Gaseous Tracking Detectors
Peter Hansen, Lecture on tracking detectors
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Overview
Straw trackers MWPCs TPCs Micropattern gas detectors Momentum measurementThanks to Christian Joram and others
from whom I borrowed slides
Peter Hansen, Lecture on tracking detectors
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Gaseous tracking detectors
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
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Signal formation
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The ATLASTransition Radiation Tracker Installation Design details Simulation and performance Calibration and Alignment Particle ID
An example gaseous tracker
Peter Hansen, Lecture on gaseous tracking detectors
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Transition Radiation Tracker
Length: Total 6802 cm
Barrel 148 cm
End-cap 257 cm
Outer diameter 206 cm
Inner diameter 96-128 cm
# straws: Total 372 832
Barrel 52 544
End-cap 319 488
# electronic channels 424 576
Weight ~1500 kg
Barrel
End-caps
Gas 70%Xe+27%CO2+3%O2
• Xe for good TR absorption
• CO2 > 6% for maximum operation stability
Gas gain 2.5104
Straw diameter - 4 mm
Wire diameter - 30 μm
Polypropylene foil/fibre radiators
Peter Hansen, Rome seminar, 04-May-07
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protons
protonsA
tlas
CMS
ATLAS
Peter Hansen, Lecture on geseous tracking detectors
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TRT performance
Bd0J/ψ Ks
0
6 keV
0.3 keVMIP threshold – precise tracking/drift time determination
TR threshold – electron/pion separation
90% electron efficiency10-2 pion rejection
~1 TR hit
~7 TR hits
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)
20 GeV beam
Peter Hansen, Lecture on gaseous tracking detectors
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The TRT Straw
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TRT commisioning 2008-2009 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
Peter Hansen, Lecture on tracking detectors
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The TRT gas
70% Xe (high amplification A=25000, absorbs X-rays) 27% CO2 (quenches ultraviolet, does not polymerize)
3% O2 (intercepts unwanted electrons)
Gas Z A ½ Emin Wi (dE/ dx)min np
(g/ cm3) (eV) (eV) (MeV/ gcm¡ 2) ions/ cmXe 54 131.3 5:49 10¡ 3 8.4 22 1.23 44
CO2 22 44 1:86 10¡ 3 5.2 33 1.62 34
Gas Z A ½ Emin Wi (dE/ dx)min np
(g/ cm3) (eV) (eV) (MeV/ gcm¡ 2) ions/ cmXe 54 131.3 5:49 10¡ 3 8.4 22 1.23 44
CO2 22 44 1:86 10¡ 3 5.2 33 1.62 34
Gas Z A ½ Emin Wi (dE/ dx)min np
(g/ cm3) (eV) (eV) (MeV/gcm¡ 2) ions/ cmXe 54 131.3 5:49 10¡ 3 8.4 22 1.23 44
CO2 22 44 1:86 10¡ 3 5.2 33 1.62 34
Gas Z A Emin Wi dE/dx Np
Xe 54 131.3 5.49 10-3 g/cm3
8.4 eV 22 eV 1.23 MeV/(g/cm2)
44 ion/cm
Co2 22 44 1.86 5.2 33 1.62 34
½
Peter Hansen, Rome seminar, 04-May-07
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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
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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
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Digitization simulation
Digitization includes Diffusion and capture Avalance formation Electronics shaping Noise Reflections from ends Propagation along wire TOF and T0 fluctuation Threshold fluctuations
Peter Hansen, Rome seminar, 04-May-07
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Custom ASIC readout
Peter Hansen, Lecture on tracking detectors
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The electric field
According to Gauss, the capacity per unit length, C, and the anode voltage, V0, determines the electric field:
Integrating from the straw wall to the wire radius and equating
The result to V0, gives
€
E(r) =CV0
2πε 0r
€
E(r) =V0
log(b a)
1
r=
0.2V0
r
€
C =2πε 0
log(b a)= 0.114 pf /cm
Peter Hansen, Lecture on tracking detectors
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Avalance development
The movement of a charge, Q, in a system with capacitance per unit length, C, by a distance dr gives a voltage signal v
Almost all avalance electrons are created in the last mean free path
€
v =Q / l
CV0
dV
drdr
€
v − = −Q / l
CV0
dV
drdr = −
Q / l
2πε 0
loga + λ
aa
a +λ
∫
Peter Hansen, Lecture on tracking detectors
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Shaping
The positive ions drift to the cathode gives rise to:
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.
€
v + = −Q / l
CV0
dV
drdr = −
Q / l
2πε 0
logb
a + λa +λ
b
∫
Peter Hansen, Rome seminar, 04-May-07
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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
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A simple calculation of A
Balancing concerns, the optimum gas amplification is 25000 In any cascade process, we have
Leading to a total amplification of
At ionization energy, W=22eV, Xe presents a cross-section of
2 10-16 cm2 and the electron has a mean free path of
€
dN
dr(r) = α (r)N(r)
€
A = exp | α (r)dr |rthresh
ranode
∫
€
λ =1
NπrXe2 = 3 • 10−5cm
Peter Hansen, Rome seminar, 04-May-07
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A simple calculation of A
The distance from the wire, where the avalance starts, is given by:
The Townsend coefficient is assumed to be proportional to the kinetic energy of the electrons
Assuming =log 2 / λ at threshold, we have
€
eE(rstart )λ = W ⇒ rstart =0.2V0
22V3 • 10−5cm
= 0.06μV0
22V
€
(r) = kNε (r) = kNeE(r)λ
€
(r) =0.0063V0
r
Peter Hansen, Rome seminar, 04-May-07
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A simple calculation of A
Finally we get
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.€
A = exp(0.0063V0 ∗log(0.06
V0
2215
))
Peter Hansen, Lecture on tracking detectors
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Drift Chambers
Peter Hansen, Lecture on tracking detectors
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The driftvelocity - naively
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:
The correct answer is
€
5cm /μs
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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
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modifications from quencher gas
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Diffusion (no field case)
The mean velocity of a particle in an ideal gas is given by Maxwell:
According to kinetic theory, a collection of particles localized at x=0 at t=0, will later have a distribution:
Where D is the diffusion coefficient
€
v =8kT
πm
€
dN
N=
1
4πDtexp(−
x 2
4Dt)dx
Peter Hansen, Lecture on gaseous tracking detectors
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The diffusion coefficient
According to statistical mechanics:
where the mean free path for an ideal gas is:
By substitition:
€
D =1
3vλ
€
λ =1
2
kT
σP
€
D =2
3 π
1
σP
(kT)3
m
Peter Hansen, Lecture on gaseous tracking detectors
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Diffusion in an electric field
A classical argument by Einstein gives for an ideal gas in thermal equilibrium with the drifting ions:
In practice, we parametrize the spread of the coordinate in
the drift direction as:
Where the characteristic energy
can be calculated for known cross-sections and energy-losses
of the electron-gas collisions.
€
D
μ=
kT
e
€
σx = 2Dt =2ε k x
eE
€
εk =eED(E)
v(E)
Peter Hansen, Lecture on gaseous tracking detectors
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The TRT resolution
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:
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.
€
σx =2 × 2eV × 0.1cm
1530V /0.2eV /cm
Peter Hansen lecture on gaseous tracking detectors
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Drift time simulation
The leading edge of signal gives the drift time of the ionization electrons and hereby the distance from the charged particle to the wire
The simulation includes diffusion, Lorentz-forces, signal propagation and shaping, channel-to-channel fluctuations in threshold and noise amplitudes (deduced from the observed noise levels), the time structure of noise – and more €
r = vDt
Peter Hansen lecture on gaseous trackling detectors
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CTB data and simulation
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.
Residuals
fromThomas
Kittelmann thesis
Sigma=0.132mm
100 GeV
pions
Peter Hansen, lecture on gaseous tracking detectors
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CTB data and simulation
Also the Time Over Threshold is reasonably well simulated
And the hit efficiency is predicted to 95% in agreement with data
Peter Hansen, Rome seminar, 04-May-07
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Tracking performance in ATLAS
Peter Hansen, Rome seminar, 04-May-07
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Calibration
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
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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)
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, Lecture on tracking detectors
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Multiwire proportional counters
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 X-rays or particles from radioactive decay.
Peter Hansen, Lecture on tracking detectors
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Multiwire proportional counters
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Second coordinate –some ideas
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The TPC
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The TPC end-plate
Peter Hansen, Lecture on tracking detectors
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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 cylindersof 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
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Electron drift in E and B fields
The TPC is immersed in a magnetic field parallel to the electric field.
this Langevin equation becomes in the stationary state
Introducing the mobility
and the cyclotron frequency
we get
€
mdv
dt= eE + e(v × B ) + Q(t)
€
0 = eE + e(v D × B ) −m
τv D
€
μ =eτ
m
€
ω =eB
m
€
v D = μE +τv D × ω
Peter Hansen, Lecture on tracking detectors
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Electron drift in E and B fields
Solving for the drift velocity:
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 ω helps!
At high ω, vD is suppressed by powers of ω
except for the effect of a B component. However, B is zero on the average according to Ampere.
€
v D =μE
1+ω 2τ 2 [ ˆ E +ωτ ˆ E × ˆ B +ω 2τ 2( ˆ E • ˆ B ) ˆ B ]
€
φ
Peter Hansen, Lecture on tracking detectors
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Electron diffusion in E and B fields
In the transverse projection an electron follows the arc of a circle with radius = vT /ω, where the mean squared velocity projected onto the transverse plane is:
After a time, t, the electron has reached a transverse distance of
so the spread after one collision is:
€
vT2 =
2λ2
3τ 2
€
2ρ sinvT t
2ρ
€
δ 2 =1
2
dt
texp(−
t
τ)[2ρ sin
vT t
2ρ]2 =
1
2
τ 2vT2
1+ω 2τ 20
∞
∫
Peter Hansen, Lecture on tracking detectors
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Electron diffusion in E and B fields
After a longer time, the transverse spread is
Thus in large magnetic fields the transverse diffusion is reduced by a factor 1+ω22
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
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.
€
σT2 (t) =
t
2
τvT2
1+ω 2τ 2 = tD0
1+ω 2τ 2
€
200μ
Peter Hansen, Lecture on tracking detectors
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The ALEPH TPC
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TPC calibration
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Why use silicon instead of gas
Peter Hansen, Lecture on tracking detectors
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Micropattern gaseous detectors
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
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Micro gaseous detectors
Peter Hansen, Lecture on tracking detectors
P 54 Gas Electron Multipliers (no spark)
Peter Hansen, Lecture on tracking detectors
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Two GEM’s are better than one
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Thin gap chambers
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Resistive plate chambers
Peter Hansen, Lecture on tracking detectors
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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
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Momentum measurement
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Momentum accuracy
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Multiple scattering
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Total momentum error
Peter Hansen, Lecture on tracking detectors
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Technology choices
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.