For the eight weeks at DESY I am a member of the TPC-Group, which is a subgroup of
FLC. The FLC-Group is planning the “International Linear Collider” (ILC) in general.
The TPC-Group designs the “Time Projection Chamber” (TPC) for the ILC.
My supervisor is Ties Behnke. Most of the time I work together with Peter Schade, a Ph.D. student.
The “International Linear Collider” (ILC) is a proposed linear particle accelerator. It will collide electrons with positrons with an collision energy of 500 to 1000GeV. It is planned to be over 30km long and will consequently be the longest linear collider in the world. The function of the ILC is not to discover new particles, but to make precision measurements of particles. One part of the ILC-detector is the “Time Projection
Chamber” (TPC).
Figure 1: Scematic view of the ILC
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One part of the detector is the “Time Projection Chamber” (TPC). It has a cylindric design, see figure... . Normally anode and cathode work like a capacitor, but because of the shielding, which is on ground, the electron will be deflected to the wall. To have a constant field strength between anode and cathode, 100 field strips are installed around the cylindrical body. Neighbourd field strips are connected about four parallel resistors, which have the function of potential dividers. So a linear potential drop is realised. It is nessesary to have a constant field, to calculate the velocity of the particles exactly, because the velocity is proportional to the electric field strength. But in the edges of the TPC the field isn’t constant, but distorted. The electric field strength also changes, if one of the resitors fails or something is indicatete in the TPC volumen, like e.g. a mirror.
Figure 2: Scematic view of the TPC
My project is to calculate the electric field strength inside the TPC. Therefore I am acquainted with “CST Studio Suite 2006”. I analyse the following problems:
1. TPC-models with different fieldstrip widths
2. TPC-model with a failing resistor
3. TPC-model with an inserted mirror and a laser-hole
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CST is a computer programm which allows to calculate electro-magnetic fields. Therefore a three dimensional model of the object, which is wanted to calculate, must be constructed. Different material properties can be given to the components of the model and charges and currents can be put on them.
To specify the behaviour of the field at every surface, boundary conditions must be set. If the model is symmetric, it is clever to use the symmetry conditions. Every symmetry plane reduces the number of data by a factor of two.
Also very important is the meshing. CST divides the volume of the model in mesh cells and calculates the electric field strength for every cell. So the calculation is more accurate, if the meshing is very fine.
3.3.1
Planar model
To calculate the electric field strength, a planar model of the TPC was constructed by
Peter Schade before. Because of the rotational symmetry it is possible to simplify the cylindric model to a planar model. The main benefit of this method is, that there is only a small part of the data you would have, if the whole cylindric TPC would be calculated. But this system only works, if the problem is symmetric. Therefore it is adapted for evaluating the electric field strength in the edges of the TPC and also for calculating the field, if a resitor fails.
Figure 3: Planar model of the TPC
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3.3.2
Cylindrical model
If you have to calculate a TPC with unsymmetric configuration, you must built a cylindrical TPC model, for example, if you indicate something locally. Consequently the necessary number of data is more sizable than of the planar modell.
Fieldmaps illustrate the electric field strength inside the drift volume of the TPC. They correspond to a cut through the center of the chamber. The fieldmaps are normalized to the desired value. The deviation is given in percent.
Drift-plots are more significant than the fieldmaps. To evaluate the field quality, the drift of an electron is simulated. In each cell starts an electron. Because of knowing the electric field in x- and z-direction, the resulting direction of the electron can be concluded. Therefore it is assumed, that the velocity is proportional to the electric field strength. The electron drifts in equal steps to the anode, the drift length is always
0.2mm. The result of this calculation is the displacement of the electron in x-direction.
In the future it would be interesting to factor the time of arrival into the drift-plotcalculations. But this in not done yet.
Figure 4: Drawing, how the drift
-plot is calculated.
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4.1.1
Aim
To get a homogeneous electric field in the drift volume, different fieldstrip geometries are calculated. Therefore I have established changeable parameters, like radius of the
TPC, the fieldstrip width and the number of fieldstrips. The pitch, that means the sum of the fieldstrip width and the gap of the fieldstrips, has the constant value of 2.8mm.
4.1.2
Fieldmaps
I have made three different models with a fieldstrip width of 1.6mm, 2.0mm and
2.4mm. The fieldmaps of the radial- and the z-component are shown here. On the left is the anode, on the right the cathode and on top and bottom are the fieldstrips.
The radial component should be zero (blue area), because we only want to have an electric field in z-direction. The z-component ought to be homogeneous, the fieldmap should be green.
In the edges of the fieldmaps are field distortions. But with wider fieldstrips the distortions become lower.
Figure 5: Width: 1.6mm, gap: 1.2mm: radial-component(left) and z-component(right)
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Figure 6: Width: 2.0mm, gap: 0.8mm: radial-component(left) and z-component(right)
Figure 7: Width: 2.4mm, gap: 0.4mm: radial-component(left) and z-component(right)
.
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4.1.3
Drift-plots
The correspondent drift-plots of the three models are shown here. They are more significant than the fieldmaps.
The scale shows the displacement of the electron in x-direction in mm. If an electron, for example, starts in a light blue area, it will arrive at the anode with a xdisplacement of 1.5mm.
The white area is lost volume. An electron starting in this area will not arrive at the anode, but will hit the wall.
Figure 8: Width: 1.6mm, gap: 1.2mm
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Figure 9: Width: 2.0mm, gap: 0.8mm
Figure 10: Width: 2.4mm, gap: 0.4mm
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4.1.4
Result
It becomes obvious, that the electric field is very homogeneous, if the fieldstrips are wide.
The best result is archieved with a fieldstrip width of 2.4mm. Fieldstrips which are wider than 2.4mm cannot be produced with an adequate effort.
4.2.1
Problem
Neighbouring fieldstrips are connected about four parallel resistors. If one of the four resistors fails, e.g. because of cold soldering, the resistance rises by a factor of 4/3.
What is the influence on the electric field strength? How does the drift of the electron change? Is sensitiv volume lost?
4.2.2
Fieldmaps
The fildmaps of two different models in z-direction are shown here. The field distortions around the failling resistor are visible very well.
Figure 11: Fieldmap z-component: width:1.6mm, gap:1.2mm
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Figure 12: Fieldmap z-component: width:2.4mm, gap:0.4mm
4.2.3
Drift-plots
Here are the drift-plots of these models:
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Figure 13: Drift-plot: width:1.6mm, gap:1.2mm
Figure 14: Dift-plot: width:2.4mm, gap:0.4mm
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4.2.4
Result
It becomes obvious that the influence of the failling resistor on the field quality is much higher, if the field is rather homogeneous.
4.3.1
Problem
Markus Ball , a Ph. D. student of the TPC-Group is testing the TPC with a laser beam.
Therefore a wedge (mirror) is inserted to the drift volume of the TPC and a small hole is cut into the cathode. Through the hole in the cathode the laser beam can enter the drift volume. The function of the mirror is to create two beams for two beam studies.
It is possible to change the angle of the laser beams and to test the whole TPC volume.
4.3.2
Fieldmap
Figure 15: Fieldmap: width:2.4mm, gap:0.4mm
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4.3.3
Drift-plot
Here the drift-plot of the planar model with the inserted mirror and the laser-hole is shown.
This drift-plot is not really correct. The area to the right of the mirror should be white too, because all electrons starting there will not arrive at the anode. They hit the mirror.
Figure 16: Dift-plot: width:2.4mm, gap:0.4mm
4.3.4
Results
The influence of the laser-hole on the field quality is much higher, than the influence of the mirror.
But the calculation is incorrect, because the problem is not rotational symmetric any longer. If the planar model is rotated by an angular of 360
◦
, the mirror is a torus and not a locally inserted object. Also the laser-hole is not only a hole, but a circle.
So a 3D-model is needed, to calculate this problem in a correct way.
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To calculate unsymmetric problems, I have designed a three dimensional model with
CST. The problem is, that this model is very huge and needs a large number of data.
So it is not possible to define such a fine mesh, as in case of the planar model, because the total number of mesh cells is limited to 300,000,000. So the calculation is not very accurate.
Here the design of the 3D-model is presented:
Figure 17: 3D-model of the TPC with inserted mirror and laser-hole
Figure 18: Cut through the 3D-model
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Figure 19: Zoom of the 3D-model
Maybe a tetrahedral mesh is better adapted to the round design of the TPC, but I have no results yet.
Here is shown, how a tetrahedral mesh would look like:
Figure 20: Tetrahedral mesh
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Figure 21: Zoom of the tetrahedral mesh
The large TPC prototype will be build next year. To get a homogenious electric field it is very important to choose the right width for the fieldstrips. The simulation predicts the best results for big fieldstrip widths. 2.4mm seam to be the best value.
Really useful are the driftplots, because you can really see what happens to the particle drifting through the TPC. If the arrival time is included in the calculation more interesting studies can be done, but there is no time left for this.
If one resistor fails, this has influences on the field of course. But if this happens in reality it is not so bad, that you can’t use the chamber any longer. This are good news for the group.
To analyse the influence of the mirror and the hole, the studies are not finished, yet.
But the hole seams to have a stronger effect on the field quality than the mirror. More precisive results need time, because the calculations become very huge.
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