to 0V. Dielectric constants in dierent regions are
set to represent the value of the corresponding material. After generating the
mesh this allows us to run the simulation and determine the eld in Xürich.
1 This is equivalent to a three dimensional model with a translation symmetry along the
third axis.
12
Figure 2.1: Xürich geometry used in electric eld simulations
The yellow parts represent the PTFE hull, the green parts are liquid Xe and
the gray parts represent metal components that were put to a certain potential
each.
If one would think about the electrode grids as (innite) conducting plates
one would expect the eld density between the cathode and the gate, the gate
and the anode and the anode and the top PMT to be 0.53 kV/cm each. This
was the original motivation for choosing those specic electrode voltages and
the average eld strength in Xürich in those regions was indeed assumed to be
close
2 to this value.
The results of the eld simulation of the Xürich setup are seen in gure
2.2. As expected there are some edge eects close to the PTFE hull, but other
than that the eld seems to be quite homogenous. Surprisingly the eld seems
to be signicantly lower than the expected 0.53 kV/cm. In order to get more
quantitative information, the eld density along the central vertical line inside
the detector is plotted and can be seen in gure 2.3. The central vertical line
is used here in order to avoid the edge eects and get a clear view of the eld
strength in dierent regions of the detector. Here we see again that the eld
is quite homogenous in each region, but in the region between the gate and
the cathode signicantly deviates from the expected value. The average of eld
density and variation inside the region between the cathode and the gate is
also calculated (the eld strength inside this region is the most relevant one
as the most interactions take place there).
For this purpose the bottom and
top boundaries of the region were set to 2.5 mm above the cathode and 2.5 mm
below the gate respectively in order to avoid including the very high eld density
3
regions that are appearing around the individual wires .
2 Inside the error set by the eld variation
3 Due to the small size of the wires (0.1 mm
The eld density is
in diameter) the eld at the surface can get as
13
Figure 2.2: Electric eld density Xürich
The color scale represents the eld density. Note the oset on the color axis.
The eld density in the red regions is mostly much higher that the 0.48 kV/cm
which is not evident due to the chosen color scale.
then integrated over the chosen area and then divided by the area. The variation
is calculated as
σE =
The variation of the
p
h(E − hEi)2 i .The resulting value is hEi = 0.451 kV/cm.
eld inside this region is σE = 0.0076 kV/cm.
The fact that the average eld is signicantly lower than expected makes
apparent that the behavior of the eld inside Xürich is not as well understood
as was assumed, thus some further investigations are required.
2.1.2 Field leakage through a wire grid
In order to better understand the inuence of wire grids on the electric eld
a very simple toy model is developed.
Specically the model is testing the
assumption that the wire grid behaves in the same way as a sold conducting
plate.
In the model, two innite conducting plates are used. The distance between
the plates is 20cm.
The upper plate is set to 100V the lower one to 0V. In
the middle between those two plates, an array of conducting wires is placed. A
sketch of the geometry can be seen in gure 2.4.The boundary conditions are
chosen in a way to represent an an arrangement of an innite amount of innitely
long wires. The potential on those wires is set to 1V. Here the bottom region
between the ground and the wire grid should represent the active region of the
detector while the upper plate represents some exterior boundary conditions. If
one goes with the assumption that the wires behave in the same way as a solid
high a few hundreds kV/cm.
14
Figure 2.3: Electric eld density along the central line in Xürich
The x-axis here represents the length along the central vertical line of the detector (seen in gure2.1) The electrode wires are positioned at 5, 35 and 40
mm.
d1
d2
r1
r2
18
16
13
12
Table 2.1: Field densities
d and
r. Dierent columns represent dierent radii of the wires (r1 = 0.025 mm and
r2 = 0.05 mm). Dierent rows represent dierent distances between the wires
(d1 = 2 mm and d2 = 1 mm).
Average eld strengths in [V/m] for the four dierent congurations of
plate would, then the eld in the region between the grid and the bottom plate
is expected to be 10V/cm.
Seeing any signicant deviations from this value
would falsify this assumption.
r1 = 0.025
d1 = 2 mm and
A total of ve dierent setups are tested with the radii of the wires
mm and
d2 = 1
r2 = 0.05
mm and the distances between the wires
mm. The fth simulation is a control run where the wires are replaced
by an innite plate.
The electric eld is analyzed in the region between the
grounded plate and the wire grid.
In all ve simulations the eld strengths and directions are extremely uniform
inside the considered region as one would expect from the assumption that the
wires behave the same as a plate would. The eld strength does however vary
considerably between the dierent setups. In the control run it is 10 V/m as
expected. The values for other setups are summarized in Table 2.1. Figure 2.5
shows the conguration and the eld in the setup with
r1
and
d1 .
There is a simple explanation for the fact that the elds do indeed dier
15
Figure 2.4: Field leakage geometry
Top and bottom represent the two metal plates, in the middle the wire grid is
seen. On left and right the periodic boundary conditions are chosen.
Figure 2.5: Field leakage
The general setup is seen here. The boundary condition are chosen so that they
simulate an innite array of wires and innite plates in the horizontal direction.
The uniformity of the eld strength is seen very well here. The eld is given in
[V/m].
16
from the naively expected value of 10 V/cm; the wires do not fully act as a
4 and thus the eld with the wires
plate, but they are partially "transparent"
looks approximately like some weighted average between the situation where the
wires are replaced by a plate and the situation where the wires are not present
at all. That is why in our simulation the high voltage on the top plate increases
the overall eld in the region below the wire grid. The same eect also appears
in our detector; the presence of the grounded bottom PMT reduces the eld
strength in the region between the cathode and the gate to a value signicantly
lower than one would expect. This is again due to the transparency of the wires,
so that the potential that the eld is seeing at the position of the wires is some
average of the cathode voltage (-2120 V) and the voltage at the PMT below (0
V). This leads than to a lower potential drop, and thus a lower average eld
density.
This eect is very important for the proper understanding of the behavior
of the electric elds in all simulations, which is vital for the development of a
proper eld shaping design described in the next section.
2.2
Xürich2 models
2.2.1 A simplied Xürich2 model
As described in section 1.2.2, Xürich2, a successor of Xürich, is being developed and a eld shaping design is required in order to achieve improved eld
homogeneity. A simplied model of Xürich2 is made. It consists of a gate and
a cathode, similar to those used in the previous model, a PTFE frame, the two
grounded PMTs at the top and bottom and a metal hull surrounding everything.
Everything else is lled with liquid xenon. In contrast to the previous simulations this model assumes a rotational symmetry of the detector. Although the
used geometry is two dimensional, the actual model is three dimensional, making this model more realistic than the previous ones. The used geometry can
be seen in gure 2.6. Although this model of Xürich2 is somewhat unrealistic
5
and is missing some important features , its simplicity makes it adequate for
seeing how one can use some kind of eld shaping design to improve the eld
homogeneity.
In all of the simulations, the PMTs, the hull of the detector and the gate
(the top wire grid) are set to ground, the cathode (the bottom wire grid) is
set to -6kV as seen in gure 2.6.
These specic voltages are chosen in order
to achieve a eld density on the order of kV/cm, which roughly represents
the desired eld strength in Xürich2. The rst analysis is done with no other
potentials and represents the basic design of the detector. As expected the eld
is very inhomogeneous
6 and it shows the need for a eld shaping design. By
4 By comparing the values obtained in dierent setups, we see that wire density, and to a
lesser extent their size, eect this "transparency".
5 For example the anode, the two xenon phases or detailed exterior boundary conditions.
6 The exact variation of the eld strongly depends on the boundary conditions, which are
chosen a bit arbitrarily in this design, but it is on the order of 20%.
17
Figure 2.6: Geometry of the simple Xürich2 model
The edges on top and bottom represent the two PMTs, the dotted lines are the
cathode and the gate wires, the block in the middle right represents the PTFE
hull and the rest is lled with liquid xenon.
The red line represents the axis
of rotational symmetry. The potentials used in the simulations are seen in the
diagram. The two resistors that are only used in the later simulations are grayed
out.
somehow specing the potential along the PTFE hull, it should be possible to
shape the eld inside and thus signicantly reduce the edge eects. After the
basic simulation dierent designs of the PTFE hull are introduced with the
intention to homogenize the electric eld inside the detector. The rst design
uses a number of eld shaping rings embedded inside the PTFE hull, the second
design is using a linear potential drop along the PTFE boundary, simulating the
behavior of the conducting PTFE. In the third design the PTFE hull is sliced up
in smaller pieces as seen in gure 2.6 and every one of those is set to a dierent
potential, representing a non-continuous version of the conducting PTFE design.
This nal design is done as a check to see if the simulation of the conducting
PTFE design is implemented correctly. The resulting eld densities can be seen
in gure 2.7.
Introduction of one of the eld shaping designs reduces our eld variation by
around a factor of two, but the variation is still quite high, especially in the lower
part of the detector and close to the PTFE hull where the form of the potential
creates dierent edge eects. The low eld at the bottom of the detector can
be understood by using the analogy to the simulations done in chapter 2.1.2;
because there is a grounded PMT below the cathode, the average eld between
the cathode and the gate is signicantly lower than the 2 kV/cm one would
naively assume if the grids were solid plates. On the other hand the potential
drop along the wall of the PTFE hull (or along the eld shaping rings) is still
18
Figure 2.7: Xürich2 eld densities with dierent eld shaping setups
The eld shaping congurations, clockwise starting from top left: the setup with
nine eld shaping rings, conducting PTFE setup, a setup where the wall is sliced
up into smaller boxes and each of them is set to a dierent potential. In graphs
2 and 3 there are some unusual elds inside the hull. Those are artefacts from
the simulation and have no physical importance. The voltages are the same as
seen in gure 2.6
19
Figure 2.8: Field with one resistor
Field density (in [kV/cm]) in the conducting PTFE design after introducing a
resistor between the cathode and the the bottom of the conducting PTFE hull.
6 kV and thus the eld is being "shaped" towards a value of approximately 2
kV/cm which is higher than the average eld.
In order to x the problem of the high eld inhomogeneities in the lower
part of the detector we need to reduce the high potential drop along the inner
hull wall. This can for example be done by introducing an additional resistor
between the cathode and the bottom of the conducting PTFE (or the last eld
shaping ring respectively). By choosing the right value for the resistor one can
make the eld get "shaped" to the correct value. By doing a series of simulations
with dierent values for the resistor its optimal value can be found.
out that it is
0.12 R0 ,
where
R0
It turns
is the resistance of the PTFE hull (the total
resistance of all the resistors between the eld shaping rings).
The resulting
eld using the resistor is seen in gure 2.8.
The variation of the eld is reduced by a factor of two by putting a resistor
on the cathode, but now a similar eect becomes apparent at the gate.
It is
much weaker because the gate itself is grounded as well as the PMT behind it,
but it is still present.
By putting another resistor between the gate and the
top of the conducting PTFE (or the rst eld shaping ring respectively) the
eect can also be signicantly reduced.
After introducing the second resistor
and optimizing its value in the same way that we did for the rst resistor we get
a conguration with a very homogenous eld as seen in gure 2.9. The relative
variation of the eld can be made to be less than 1% with this design.
This simplied model gives some insight into the working mechanism of eld
shaping, but in order to further develop the concrete eld shaping design a more
20
Figure 2.9: Field with two resistors
Field density (in [kV/cm]) in the conducting PTFE design after introducing a
resistor between the cathode and the the bottom of the conducting PTFE hull
and another one between the gate and the top of the conducting PTFE hull.
The resualtig variation is less then 1%.
sophisticated model is required and is developed in the next section.
2.2.2 3D model
The following simulations are preformed with an advanced Xürich2 model. The
main improvements of this model over the simple model are the introduction
of an anode, 4 mm above the gate, two xenon phases (liquid and gas, with the
liquid level between gate and anode), and a full 3D geometry including realistic
wires. The cylindrical symmetry of the design is exploited by simulating only
a quarter of the detector and assuming mirror symmetry along the two planes
on each edge.
The full geometry is seen in gure 2.10.
All of simulations
described in this chapter are done with both the conducting PTFE and the eld
shaping rings. For the most time the two solutions look (up to some minor edge
eects) the same, so for the most part only the conducting PTFE design will
be described here. The simulations explicitly done for one setup are declared as
such.
The voltages are initially set to -3 kV, 0 kV, 4 kV for the cathode, the
gate and the anode respectively. Making the hull out of conducting PTFE and
connecting it directly to the cathode and the gate leads to an unsatisfyingly
high eld variation (~15%) as seen in gure 2.11. This eect is analogous to
the grid eld leakage eect seen in section 2.2.1.
Trying to apply a solution
analogous to the simple model does not work directly, because the wire nature
21
Figure 2.10: Xürich2 3D geometry
A 3D view of the Xürich2 model. The lengths are given in [mm].
of gate means that the high anode voltage has an eect on the eld between
the gate and the cathode. Specically it makes the eld higher than 1 kV/cm
that one would expect from the the gate and cathode voltages only. This means
that the voltage gradient along the PTFE wall should be higher than 1 kV/cm.
This does not work by simply introducing a resistor between the gate and the
PTFE hull, because a resistor can only create a potential drop, and thus lower
the potential gradient along the hull wall, not increase it. Two simple design
alterations can be made in order to solve this problem; one can either connect
the hull to the anode via a resistor or alternatively one can introduce a gap
7
between the gate and the top of the conducting PTFE hull . The two solutions
increase the potential dierence between the top and the bottom of the hull or
decrease the distance between the top and the bottom. Both things lead to a
higher potential gradient along the wall and the resulting elds look very similar
and an example can be seen in gure 2.12.
2.2.2.1 Variation of the cathode voltage
In practice one is interested in operating the detector at various eld strengths
in the region between the cathode and the gate. This can by done be having a
variable cathode voltage. For this purpose the cathode voltage is varied between
-0.3kV and -9kV in the simulations while the anode and the gate voltage are
held constant. Several designs described in the previous section are tested for
7 In
practice one would e.g. put a piece of normal PTFE in between.
22
Figure 2.11: 3D model; basic eld
The eld density in the basic setup of the 3D model using conducting PTFE.
Lengths are in [mm], eld density in [kV/cm].
Figure 2.12: Field with cathode connection
The eld density in the 3D model using conducting PTFE after connecting the
cathode and the bottom of the PTFE hull via a resistor. Note the dierent color
scale than what was used in gure 2.11.
23
Conducting Teflon, top part connected to the anode
Conducting Teflon with a gap, optimized for high fields
Conducting Teflon with a gap, optimized for low fields
10 field shaping rings, spacing optimized for low field
10 field shaping rings, spacing optimized for low field
Relative field deviation
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5
1
1.5
2
Mean field density [kV/cm]
2.5
Figure 2.13: Field variation comparison with a variable cathode voltage
One can see here the average relative eld deviation for various mean elds for
some of the more successful designs.
this voltage range. Those are design with dierent gap sizes, conducting PTFE
or rings and the design with the resistor connecting the top of the PTFE to
the anode. The resulting variation, deen as
σE =
p
h(E − hEi)2 i,
of the eld
inside the detector for some of these designs is seen in gure2.13.
From these simulations we conclude that all of the tested design need to be
optimized for a certain cathode voltage, where they oer quite good results.
However all of the designs break down if the cathode voltage is changed from
the value they are optimized for and none of them can satisfy the requirement
of a low eld variation for the entire range of dierent cathode voltages. The
relative eld variation exceeds 20% for every design at a certain voltage, which
is too much for our purposes. This is again a consequence of the wire nature of
the electrodes and the fact that the eld is leaking through the gate wires. This
means that the eld between the cathode and the gate is eected not only by
the cathode and the gate voltages , but also by the anode voltage. None of the
designs can satisfactorily account for this dependance on all three voltages.
Dynamic eld optimization
A dierent approach is tested; simulations are
preformed with the goal of nding the optimal potential
Vopt
on the top of the
PTFE hull for a specic cathode voltage, such as to minimize the variation of
the eld. So for each cathode voltage several simulations with dierent voltages
on the PTFE hull are done and the voltage that gives the minimal variation of
the eld is selected as
Vopt .
It is a priori not clear how this could be achieved
in the real detector design, but one possibility would be to e.g. introduce an
additional voltage supply that connects directly to the PTFE hull and xes
independently of the grid electrodes.
in gure 2.14.
Vopt
The results of the simulations are seen
A notable feature of the results is the almost perfectly linear
24
400
200
V
opt
[V]
0
−200
−400
−600
−800
−9
−8
−7
−6
−5
−4
Vc [kV]
−3
−2
−1
0
Figure 2.14: Optimal voltage on PTFE top for a certain cathode voltage
Blue points represent simulations, red line is a linear t.
dependance between the cathode voltage
Vc
and
Vopt .
Because of this it seems
likely that the desired behavior can be achieved by a clever arrangement of
resistors.
Placing resistors between each electrode and the hull
One can intro-
duce three dierent resistors, connecting the cathode and the bottom of the
PTFE hull, the gate and the top of the PTFE hull and the anode and the top
of the PTFE hull. A schematic diagram of the design is seen in gure2.15. A
simple calculation leads to the formula for
V0 =
VA
VG
VC
RA + RG + R
1
1
1
RA + RG + R
= VC
V0 .
1
R
RA
+
R
RG
+1
+
VA RRA + VG RRG
R
RA
+
R
RG
+1
V0 and Vc . By choosing
RA
RG
and
one can get the desired values for the
R
R
R
slope and the oset. The optimal value for C is determined by the requirement
R
As one can see this gives us a linear relation between
the appropriate values for
that the eld is homogenous in the lower part of the detector. For the optimal
values determined through the simulations see section 2.2.2.3.
2.2.2.2 Field at the liquid surface
So far we have focused on the eld in the region between the cathode and
the gate.
The eld between the anode and the gate is of some interest too,
mainly because the eciency with which the electrons are extracted from the
liquid depends on the electric eld strength at the surface. This eect is seen in
gure 2.16[15]. The only large deviation from the desired value of 10 kv/cm are
present in the region close to the hull. This eect can be seen in gure 2.17 and
8
2.18which shows the eld density at the liquid surface . In the detector there is
a PTFE ring separating the anode and the gate frames. A possible solution to
8 In the simulation the eld was actually measured at 0.01 mm above the surface because
the eld at the surface is not well dened.
25
3
Figure 2.15: Circuit schematics
VA , V C , V G
represent the corresponding electrode potentials,
sent the three resistors,
RT
RA , RC , RG
repre-
represents the resistance of the conducting PTFE
hull (or the total resistance of all the resistors between the eld shaping rings).
V0
is the voltage at the top of the PTFE hull that we want to specify.
the problem of high elds close to the hull is to simply make the inner radius of
this PTFE ring smaller than the inner radius of the frames, eectively cutting
o the region with the high eld.
By trying out dierent inner radii for the
PTFE ring, it turns out that the value which leads to a minimal eld variation
is 16.69 mm (note that the inner radius of the frames is 18.75mm). The eld
density distribution after this change can be seen in gure2.19.
Another interesting question here is how the eld density on the liquid surface behaves if the liquid level changes.
No detailed analysis is done on this,
but qualitatively it can be said that raising the liquid level or lowering it for up
to 0.7 mm has no large eect on the average eld on the surface (change is at
most on the order of 10%). If the liquid level drops for more than 0.7 mm the
average eld density on the surface starts rapidly decreasing. Another eect is
that if the liquid level is raised the homogeneity of the eld on the surface gets
worsened because of the proximity to the anode wires. The same eect becomes
apparent from the gate grid but only if the liquid level is lowered for more than
0.7 mm.
Several simulations are also made where the anode voltage diers from the
default value of 4kV. The resulting shape and the variation of the eld remains
unchanged in the entire detector as long as one scales the cathode voltage accordingly. The eld density scales linearly with the chosen voltages as one would
expect.
2.2.2.3 The nal design
Because it was shown that conducting PTFE alone cannot be used for the
eld shaping purposes (see section 3.2), the focus of the simulations is shifted
26
Figure 2.16: Extraction eciency
Electron extraction yield as a function of electric eld in the gas phase. At a eld
higher than 10 kV/cm, all drifting electrons can be extracted from the liquid to
the gas xenon.[15]
Figure 2.17: Field density at the liquid surface; top view
This image represents a top view of the electric eld in the gaseous phase right
above the liquid surface. The black line represents the inner edge of the PTFE
hull. Note the high eld close to it. Some of the structure seen on the surface
is a numerical artifact and comes from the nite size of the meshing.
27
Figure 2.18: Field density at the liquid surface; side view
This image represents a top view of the electric eld in the gaseous phase right
above the liquid surface.
10
Field density [kV/cm]
9.8
9.6
9.4
9.2
9
0
2.5
5
7.5
Radius [mm]
10
12.5
15
Figure 2.19: Surface eld density at various radii
Here the average eld density at the liquid surface can be seen as a function of
the distance from the center of the detector after choosing the optimal value for
the inner radius of the PTFE ring. The data points have been binned in 1 mm
bins in order to smooth out the otherwise very noisy plot.
28
0.08
5 rings
7 rings
9 rings
Relative field deviation
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0.5
1
1.5
Mean field density [kV/cm]
2
Figure 2.20: Number of rings comparison
This plot shows the mean relative variation for dierent mean eld values. Different colors represent setups with a dierent number of eld shaping rings.
towards eld shaping rings design. In this model several parameters still have
to be chosen.
These are the number, the positions and the diameters of the
rings. In all cases the eld homogeneity has to be weighted against technical
feasibility of the design.
For choosing the number of rings, several models are made with dierent
number of rings. For every model the values of the three resistors are optimized
and the nal design tested with dierent cathode voltages. In all of the models
the resistors were set up as described in section 2.2.2.1. The values for the resistors were chosen so that the variation for all the cathode voltages is minimized.
The resulting eld variations for some of the designs are seen in gure2.20.
Higher amount of rings lead to lower eld variation, but it also makes it more
dicult to technically build detector. Finally the value of
7 rings
is selected
as a compromise.
A large part of the remaining inhomogeneity come from the cathode and
the gate frames.
In order to minimize this eect one should choose a small
ring diameter and place the rst and the last ring close to the frames. However
because a notch has to be made in the PTFE at the positions where the rings
will come, small diameters and the proximity to the frames also create thin
PTFE layers and compromise the structural stability of the hull. Thus nally
a value of 20.25 mm for the inner diameter of the rings and 1.5 mm for the
distance between the frames and the closest rings are chosen as a compromise.
The distances between the individual rings are chosen constant, as this simplies
the design of the resistors between the rings. The optimal values for the resistors
are determined in the same way as described in section 2.2.2.1.
values turn out to be
RC = 8.48 R, RA = 101.4 R, RG = 7.03 R
The optimal
for the resistor
between the cathode and the last ring, the anode and the rst ring and the gate
29
0.1
3
Relative field deviation
2
0.06
1.5
0.04
1
0.02
0
0
Mean field [kV/cm]
2.5
0.08
0.5
−1
−2
−3
−4
−5
−6
Cathode voltage [kV]
−7
−8
−9
0
Figure 2.21: Mean eld and deviation in the nal design
and the rst ring as seen in the sketch 2.15 respectively. Here
R
is the value for
the resistors that are placed between two successive rings. This value remains
as a parameter that can be chosen freely without eecting the electric eld. For
the shake of simplicity it is also reasonable if one would round those ratios to 8,
100 and 7 respectively. The increase in the relative variation resulting in those
changes would be on average 0.5%.
The eld variation and the average eld density for dierent cathode voltages
in the nal design is seen in gure2.21.
Another interesting property besides the eld variation is also the direction
of the eld lines, as those determine the path of the drifting electrons. These
look qualitatively the same for all cathode voltages.
An example is seen in
gure2.22. A really nice property is that on the edges of the region between the
gate and the anode the eld lines point outwards. This means that the drifting
electrons move away from the PTFE walls, resulting in less yield loss due to to
charges hitting the hull.
30
Figure 2.22: Field lines in the nal design
The directions of the eld lines in the nal design are seen here in red.
31
Chapter 3
Measuring the properties of
conducting PTFE
As mentioned in chapter 2.1 in order to achieve homogeneity of the electric eld
inside the detector, two approaches are studied. One is using eld shaping rings,
the other one would be to make the detector hull out of conducting PTFE. The
conducting PTFE would provide a continuous potential drop in contrast to only
a few discrete voltage steps provided by the rings. Thus one would expect better
results to be achievable with conducting PTFE than with rings.
There are several important reasons why PTFE is normally used in time
projection chamber design; it reects the ultra violet scintillation light which
greatly reduces light losses, it is one of very few plastics that is stable in a
vacuum and does not emit any considerable amounts of gases, its dielectric constant is very close to that of liquid xenon which means one does not have large
eld discontinuities on the boundaries. The main problem with the conducting
PTFE is that it has not been used for such devices and it is not known how
it behaves under the conditions present inside the detector. For this purpose a
∼ 30
cm long,
6
cm wide cylinder of the material is ordered from the manufac-
turer, Boedeker Plastics, and some of the physical properties relevant for the
experiment are measured.
3.1
Resistivity distribution
Probably the most important property of conducting PTFE is its nite resistivity. For the value of its resistivity the manufacturer gives
as the surface resistivity of a
00
1/8
1010 − 1012 Ω/
thick sheet. Although the exact value of the
resistivity is not that important for our purposes, we do need a certain degree of
homogeneity within the material. If this range of two orders of magnitude would
represent the variation of the resistivity within one PTFE piece, the material
could denitely not be used for our eld shaping purposes, since the potential
change would vary by this amount too.
32
Current [nA]
Voltage
1kV
1kV
5kV
5kV
Block 1
16
16
102
101
Block 2
11
13
116
117
Block 3
12
15
108
106
Block 4
15
17
143
131
Block 5
15
13
123
111
Block 6
12
14
99
105
Block 7
10
13
102
109
Block 8
11
15
113
118
Table 3.1: Current measurement results
Measured current in [nA] when the corresponding voltage is applied to the
copper diodes. Those are glued to the PTFE blocks.
In order to test the resistivity distribution a total of eight
1cm × 1cm × 4cm
blocks are cut out from dierent sides of the original PTFE cylinder. Copper
connectors are glued to each side of every block using a conducting glue in order
to easily be able to apply a high voltage. For every block a voltage of 1 and 5
kV are applied and the resulting current is measured. The circuit can also be
seen in 3.1. Because the measured current is quite prone to uctuations, the
whole measurement is done a second time in order to get an estimate on the
error. The results are summarized in Table3.1.
The resistivity is calculated from the average current for the specic voltage.
The variation due to inhomogeneity is calculated from the variation of
the currents between dierent blocks and the error on both values is calculated
from the variation of the currents in the measurements of the same blocks. The
obtained values are:
ρ1kV
=
18.8 ± 2.2ih ± 3.8err GΩ cm
ρ5kV
=
11.2 ± 1.0ih ± 0.6err GΩ cm
The variation of the resistivity seems to be about the same between dierent
blocks as it is between dierent measurements of the same block. This means
we have no signicant inhomogeneities in the material.
However, there is an
unexpected feature about the results that needs some further investigations,
and that is the large discrepancy between the resistivity at the two dierent
voltages. An assumption is that the glue connecting the copper plates to the
PTFE piece does exhibit some unusual behavior and somehow has an eect
on the current.
Because the glue could seriously compromise the purity of
the xenon inside the detector, the usage of the glue inside the real detector is
excluded and a dierent kind of connection would have to be used. Therefore
another measurement is done, trying to measure the resistivity of the blocks
using direct connection between the electrodes and the PTFE. For this purpose
a sandwich of insulator - copper plate - PTFE block - copper plate - insulator is
33
Current [nA]
Voltage
1kV
5kV
Block 1
20
111
Block 2
17
93
Block 3
15
83
Block 4
18
99
Block 5
20
107
Block 6
16
90
Block 7
22
117
Block 8
16
90
Table 3.2: Current measurement results, no glue setup
Measured current in [nA] when the corresponding voltage is applied to the
copper diodes. No glue is used in this measurement.
Figure 3.1: Resistance measurement circuit
On top is our ampere meter, on bottom the high voltage supply, on left the
Teon block.
made and pressed together tightly using a clamp. The resistivity of the PTFE
block is then measured using the same method as before. Because the setup is
much more elaborate than the previous one only one measurement per block is
taken. The measured currents are summarized in Table3.2.
Because we only have one data point per block we cannot estimate how much
of the variation is due to the measurement uncertainty and how much due to
the dierences between the blocks. Because the inhomogeneities were shown to
be negligible in the last measurement they are neglected here. Calculating the
resistivity from these data gives us:
ρ1kV
=
14.1 ± 1.7 GΩ cm
ρ5kV
=
12.8 ± 1.4 GΩ cm
The two values are consistent with each other which shows that the assumption of liner voltage vs. current behavior is justied and the deviation seen in
the rst measurement was probably due to the eect of the glue.
34
Temp [K]
1kV
5kV
295
26
134
77
0
0
107
0
0
115
0
0
140
-
0
160
-
0
166
-
0
180
-
0
190
-
0.2 ± 0.2
240
-
5?
250
-
100?
295
45?
275?
295
17
99
Table 3.3: Current vs. Temperature data
The current in [nA] measured at dierent temperatures and applied voltages.
The values are arranged in the order in which they were taken. The error on
the measurement at 190K means that the uctuations on the measured current
are of the same order as the value, thus the value is consistent with zero. The
question mark (?) means that considerable amounts of ice crystals formed on
the PTFE block, thus possibly signicantly increasing the conductivity.
3.2
Temperature dependance of the resistivity
All of the resistivity measurements from section 3.1 were preformed at room
temperature.
Because the detector will be operating at signicantly lower
temperatures[16] the temperature dependence of the resistivity is measured.
A screw with attached wires is screwed into each side of the block. This setup
is much more robust than the previous and it can be simply lowered into a liquid nitrogen dewar, but we lose the property of having a well dened geometry
and the ability to calculate the resistivity directly.
Thus all of the measured
currents are to be viewed relative to the value measured at room temperature.
In order to achieve dierent temperatures the PTFE block was put at dierent
positions above the liquid level inside a liquid nitrogen dewar.
The measure-
ment of the temperature is preformed using a Pt100 temperature sensor that is
lowered down into the nitrogen tank to the same position as the PTFE block.
The measurement of the resistivity works in the same way as described in the
previous section. The results are summarized in the Table 3.3. The resulting
conductivity as a function of the temperature if shown in gure3.2.
Unfortunately when the temperature reached the interesting region at about
200K considerable amounts of water ice started to sublime on the surface of the
PTFE thus possibly signicantly increasing the conductivity. One can however
conclude that the material has no measurable conductivity up to at least 190K,
which means it cannot actually be used in the detector for eld shaping purposes.
35
Figure 3.2: Temperature dependance of the conductivity
The conductivity is normalized using the average of the room temperature measurements and the values of the conductivity measured in the previous section
and plotted as a function of temperature, the questionable values where the
water vapor probably had a mayor inuence are left out.
One can however imagine using a design with eld shaping rings, but still making
the hull out of conducting PTFE, because the material will have some very small
nonzero conductivity at the operating temperature. This could still be enough
to dissipate the surface charges that build up at the detector walls over time.
3.3
Outgassing
The reason why PTFE is used in the detector design is that PTFE is one of very
few plastics that is stable in a vacuum and does not produce any considerable
amounts of outgassing.
It is however not yet known whether the conducting
PTFE has the same desirable property.
the goal of answering this question.
Several measurements are done with
A vacuum chamber with PTFE (both
normal and conducting) inside is connected to a mass spectrometer and the
amount of dierent substances in the vacuum is measured.
A common practice for reducing the outgassing is baking: the idea is to heat
up the vacuum chamber to
∼ 100 − 200 ◦ C
over some time and than let it cool
down again. The same procedure is applied here, so a total of ve measurements
are done; with normal and conducting PTFE in the vacuum chamber, before and
after the baking. The fth measurement is a control run with an empty vacuum
chamber.
The conducting PTFE spectrum is seen in gure 3.3.
Comparison
between the conducting and normal PTFE spectra after baking is seen in gure
36
18:H2O
1:H
2:H2
before baking
after baking
28:N2
17:OH
Partial preassure [mbar]
−8
10
43:ethanol
16:O
13,15:CHx
26,27,29:
C2Hx
−9
38−42:C3Hx
CXHY
???
32:O2
14:N
12:C
10
−10
10
0
10
20
30
40
mass [amu]
50
60
70
80
Figure 3.3: Conducting PTFE spectrum
The mass spectrum of the conducting PTFE pieces before and after the baking.
The origin of the most prominent peaks was guessed by their mass. Note the
logarithmic y-axis.
3.4. The spectra before baking are qualitatively the same and are therefore not
included here.
It is not clear where all the organic compounds come from, but a possible
explanation is the fracturing of ethanol, which was used to clean the samples
before putting them into the vacuum. It is however clear that there is qualitatively no dierence between the spectrum of the normal and the conducting
PTFE. As it is well known that normal PTFE works well in a vacuum we can
conclude that the same is true for the conducting PTFE. The dierences in the
concentrations might be due to dierent surface areas and volumes of the PTFE
pieces and dierent lengths of pumping.
37
−7
10
Conducting PTFE
Normal PTFE
18:H2O
1:H
2:H2
28:N2
17:OH
Partial preassure [mbar]
−8
10
43:ethanol
CXHY
???
16:O
38−42:C3Hx
13,15:CHx
−9
10
26,27,29:
C2Hx
32:O2
14:N
12:C
−10
10
−11
10
0
10
20
30
40
Mass [amu]
50
60
70
80
Figure 3.4: Conducting and normal PTFE spectra comparison
Comparison of the mass spectra after the baking of conducting and normal
PTFE. Note the logarithmic y-axis.
38
Chapter 4
Conclusion
In Chapter 1 the motivation for this thesis was given by motivating direct dark
matter detection experiments and thus also Xürich. Section 2.1 explored some
simple properties of the eld caused by the grid nature of the electrodes. These
concepts were used in section 2.2 in order to develop a design of Xürich2 that
has an acceptable electric eld variation, but still remains relatively simple to
construct. The nal design has a large exibility and has a low eld variation
over a wide range of dierent cathode and anode voltages. Simultaneously to
the simulations of Xürich2 measurements of several properties of conducting
PTFE were made in order to test the feasibility of the conducting PTFE designs. Those are described in chapter 3. It turned out that conducting PTFE
looses its conductivity below around 200K, which is above the operating temperature of the detector. This means conducting PTFE could not be used for
eld shaping purposes. Even though the nal design thus uses rings for the eld
shaping purposes, it was still decided that the detector hull will be made out
of conducting PTFE in the hope that it will help dissipate accumulated surface
charges.
The Xürich2 detector is currently being build using the eld shaping design
developed in this thesis. Upon completion the detector will be used to preform
similar measurements to its predecessor, Xürich; mainly the determination of
light and charge yields of low-energy nuclear recoils in liquid xenon at various
eld strengths.
39
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