Download Tracking Detectors

Gaseous Tracking Detectors
P2
Overview
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Straw trackers
MWPCs
TPCs
Micropattern gas detectors
Momentum measurement
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Thanks to Christian Joram and others
from whom I borrowed slides
Peter Hansen, Lecture on tracking detectors
P3
Gaseous tracking detectors
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Provides economic tracking over large areas
Measures primary ionization of charged tracks in the gas
Works by having avalances of secondary ionization
initiated when the primary ionization hits a small-area
anode. This provides built-in amplification.
Peter Hansen, Lecture on tracking detectors
P4
Signal formation
Peter Hansen, Lecture on tracking detectors
P5
An example gaseous tracker
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The ATLASTransition Radiation Tracker
Installation
Design details
Simulation and performance
Calibration and Alignment
Particle ID
P6
Transition Radiation Tracker
Barrel
End-caps
Length:
Total
Barrel
End-cap
Outer diameter
Inner diameter
6802 cm
148 cm
257 cm
206 cm
96-128 cm
# straws: Total
Barrel
End-cap
# electronic channels
Weight

Straw diameter - 4 mm

Wire diameter - 30 μm
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372 832
52 544
319 488
424 576
~1500 kg
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Polypropylene foil/fibre
radiators
Gas 70%Xe+27%CO2+3%O2
• Xe for good TR
absorption
• CO2 > 6% for maximum
operation stability
Gas gain 2.5104
Peter Hansen, Lecture on gaseous tracking detectors
P7
CMS
ATLAS
protons
protons
Peter Hansen, Rome seminar, 04-May-07
P8
TRT performance
20 GeV beam
~1 TR hit
~7 TR hits
Bd0J/ψ Ks0
90% electron efficiency
10-2 pion rejection
High-γ charged particles (e.g.
electrons) emit transition radiation
(X-rays) when they traverse the
radiators, detected in the straw tubes
as larger energy deposition (8-10 KeV)
TR threshold – electron/pion separation
MIP threshold – precise tracking/drift time determination
6 keV
0.3 keV
Peter Hansen, Lecture on geseous tracking detectors
P9
The TRT Straw
Peter Hansen, Lecture on gaseous tracking detectors
P 10
TRT commisioning 2008-2009
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The TRT barrel and end-caps
were installed in their final
position inside the cryostat in
2008 with all services.
One “splash-event” in 2008 was
very useful for timing all the
channels relative to each other.
Commissioning in 2009 with
cosmic rays. The tracking
resolution was found to be 160
microns. The High Threshold
probability was found as
expected.
The first collisions Dec2009
Peter Hansen, Lecture on gaseous tracking detectors
P 12
The TRT gas
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70% Xe (high amplification A=25000, absorbs X-rays)
27% CO2 (quenches ultraviolet, does not polymerize)
3% O2 (intercepts unwanted electrons)
Gas
Z
A

Emin
Wi
dE/dx
Xe
54
131.3
5.49
10-3
g/cm3
8.4 eV
22 eV
1.23
44
MeV/(g ion/cm
/cm2)
Co2
22
44
1.86
5.2
33
1.62
Np
34
Peter Hansen, Lecture on tracking detectors
P 13
Drift of electrons in a B field
New gas stabilizes
drift velocity in B field.
-and it does not eat glass
Peter Hansen, Rome seminar, 04-May-07
P 14
GEANT4 Simulation
Primary clusters formed according to PAI model
Custom TR physics process
Fiber radiator
Photon x-sect
Peter Hansen, Rome seminar, 04-May-07
P 15
Digitization simulation
Digitization includes
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Diffusion and capture
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Avalance formation
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Electronics shaping
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Noise
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Reflections from ends
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Propagation along wire
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TOF and T0 fluctuation
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Threshold fluctuations
Peter Hansen, Rome seminar, 04-May-07
P 16
Custom ASIC readout
Peter Hansen, Rome seminar, 04-May-07
P 17
The electric field
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According to Gauss, the capacity per unit length, C,
and the anode voltage, V0, determines the electric
field:
CV0
E(r) 
2 0 r
Integrating from the straw wall to the wire radius and equating
The result to V0, gives


V0 1 0.2V0
E(r) 

b
r
log( a) r
2 0
C
 0.114 pf /cm
b
log( a)
Peter Hansen, Lecture on tracking detectors
P 18
Avalance development
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The movement of a charge, Q, in a system with capacitance
per unit length, C, by a distance dr gives a voltage signal v
Q /l dV
v
dr
CV0 dr
Almost all avalance electrons are created in the last mean
free path


a 
Q/l
dV
Q/l
a

v 
dr  
log

CV0 a dr
2 0
a
Peter Hansen, Lecture on tracking detectors
P 19
Shaping
The positive ions drift to the cathode gives rise to:
Q/l b dV
Q/l
b
v 
 dr   2 log a  
CV0 a   dr
0

This contribution is about 50 times larger than that of the
electrons. But it is a slow signal.

By terminating the wire in a resistance, the signal is
differentiated with a time constant, RC.
For the TRT, the rise-time is 8ns and the duration only 20ns.
Peter Hansen, Lecture on tracking detectors
P 20
Pulse shaping
Problem:
Long tail (much longer than
the 25ns bunch spacing)
from the positive ions
moving outwards
Solution:
The ASDBLR front-end chip
restores the baseline within ~20ns
Peter Hansen, Rome seminar, 04-May-07
P 21
A simple calculation of A
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Balancing concerns, the optimum gas amplification is 25000
In any cascade process, we have
dN
(r)   (r)N(r)
dr
Leading to a total amplification of

A  exp |
ranode
  (r)dr |
rthresh
At ionization energy, W=22eV, Xe presents a cross-section of
2 10-16 cm2 and the electron has a mean free path of

1
5


3

10
cm
2
NrXe
Peter Hansen, Rome seminar, 04-May-07
P 22
A simple calculation of A
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The distance from the wire, where the avalance starts, is
given by: eE(r )  W  r  0.2V0 3  10 5 cm
start
start
 0.06 
22V
V0
22V
The Townsend coefficient is assumed to be proportional to the
kinetic energy of the electrons

 (r)  kN (r)  kNeE(r)
Assuming =log 2 /  at threshold, we have

0.0063V0
 (r) 
r
Peter Hansen, Rome seminar, 04-May-07
P 23
A simple calculation of A
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Finally we get
V0
0.06
22 ))
A  exp(0.0063V0 log(
15
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This leads for the TRT to the target amplification of 25000 at
a voltage of 1513 Volts, probably by luck this is close to the
truevalue 1530 Volts.
Peter Hansen, Rome seminar, 04-May-07
P 24
Drift Chambers
Peter Hansen, Lecture on tracking detectors
P 25
The driftvelocity - naively
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Assuming the electron is brought to halt at each collision
and that the mean free path is independent of energy, we
have at 1mm from a TRT wire:
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The correct answer is
5cm / s
Peter Hansen, Lecture on tracking detectors
P 26
Complications
The difference between prediction and fact is due to:
 Dependence on electron energy of cross-section
(mainly the Ramsauer minimum around 1eV)
 The quencher gas.
 The magnetic field bending the drift-trajectories up/down
 Diffusion
Peter Hansen, Lecture on tracking detectors
P 27
modifications from quencher gas
Peter Hansen, Lecture on tracking detectors
P 28
Diffusion (no field case)
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The mean velocity of a particle in an ideal gas is given by
Maxwell:
8kT
v
m
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According to kinetic theory, a collection of particles localized
at x=0 at t=0, will later have a distribution:

2
dN
1
x

exp(
)dx
N
4Dt
4Dt
Where D is the diffusion coefficient

Peter Hansen, Lecture on tracking detectors
P 29
The diffusion coefficient
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According to statistical mechanics:
1
D  v
3
where the mean free path for an ideal gas is:

1 kT

2 P
By substitition:

1 (kT)3
D
m
3  P
2
Peter Hansen, Lecture on gaseous tracking detectors
P 30
Diffusion in an electric field
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A classical argument by Einstein gives for an ideal gas in
thermal equilibrium with the drifting ions:
D kT

 e
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In practice, we parametrize the spread of the coordinate in
the drift direction as:

2 k x
x  2Dt 
eE
eED(E)
k 
Where the characteristic energy
v(E)
 for known cross-sections and energy-losses
can be calculated
of the electron-gas collisions.

Peter Hansen, Lecture on gaseous tracking detectors
P 31
The TRT resolution
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The gasses in the TRT have a characteristic energy of about 2 eV. Thus
we have for the coordinate perpendicular to the wires a spread of
0.114mm:
2  2eV  0.1cm
x 
1530V /0.2eV /cm
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For an average of 10 primary ion pairs, the distance of the closest
electron to the wire has a spread of about 0.012mm
The drift-time
binning in 3.125ns contributes 0.043mm
Noise and gain variations gives 0.035mm
Uncertainties in wire position and time=0 gives 0.036mm
All together this gives a coordinate resolution of about 0.132mm, in
excellent agreement with detailled calculations – and with data.
Peter Hansen, Lecture on gaseous tracking detectors
P 32
Drift time simulation
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The leading edge of signal gives the drift time of the
ionization electrons and hereby the distance from the
charged particle to the wire
r  vD t
The simulation includes diffusion, Lorentz-forces, signal
propagation and shaping, channel-to-channel fluctuations in
threshold and noise amplitudes (deduced from the
 the time structure of noise – and
observed noise levels),
more
Peter Hansen lecture on gaseous tracking detectors
P 33
CTB data and simulation
Residuals
fromThomas
Kittelmann thesis
Sigma=0.132mm
100 GeV
pions
Perfect agreement! But only if using an average threshold of 161eV where previous it was 300eV. The explanation is probably new noise and
threshold fluctuations in MC – but there is no profound understanding.
Peter Hansen lecture on gaseous trackling detectors
P 34
CTB data and simulation
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Also the Time Over Threshold is reasonably well simulated
And the hit efficiency is predicted to 95% in agreement with data
Peter Hansen, lecture on gaseous tracking detectors
P 35
Tracking performance in ATLAS
Peter Hansen, Rome seminar, 04-May-07
P 36
Calibration
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Calibration is concerned with T0, the R(t-T0) relation, the high
threshold probability and noise removal.
The ”V-plot” of time versus track impact position is used
Peter Hansen, Rome seminar, 04-May-07
P 37
Calibration
The tip of the V yields T0 (and, if a single wire is plotted,
also the wire position).
 The peak position in each 3ns bin of t-T0 yields R(t-T0)
 (Note that the average position is not good because of tails
at long arrival times for tracks passing close to the wire)
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Peter Hansen, Rome seminar, 04-May-07
P 38
Electron Identification in test beam
Performace of combined pion rejection at 90% electron efficiency
Universality of the HT probability
Peter Hansen, Rome seminar, 04-May-07
P 39
Multiwire proportional counters
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In 1968 it was shown by Charpak that an array of many
closely spaced anode-wires in the same chamber could
each act as an independent proportional counter.
This provided an affordable way of measuring particles
over large areas, and the technique was quickly adopted in
high energy physics.
Later it has found applications in all kinds of imaging of Xrays or particles from radioactive decay.
Peter Hansen, Lecture on tracking detectors
P 40
Multiwire proportional counters
Peter Hansen, Lecture on tracking detectors
P 41
Second coordinate –some ideas
Peter Hansen, Lecture on tracking detectors
P 42
The TPC
Peter Hansen, Lecture on tracking detectors
P 43
The TPC end-plate
Peter Hansen, Lecture on tracking detectors
P 44
The TPC field cage
Experience shows that the greatest challenge in a TPC is to maintain a
constant axial electric field.
This field is made by electrodes on the inner and outer cylinders
of the Field Cage, connected to a resistor chain.
Some useful elements are:
 A Gating Grid to avoid space-charges.
 Tight mechanical tolerances wrt the ideal cylindrical shape (while
keeping the material budget low).
 Severe cleaniness, (the tiniest piece of fiber in the cage may short-cut
two electrodes and distort the field.)
 As little as possible of insulator exposed to the drift-volume to avoid
build-up of charge on the insulator.
 Perfect matching of equipotential surfaces at the end plane is needed to
avoid transverse field components.
Peter Hansen, Lecture on tracking detectors
P 45
Electron drift in E and B fields
The TPC is immersed in a magnetic field parallel to the
electric field.
dv
m
 eE  e(v  B )  Q(t)
dt
this Langevin equation becomes in the stationary state
m
0  eE  e(v D  B )  v D


e
Introducing the mobility  
m
eB
and the cyclotron frequency
 

m
we get
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
v D  E  v D  

Peter Hansen, Lecture on tracking detectors
P 46
Electron drift in E and B fields
Solving for the drift velocity:
E
ˆ  Eˆ  Bˆ   2 2 ( Eˆ  Bˆ ) Bˆ ]
vD 
[
E
1  2 2
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Since the coordinate resolution is high in the azimuthal
direction, in order to measure the momentum well, a 
component
of the velocity due to field distortions is very

dangerous. But high  helps!
At high , vD is suppressed by powers of 
except for the effect of a B component. However, B is
zero on the average according to Ampere. 
Peter Hansen, Lecture on tracking detectors
P 47
Electron diffusion in E and B fields
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In the transverse projection an electron follows the arc of a
circle with radius  = vT /, where the mean squared
velocity projected onto the transverse plane is:
2
2

vT2  2
3
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After a time, t, the electron has reached a transverse
vT t
distance of 2 sin


2
so the spread after one collision is:

1
2
 
2


0
dt
t
vT t 2 1  2vT2
exp( )[2  sin
] 
t

2
2 1  2 2
Peter Hansen, Lecture on tracking detectors
P 48
Electron diffusion in E and B fields
After a longer time, the transverse spread is
2
t

v
D0
2
T
T (t) 
t
2 1  2 2
1  2 2
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Thus in large magnetic fields the transverse diffusion is
reduced by a factor 1+22

e.g. for Ar/Ethane and B=1.5Tesla the reduction is a factor
50. This is what makes a TPC possible!
Thus you can get a precision of about 200
for about 30 points on each track over a 1m-2m radial
distance from the collision point.
Note that this is without any significant
multiple scattering

and with a good resolution also in the longitudinal direction.
It is also relatively CHEAP, since it is mainly gas.
Peter Hansen, Lecture on tracking detectors
P 49
The ALEPH TPC
Peter Hansen, Lecture on tracking detectors
P 50
TPC calibration
Peter Hansen, Lecture on tracking detectors
P 51
Why use silicon instead of gas
Peter Hansen, Lecture on tracking detectors
P 52
Micropattern gaseous detectors
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Silicon detectors are still very expensive over large areas,
and they suffer from radiation damage.
Although they give 10000 more charges, they have no
inbuilt amplification and are slow to read out.
So if gaseous counters could be made small, fast and
precise, they would be quite attractive.
The way to go is to employ the same precision methods for
fabricating micro-structures in silicon on the gas detector
readouts.
Peter Hansen, Lecture on tracking detectors
P 53
Micro gaseous detectors
Peter Hansen, Lecture on tracking detectors
P 54
Gas Electron Multipliers (no spark)
Peter Hansen, Lecture on tracking detectors
P 55
Two GEM’s are better than one
Peter Hansen, Lecture on tracking detectors
P 56
Thin gap chambers
Peter Hansen, Lecture on tracking detectors
P 57
Resistive plate chambers
Peter Hansen, Lecture on tracking detectors
P 58
From coordinates to momenta
Given a number of ”track hit-coordinates” from the various
detector elements, the parameters of the track is
determined from a least squares fit.
In a solenoidal field geometry, the parameters are those of a
helix:
 The track position at closest approach (perigee) to the
beamline (3 parameters)
 The angle of the track to the beamline (polar angle)
 The signed curvature +-1/R
Peter Hansen, Lecture on tracking detectors
P 59
Momentum measurement
Peter Hansen, Lecture on tracking detectors
P 60
Momentum accuracy
Peter Hansen, Lecture on tracking detectors
P 61
Multiple scattering
Peter Hansen, Lecture on tracking detectors
P 62
Total momentum error
Peter Hansen, Lecture on tracking detectors
P 63
Technology choices
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Since the TPC is so superior why is it not used at the LHC?
This is because it is too slow. It is in fact used in ALICE who
do not depend on a very high intensity beam.

Why then are the micropattern gas detectors not used?
Well, they are for trigger chambers. But for the main
trackers the technology was deemed too risky at the time of
decision.
Peter Hansen, Lecture on tracking detectors