tracking of charged particles - university of...
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III/1Particle Physics Detectors, 2010 Stephan Eisenhardt
Trackingof
Charged Particles
Physics of gaseous chambers for charges particle trackingTypes of tracking chambers
not covered: solid state detectors→ see lecture of Richard Bates
III/2Particle Physics Detectors, 2010 Stephan Eisenhardt
Tracking DetectorsTracking in 1932: Cloud Chamber(detection of antimatter)
Tracking in 2001: STAR TPC(study of Quark-Gluon-Plasma)
~5 cm 200 cm
2000: L3 Higgs candidate~1994: DELPHI B mesonτB ≈ 1.6 psL = βγ cτ
≈ βγ ⋅ 480 μm
III/3Particle Physics Detectors, 2010 Stephan Eisenhardt
Momentum Measurement ISagitta s: measures momentum
Need at least 3 measurements:
For N equidistant measurements (Glückstern, NIM 24 (1963)381)
improves with BL2!! and N1/2
Examples:- pT=1GeV/c, L=1m, B=1T - pT=100GeV/c, L=5m, B=1.5T
σ(x)=200μm, N=10 : σ(x)=1.5mm, N=6 :
Lorentz force:F = q B v
L
ρ
s
θ
B
y
x
r
( )
TTTT
TT
pBLsLBppp
rLsrrsrrL
TmBrpqBrprmvF
2
22
2
83.0and3.0sin
882cos1and2sin2
][3.0]cGeV[or
≈=≈=Δ
=→≈−=≈=
==→=
θθ
θθθθ
223
23
3.08)()()()(
BLpx
sx
ss
pp T
T
T
⋅⋅
===σσσσ
( ))4(
7203.0
)(2
.
+⋅⋅
=NBL
pxpp T
meas
T
T σσ
( ) mmand 5.37%48.0 =≈ spp
T
Tσ
231
2xxxs +
−=
( ) mmand 4.1%11 =≈ spp
T
Tσ
III/4Particle Physics Detectors, 2010 Stephan Eisenhardt
Multiple ScatteringCharged (z) particles suffer elastic Coulomb scatterings from nuclei (Z):
Average scattering angle:
Multiple Scattering: width =In thick material layer:
Gaussian shape for central 98% of distribution:– X0 = radiation length– accuracy ≤ 11% for 10-3 < L/X0 < 100
2sin14 4
22
θβσ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
Ω pcmzZr
dd e
e
0=θ
Rutherford formula
L
θplane
rplane
RMSRMSplaneplane space
θθθθ2
120 ===
P
θplane0
θ0
Gaussian
sin-4(θ/2)
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧−= 2
0
2
0 2exp
21
θθ
θπθ plane
planeP
⎭⎬⎫
⎩⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
000 ln038.016.13
XL
XLz
cpMeV
βθ
III/5Particle Physics Detectors, 2010 Stephan Eisenhardt
Momentum Measurement IIMultiple scattering contributes to momentum measurement error:
independent of p!but X0 ∝ N
Total measurement error:
Experiments with solenoid magnet:
measurement error:
Optimum N: trade measurement resolution against material budget
In practice often:
0
0
0
1045.03.0
0136.0)(
10136.0sin)(
LXBBLXL
pp
XL
pppp
MS
T
planeRMS
MS
==
⋅≈=
σ
θσ
σ(p)/p
σ(p)/p
σ(p)/p
p
MS
meas.total error
Example:Ar (X0=110m) L=1m, B=1T
%5.0)(≈
MS
Tppσ
222.
2)(
MSTmeasT
bpapp
+⋅=⎟⎟⎠
⎞⎜⎜⎝
⎛σ
)1()1(12)()( .
+−
=NNN
Lzmeas σθσ
( ) ( )T
T
pp
pp σσ
≈
θsinppT =
III/6Particle Physics Detectors, 2010 Stephan Eisenhardt
Ionisation of GasesCharged particles ionise the atoms of a gas:
– X+p → X* + p excitation– X+p → X+ + p + e- ionisation
δ-rays: e- with enough energy to create new e--ion pairs:
Number of created e--ion pairs:
– ΔE = total energy loss– Δx = distance traveled– Wi = effective <energy loss> per pair ≈ 30 eV
Example: CO2– ΔE ≈ 3 keV cm-1
– ntotal ≈ 100 e--ion pairs / cm
primary ionisation
secondary ionisation
ii Wx
dxdE
WEn
Znn
Zn
Δ=
Δ=
≈⋅≈
≈
total
1-1-primarytotal
-1-1primary
atmcm55.443
atmcm45.1
K
III/7Particle Physics Detectors, 2010 Stephan Eisenhardt
data: Harris et al. (1977)dotted curve: Landau(1944)dashed curve: Maccabee & Papworth(1969)
(Landau’s method)solid curve: Allison and Cobb (1980)
Landau Fluctuationsmean energy loss: <dE/dx>
ΔE = energy loss depositedin a layer of finite thickness
For thin layers and gases (low density):– ΔE has large fluctuations!– only few collisions, some with high ΔE– ΔE distribution has large contributions at high losses
→ “Landau tails”
– first parameterised by Landau in 1944– subsequently improved
For many measurements in a detector:– truncated mean of ΔE as estimate for <dE/dx>
Energy loss ΔE in 1.5cm Argon +7% CH4
π- e-
III/8Particle Physics Detectors, 2010 Stephan Eisenhardt
+V0
GND
Gaseous Ionisation DetectorsReminder: Basic Principle
Need Gas Amplification:a) primary e- drift towards anodeb) with gained Tkin e- ionises further atoms → avalanchec) e- and ion cloud drift apartd) e- cloud surround anode wire, induces signale) ion cloud withdraws from anode on larger time scale
and induces signal– close to wire: large E ≥ 1kV/cm– gas amplification A with gain up to 106
exponential gain
α = Townsend coefficient (e--ion pairs/cm)
( )
arCVrV
rCVrE
ln2
)(
12
0
0
0
0
⋅=
⋅=
πε
πε
( ) ( )xrxE ennenn αα00 or either ==
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡== ∫
Cr
a
drrnnA αexp
0
~100 e--ion pairs / cm
III/9Particle Physics Detectors, 2010 Stephan Eisenhardt
spacecharge
V
Q [
e]Operation Modes
Ionisation chamber– no multiplication
Proportional counter– Signal proportional to nprimary
– dE/dx measurement– localised avalanche
Limited proportional / Streamer mode– secondary avalanches along wire– high gain
Geiger-Müeller counter– avalanche along full wire
Reminder:
III/10Particle Physics Detectors, 2010 Stephan Eisenhardt
Signal ShapeCylindrical proportional chamber: with electrostatic energy of field W=1/2 lCV0
2 (l = cylinder length)– a = wire radius e.g. 10 μm– b = chamber radius e.g. 10 mm– rc = critical radius, where avalanche starts e.g. 1 μm
Electron avalanche and drifting ionsinduce signals on anode:
– with different strength: ions dominate: V-/V+ ~ 0.01 !!– on different time scales: e-: O(10ns), ions: O(100ns)
Drift velocity v: (using V+ only)
– μ = mobility
Time development of pulse:
c
b
ra
ca
ra
rab
lqdrrE
lCVqV
ara
lqdrrE
lCVqV
c
c
+⋅==
+⋅
−=
−=
∫
∫
+
+
+
−
ln2
)(
ln2
)(
00
00
πε
πε
21
0
02
0
0
)(
12
)(
⎟⎟⎠
⎞⎜⎜⎝
⎛+=⇒
===
tCVatr
rCVrE
dtdrv
πεμ
πεμμ
⎟⎟⎠
⎞⎜⎜⎝
⎛+−=
−== ∫
ta
CVl
q
atr
lqdt
drdVtV
tr
a
20
0
0
0
)(
1ln4
)(ln2
)(
πεμ
πε
πεin practise:pulse clipping by RC of differentiator
III/11Particle Physics Detectors, 2010 Stephan Eisenhardt
Choice of GasGas selection:– noble, inert: Ar, CO2, He– high specific ionisation
But: secondary emission of electrons– from de-excitation of UV γ– new avalanches started– leads to constant discharges
Example: Argon– photons with E = 11.6 eV – produces e- at cathode
Quenching needed!! Ar *11.6 eV
Cu
e-
cathode
III/12Particle Physics Detectors, 2010 Stephan Eisenhardt
QuenchingPolyatomic gases act as “quenchers”:– C2H5OH, CH4, C2H6, C4H10, …– Absorption of photons in large energy range
by vibration and rotation energy levels– concentration chosen to limit free path of γ to O(a)
→ UV γ don’t reach cathode→ ions transfer ionisation to quenching gas
where energy too small for ionisation…
Possible problems– dissociation of molecules
→ whiskers on wires→ breakdown
– coating of wires→ “aging”
Solutions– a few 100 ppm of water !?!
III/13Particle Physics Detectors, 2010 Stephan Eisenhardt
Multiwire Proportional ChambersUntil about 1970– mostly optical tracking devices:
cloud chamber, bubble chamber, spark chamber, emulsions– slow for data taking and analysis
Revolution of 1968– MWPC invented by Charpak (Nobel prize 1992)– plane of anode wires act as individual proportional counters
Typical dimensions: L = 5 mm, d = 1 mm, awire= 20 μm
MWPC:– fast electronic device– wire address: 1-dimensional spatial resolution
– high cost in channels (electronics)– further improvement on resolution desirable
m30012
μσ ≥≈d
x
field and equipotential lines around anode wires
III/14Particle Physics Detectors, 2010 Stephan Eisenhardt
Drift Chambers
anode
TDCStartStop
DELAYscintillator
drift
low field region drift
high field region gas amplification
First studies:T. Bressani, G. Charpak, D. Rahm, C. Zupancic, 1969First operation drift chamber:A.H. Walenta, J. Heintze, B. Schürlein, NIM 92 (1971) 373
Improvement of spatial resolution: Drift Chamber– large volume with low field region (~constant field): drift– high field region: gas amplification
Time measurement:– start: scintillator trigger, collider bunches– stop: arrival time of drift e-
Complications:– Drift velocity– Diffusion– Magnetic fields
Spatial resolution:– electronics, ionisation, diffusion – not limited by cell size– fewer wires than MWPC electronics, structure cost
III/15Particle Physics Detectors, 2010 Stephan Eisenhardt
Drift VelocitiesRange of vD:– 50 mm/μs --- fast gases (Ar, …)– 5 mm/μs --- slow gases (CO2)
(F. Sauli, CERN 77-09)
Argon-Methane
Argon-Isobutane
(A. Breskin et al. NIM 124 (1975) 189)
mm
/μs
cm/μ
s
V/cmV/cm / mm Hg
III/16Particle Physics Detectors, 2010 Stephan Eisenhardt
DiffusionDrift with no external fields: Diffusion
– e- and ions thermalise due to collisions with atoms
– linear and volume diffusion coefficient:
“Cool” gases, e.g. CO2– e- thermal up to E ~ 2kV/cm– expect small and isotropic diffusion
“Hot” gases, e.g. Argon– e- non thermal at E ~V/cm – expect non-isotropic Diffusion, DL along E-field
meV3523
≈= kTTkin
DtE
DxDt Lx 622 === σμ
σ
σL (1 cm) = 57 μm
σT (1 cm) = 180 μm
Ar-10%CH4-i-2.8%C4H10
V/cm / Torr
D/μ
x [mm]σ[
μm]
σ x [c
m] f
or 1
cm d
rift
E [V/cm] @ 1 atm
III/17Particle Physics Detectors, 2010 Stephan Eisenhardt
Drift in Fields
x
y
EB
vD
αL
ωτα =Ltan
External fields E and B:– diffusion equation, interested in time-independent solution
– B = 0 :
E and B perpendicular:
Lorentz angle αL:
DD vmBveEedtvd rrrrr
τ−×+== )(0
frequency) (cyclotron:
(mobility):
)collisionsbetween (mean time:
mBe
me
r
=
=
ω
τμ
τ
⎥⎦
⎤⎢⎣
⎡ ⋅+
×+
+= 2
2222
)()(1 B
BBEB
BEEvD
rrrrrrr τωωτ
τωμ
EvD
rr μ=
zz
xy
xx
Ev
Ev
Ev
μτω
ωτμ
τωμ
=+
−=
+=
22
22
1
11
III/18Particle Physics Detectors, 2010 Stephan Eisenhardt
Determination of z-Coordinatecrossed wires (2-dim chamber, usually small angle):segmented cathode readout
Differential timing:– measure arrival time at both wire ends– time difference gives z-coordinate
Charge division:– resistive anode wire (Carbon R = 2kΩ/cm)– charge division proportional to wire length L:– reached accuracy:
down to:
Stereo-Layers:– alternated with axial layers– γ = ±2-6°– match signal hits of layers– occupancy limit: combinatorics!
nsm2.0with ≈∝ signalsignaltz vvσσ
BA
A
QQQLz+
=
Lz ⋅= %4.0σ
Example: JADE drift chamber– L = 234cm– σz = 1.6cm = 0.7%·L
Example: TASSO drift chamber– L = 350cm– γ = ±4°– σz ~ 3mm
y
L
QBQA
track
yL
track
CFD CFDΔT
Example: OPAL drift chamber– σt = 100 ps– σz = 4cm
III/19Particle Physics Detectors, 2010 Stephan Eisenhardt
Drift Chamber Geometries
%45.0%15.0 +⋅= TT
P PP
Tσ
Potential wires mandatoryVarious drift cell geometries in use:
– cylinder, square, hexagonal:short drift paths, small B effects
– closed, open:many vs. few potential wiresat cost of homogeneity of E
– jet (projecting):many points along trackat cost of long drift paths, B effects!and complicated E field
Example: BaBar– 40 layers– resolution:
TASSOopen
ARGUSclosed
JADEjet
III/20Particle Physics Detectors, 2010 Stephan Eisenhardt
Planar Drift ChambersGeometry optimisation:
– want constant drift velocity→ choose gas with little variation vD(E)→ linear space - drift time relation
– shape E field
III/21Particle Physics Detectors, 2010 Stephan Eisenhardt
Time Expansion ChamberL3:
– Cool gas: CO2-i-C4H10– small diffusion– grid wires to prevent ions
entering the drift volume– very good time resolution– maintain drift velocity to ‰ level
III/22Particle Physics Detectors, 2010 Stephan Eisenhardt
Time Projection ChamberAllows full 3-dimensional reconstruction & dE/dx measurement: “el. Bubble Chamber”– big gas cylinder (ALEPH: Ø 3.6M, L=4.4 m, Ar-Methane @ 10bar)– E and B field parallel: Lorentz force vanishes– B field reduces diffusion– End caps equipped with MWPC– x-y from wires and segmented cathodes– z from drift time– dE/dx information
→ particle identification, still very difficult for systematics
Long drift distances– need excellent gas quality– precise calibration of vD
Space charge problem:– from positive ions entering drift volume– solution: gating (needs trigger)
ALEPH resolution: (isolated leptons)σRφ = 173 μmσz = 740 μm
Gate open Gate closed
ΔVg = 150 V
ALEPH TPC(ALEPH coll., NIM A 294 (1990) 121,
W. Atwood et. Al, NIM A 306 (1991) 446)
III/23Particle Physics Detectors, 2010 Stephan Eisenhardt
Thin Gap ChambersThin Gap chambers (TPC)
– saturated mode– thin insulator prevents sparking– limited by graphite resistitivity– large gain 106
– fast, 2 ns risetime
CheapLarge area→ Muon chambers
G10 (support)
cathode pads ground plane
graphite
3.2
mm
2 mm4kV
50 μm
Gas: CO2/n-pentane
(≈ 50/50)
III/24Particle Physics Detectors, 2010 Stephan Eisenhardt
Resistive Plate ChambersSingle-Gap RPC:
– close to streamer mode– fast time dispersion (1…2 ns)– rasonable rate capabilities:
up to 1 kHz/cm2
– cheap
Double-Gap and Multi-Gap RPC:– improves efficiency and timing
2 m
m bakelite(melamine phenolic laminate)
pickup strips
10 kV
spacer
15 kV
Gas: C2F4H2, (C2F5H) + few % isobutane
used for:LHCb muon system
III/25Particle Physics Detectors, 2010 Stephan Eisenhardt
Tracking for the New Millenium
1980s and 90s:– golden area of gaseous wire chambers– e+e- colliders: LEP, SLC, B-factories – hadron colliders/fixed target: CDF, NA48/49, H1/ZEUS
LHC (and ILC is not too far as well):– bunch crossing rate 40 MHz / 25 ns– Luminosity 1034 cm-2 s-1
– ~ 30 overlapping events per bunch crossing– 1900 charged + 1600 neutral particles
Are we up for this new challenge?– need faster tracking detectors– need higher rate capabilities– need larger areas, lower cost
Simulated H → 4μ event in ATLAS
III/26Particle Physics Detectors, 2010 Stephan Eisenhardt
Micro-Strip Gas Chambers I
(A. Oed, NIM A 263 (1988) 352)Micro-Strip Gas Chambers – thin metal (Au) strips on insulating (glass) surface– photolithography for production– mechanically small and precise – relatively cheap
Gas multiplication– fast ion drift time, reduced built-up of charge– high rate capability ~106 /cm2 s
III/27Particle Physics Detectors, 2010 Stephan Eisenhardt
Micro-Strip Gas Chambers IIRate capability:
Signal shape: (cluster charge)
III/28Particle Physics Detectors, 2010 Stephan Eisenhardt
Discharges and AgeingAgeing:
– production of polymeric compounds in avalanchessticking to the electrodes or to the insulator
– careful selection of materials and gas– 10 yrs LHC or ~0.1 C/cm2
Discharges:– If gain > 107-108: Raether’s limit
growth of filament– Passivation needed:
non-conductive protection of cathode edges
III/29Particle Physics Detectors, 2010 Stephan Eisenhardt
Micro – Anything GoesMicro-Gap Chamber:
– MSGC, micro-wire, micro-dot – compteur à trous (CAT), micro-CAT/WELL – micro groove – gas electron multiplier (GEM)
Micomegas:– Gas: Ar-DME (≈80:20)
2-6
mm
100 μm
51
9metal 1(cathode)
metal 2(anode)
insulator
gold cathode on ceramic substrate5 μm wire on 40 μm wide polyimide strips
100 μm
3 m
m
HV 1
HV 2
conversion gap
amplification gapmicro grid
copper stripson kapton foil
317 μm
70 μm
E ≈ kV/cmE ≈ 45 kV/cm
Micro gap wire chamber
Micro gap chamber
Lots of Micro-maniacs are having fun!
… but life is complicated…
III/30Particle Physics Detectors, 2010 Stephan Eisenhardt
Gas Electron MultiplierGas Electron Multiplier
– drift region– GEM foil (Kapton)– induction region– e.g. Printed Circuit Board for collection
Why GEMs?– for rate capability
when combined with MWPC or MSGC for collection– Double GEM, Triple GEM
(R. Bouclier et al., NIM A 396 (1997) 50)
140 − 200 μm
50 − 120 μm50 μm Kapton + 2 x 5-18 μm Copper
GEM foil:– shaped to produce
high E field→ high local e- multiplication
III/31Particle Physics Detectors, 2010 Stephan Eisenhardt
GEM - Gain and Rates
GEM + MSGC:
Double-GEM + PCB:– very high rate: 5·107 /cm2 s– reasonable gain: > 104
III/32Particle Physics Detectors, 2010 Stephan Eisenhardt
GEM+MSGCExample: HERA-B experiment
– 184 chambers of area 25x25 cm2
– particle flux 2-25 kHz/mm2
(outer-inner part)– radiation: 1Mrad/year
III/33Particle Physics Detectors, 2010 Stephan Eisenhardt