Bethe-Bloch formula

Gaseous detectors Detector concepts for HEP

High Energy Physics school in Egypt , Cairo -November 2010 G. Iaselli

Bethe-Bloch formula

Bethe-Bloch formula





Cluster of electronsCluster of electrons



Primary ionization



Total ionization



The collection of these electrons on an appropriate electrode produces our signal. To drive the electrons towards the electrode an electric field is needed!

Anode

Cathode

Drift and Diffusion Drift and Diffusion



Drift and Diffusion of electron in gases Drift and Diffusion of electron in gases



Low electric field. Ionization regionNumber of electrons is independent on the applied field

Low electric field. Ionization regionNumber of electrons is independent on the applied field

If the electric field is too low, there is recombination between ions

If the electric field is too low, there is recombination between ions



R

d - q

cathode

anodesignal

-Vox

x

A charge q at a distance x from the anode has U=qV(x)

For a displacement of dx U=qV(x+dx)-qV(x)=qEdx

should be compensated from the power supply energy V0idt=V0dq

qEdx=V0idt

i=q(v/d) i is the current signal

A charge q at a distance x from the anode has U=qV(x)

For a displacement of dx U=qV(x+dx)-qV(x)=qEdx

should be compensated from the power supply energy V0idt=V0dq

qEdx=V0idt

i=q(v/d) i is the current signal

Constant electric filed E=V0/dConstant electric filed E=V0/d

Ionization chambersIonization chambers

ii



d-

--

+

++

t

i(t)

R1

R2

C2

C1

-HV

A

If R2C2 e R2C1 small in comparison to t = d/v

Current signal on R2

Q is the charge induced on the electrode

If R2C2 e R2C1 small in comparison to t = d/v

Current signal on R2

Q is the charge induced on the electrode

We neglect the signal due to positive ions because they arrive much laterWe neglect the signal due to positive ions because they arrive much later

If more clusters at different x, add all the contributions

Q(t)=q0

If more clusters at different x, add all the contributions

Q(t)=q0



E

Anode

Cathode1 cm of Argon produces about 100 electrons. Very small signal to detect. Amplification is needed!!!

1 cm of Argon produces about 100 electrons. Very small signal to detect. Amplification is needed!!!

Increase the electric field so that each primary electron is accelerated and gets enough energy to produce other ionizations

Increase the electric field so that each primary electron is accelerated and gets enough energy to produce other ionizations

= Townsend coefficient = Townsend coefficient

1

1 Average free pathxEenxn )(

0)( xEenxn )(0)(

d



• Limited proportional M < 108

• Streamer 108 < M <1010

• Geiger M >1010

• Limited proportional M < 108

• Streamer 108 < M <1010

• Geiger M >1010



GainGain

Korff relation Korff relation

ddxx

n

nM

00

)(exp

ddxx

n

nM

00

)(exp

E

Bp

Aep

E

Bp

Aep



a

b

r

E

1/r

a

cathode

anode

gas

Ethreshold

a

rCVrV

r

CVrE

ln2

)(

1

2

0

0

0

0

C = capacitance / unit length

Proportional regionCollected charge proportional to initial ionization

Proportional regionCollected charge proportional to initial ionization

6

0

10n

nM 6

0

10n

nM

The cylindrical geometry is suitable to easily achieve high electric fields a = 8 10-5 mb= 10-2 mHV =500 V

E = 5 104 V/m

The cylindrical geometry is suitable to easily achieve high electric fields a = 8 10-5 mb= 10-2 mHV =500 V

E = 5 104 V/m



Avalanche

It develops close to central electrode at a radius of 4 10-4 m

Avalanche

It develops close to central electrode at a radius of 4 10-4 m



Wire proportional chamberWire proportional chamber

a= 10 mm, b=10 mm r’=a +1 mm

The induced signal is due to positive ions

a= 10 mm, b=10 mm r’=a +1 mm

The induced signal is due to positive ions

2a

b

anode

cathode

R

+V0



Cylindrical geometry is not the only one able to generate strong electric fieldCylindrical geometry is not the only one able to generate strong electric field



Noble gases emits photons if excited (argon emits 11.6 eV photons).

Threshold energy for metal ionization is lower (e.g. Cu 7.7 eV)

Noble gases emits photons if excited (argon emits 11.6 eV photons).

Threshold energy for metal ionization is lower (e.g. Cu 7.7 eV)

QuenchersThe addition of polyatomic gases ( CH4,C4H10, ethane, CO2, BF3) is needed to absorb photons

QuenchersThe addition of polyatomic gases ( CH4,C4H10, ethane, CO2, BF3) is needed to absorb photons

Already important in the proportional regime.Already important in the proportional regime.



In 1968 Charpak proposed the first Multi Wire Proportional Chamber (MWPC)

In an array of anodic tightly spaced wires, each is like a proportional counter.

In 1968 Charpak proposed the first Multi Wire Proportional Chamber (MWPC)

In an array of anodic tightly spaced wires, each is like a proportional counter.

Typical parameters:L = 5 mm, d = 1÷2 mm, Rwire~ 20 m

Typical parameters:L = 5 mm, d = 1÷2 mm, Rwire~ 20 m

field lines and equipotentials around anode wires

The position of the particle can be definedThe position of the particle can be defined



Anode Cathode

(V=0)

Cathode (V=0)

Far from the anode the field is uniform.Each wire work as a ”proportional chamber”

Far from the anode the field is uniform.Each wire work as a ”proportional chamber”

d

L

x

yC is the capacity per unit length C is the capacity per unit length

da

dL

C ln

2

da

dL

C ln

2

a = wire radiusa = wire radius



However for inclined tracks , more wires may be involvedHowever for inclined tracks , more wires may be involved

Ls

Different signal are generated but in different times. Our interest is for the first.

Therefore we can:• Set the gate of reading electronic system to

accept only the fast signals;• Introduce a percentage of electronegative gas to

stop the electrons generated far from anode.

Different signal are generated but in different times. Our interest is for the first.

Therefore we can:• Set the gate of reading electronic system to

accept only the fast signals;• Introduce a percentage of electronegative gas to

stop the electrons generated far from anode.



y

L

QBQA

track

%4.0 toup

L

y

QQ

Q

L

y

BA

B

Two coordinatesTwo coordinates

Double layer of wiresDouble layer of wiresCharge division Charge division

Time difference Time difference



The cathode is segmented in strips where a signal is induced. If each strip is at the coordinate zi , the center o gravity is:

The cathode is segmented in strips where a signal is induced. If each strip is at the coordinate zi , the center o gravity is:

i

ii

q

zqz

i

ii

q

zqz

The cathode strip chambersThe cathode strip chambers



The avalanche around an anode wire creates an induced charge distribution on the cathode, with a FWHM roughly 1.5 times the anode to cathode distance.

The CMS designThe CMS design



The CMS CSCThe CMS CSC

~ 70 m ~ 70 m



Drift ChamberDrift Chamber

Measure arrival time of electrons at sense wire relative to a time t0.

anode

TDCStartStop

DELAYscintillator

drift

low field region drift

high field region gas amplification

dttvx D )(

x



Advantage of drift chamber with respect to MWPCEasier mechanical construction (higher distance between wires)Lower number of wire less complex electronic (but more expansive)Higher precision (no more limited by the wire distance)

Advantage of drift chamber with respect to MWPCEasier mechanical construction (higher distance between wires)Lower number of wire less complex electronic (but more expansive)Higher precision (no more limited by the wire distance)

Fundamental parameters

Optimize geometry to have E constant

Gas which allow constant drift velocity Vd

(Vd ~ 50 mm/s in Argon-Isobutene 75%-25% and E~700-800V/cm)

Fundamental parameters

Optimize geometry to have E constant

Gas which allow constant drift velocity Vd

(Vd ~ 50 mm/s in Argon-Isobutene 75%-25% and E~700-800V/cm)

Introduce field wires Introduce field wires



Resolution determined by• diffusion, • path fluctuations, • electronics • primary ionization

statistics

Resolution determined by• diffusion, • path fluctuations, • electronics • primary ionization

statistics

sense field

Resolution is better for tracks passing at larger distance from the sense wire… but at very large distance the diffusion enter in the game

Resolution is better for tracks passing at larger distance from the sense wire… but at very large distance the diffusion enter in the game



Resolution determined by primary ionization statistics

Resolution determined by primary ionization statistics



Transverse diffusion substantially reduced in some gases if E || BTransverse diffusion substantially reduced in some gases if E || B



The CMS drift chamberThe CMS drift chamber



TPC (Time Projection Chamber)TPC (Time Projection Chamber)

Small quantity of material (only gas). Multiple-scattering and photon conversion is minimized

Small quantity of material (only gas). Multiple-scattering and photon conversion is minimized

B

Central electrode (≈ -50kV)gas

Read out plane

Anode wires

Cathode padsz

y

x

Z coordinates measured by the drift time

X and Y measured on anode wires and cathode pads

Z coordinates measured by the drift time

X and Y measured on anode wires and cathode pads

MWPCMWPC



y

z

x

E

B drift

chargedtrack

wire chamber to detect projected tracks

gas volume with E & B fields



•The TPC allows to determine a point in the space ( x,y,z)

•The analog signal on the anode measures dE/dx

•E//B drift velocity parallel to E e B. Diffusion perpendicular to E is reduced. Electron move around B with a radius of about 1 mm (E ~ 50KV e B ~1.5 T )

Requirements:•To measure Z is necessary a good knowledge of Vd

•Laser Calibration and correction for pressure and temperature needed

•Very clean gas

Aleph TPC L = 4.4 m, Diameter = 3.6 m,

•The TPC allows to determine a point in the space ( x,y,z)

•The analog signal on the anode measures dE/dx

•E//B drift velocity parallel to E e B. Diffusion perpendicular to E is reduced. Electron move around B with a radius of about 1 mm (E ~ 50KV e B ~1.5 T )

Requirements:•To measure Z is necessary a good knowledge of Vd

•Laser Calibration and correction for pressure and temperature needed

•Very clean gas

Aleph TPC L = 4.4 m, Diameter = 3.6 m,



Aleph TPCAleph TPC



MWPC limitationMWPC limitation

Rate (mm -1 s-1)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

103 104 105 106 107 108

Rel

ativ

e ga

in

MWPC

MWPC Gain-Rate

Wire spacing: 1-2 mm

Rate capability: limited by space chargeRate capability: limited by space charge



Thin metal-coated polymer foil chemically pierced by a high density of holes.On application of a voltage gradient, electrons released on the top side drift into the hole, multiply in avalanche and transfer the other side.Proportional gains above 103 are obtained in most common gases.

Thin metal-coated polymer foil chemically pierced by a high density of holes.On application of a voltage gradient, electrons released on the top side drift into the hole, multiply in avalanche and transfer the other side.Proportional gains above 103 are obtained in most common gases.

70 µm

Gas Electron Multiplier (GEM)Gas Electron Multiplier (GEM)





Basic principlesBasic principles



Basic GEM DetectorBasic GEM Detector

PATTERNEDREADOUT BOARD

1 mm

3 mm DRIFT

INDUCTION

MULTIPLICATION

-VD

-VTOP

-VBOT

VGEM

- Readout separated from multiplying electrodes- Multiple cascaded structures possible (large

gains, feedback suppression)- Cheap and reliable

- Readout separated from multiplying electrodes- Multiple cascaded structures possible (large

gains, feedback suppression)- Cheap and reliable



FAST ELECTRON SIGNAL

No positive ion tail: very good multi-track and time resolutionNo positive ion tail: very good multi-track and time resolution

S1 S2 S3 S4

Induction gap

e-

e-

I+Ar-CO2 70-30



Single GEM + readout padsSingle GEM + readout pads



Double GEM + readout pads

Same gain at lower voltage

Less discharges

Double GEM + readout pads

Same gain at lower voltage

Less discharges



SPACE RESOLUTION~ 40 µm rmsCLUSTER SIZE ~ 500 µm FWHM

SPACE RESOLUTION~ 40 µm rmsCLUSTER SIZE ~ 500 µm FWHM

A. Bressan et al, Nucl. Instr. And Meth. A425(1999)262

EFFICIENCY FOR MINIMUM IONIZING PARTICLES3 mm gap

EFFICIENCY FOR MINIMUM IONIZING PARTICLES3 mm gap





Saturated avalanche

•Increase the gain up to 107

•Better signal •No need for amplification

But

•Only position measurement •dE/dx no possible

Saturated avalanche

•Increase the gain up to 107

•Better signal •No need for amplification

But

•Only position measurement •dE/dx no possible

A small quantity of electronegative gas (freon ) is needed to reduce the number of electrons in the avalanche

A small quantity of electronegative gas (freon ) is needed to reduce the number of electrons in the avalanche



Streamer mode - Geiger mode

Gain > to 108

Streamer mode - Geiger mode

Gain > to 108

AvalancheAvalanchestreamerstreamer spar

kspark



StreamerWhen the gain is greater then 10 8 (Raether limit)

•The electron spatial charge produce a decrease of the electric field• Recombination e- -positive ions• Production of ultraviolet photons• Production of secondary avalanches from these photons

StreamerWhen the gain is greater then 10 8 (Raether limit)

•The electron spatial charge produce a decrease of the electric field• Recombination e- -positive ions• Production of ultraviolet photons• Production of secondary avalanches from these photons

E~0 , e-~108E~0 , e-~108



A modern deviceA modern device

Geiger –Muller counter in the Fermi laboratory

Geiger –Muller counter in the Fermi laboratory

A Geiger-Mueller (GM) tube is a gas-filled radiation detector. It commonly takes the form of a cylindrical outer shell (cathode) and the sealed gas-filled space with a thin central wire of about 30 m (the anode) held at ~ 1 KV positive voltage with respect to the cathode.

The fill gas is generally argon at a pressure of less than 0.l atm plus a small quantity of a quenching vapor.

A Geiger-Mueller (GM) tube is a gas-filled radiation detector. It commonly takes the form of a cylindrical outer shell (cathode) and the sealed gas-filled space with a thin central wire of about 30 m (the anode) held at ~ 1 KV positive voltage with respect to the cathode.

The fill gas is generally argon at a pressure of less than 0.l atm plus a small quantity of a quenching vapor.

The Geiger counter detects some or all of the four major types of ionizing radiation, namely Alpha, Beta, Gamma, and X-rays.

The Geiger counter detects some or all of the four major types of ionizing radiation, namely Alpha, Beta, Gamma, and X-rays.



Collisions with the fill gas produce excited states (~11.6eV) that decay with the emission of a UV photon and electron-ion pairs (~26.4 eV for argon). The new electrons, plus the original, are accelerated to produce a cascade of ionization called "gas multiplication" or a Townsend avalanche. The multiplication factor for one avalanche is typically 106 to 108.

Collisions with the fill gas produce excited states (~11.6eV) that decay with the emission of a UV photon and electron-ion pairs (~26.4 eV for argon). The new electrons, plus the original, are accelerated to produce a cascade of ionization called "gas multiplication" or a Townsend avalanche. The multiplication factor for one avalanche is typically 106 to 108.



anode

cathode

R

+V0

The anode is supplied through a high R so that its voltage is under threshold for the Geiger mode during the discharge.

The RC constant should ensure that the detectotor is under threshold during the time the ions take to reach the cathode = milliseconds low rate

The anode is supplied through a high R so that its voltage is under threshold for the Geiger mode during the discharge.

The RC constant should ensure that the detectotor is under threshold during the time the ions take to reach the cathode = milliseconds low rate

Also: resistive quenchingAlso: resistive quenching

The full wire is interested in the discharge process Only “courting rate” is possible

The full wire is interested in the discharge process Only “courting rate” is possible



By adding a higher percentage of quencher, the discharge can be limited to only a small portion of the wire

Wire diameter: ~ 50÷100 mmGas mixture: ≤ 60% Argon , ≥ 40% Isobutene, few % Freon Wire voltage: ~5 KV

Wire diameter: ~ 50÷100 mmGas mixture: ≤ 60% Argon , ≥ 40% Isobutene, few % Freon Wire voltage: ~5 KV

Sense wireSense wire

Cathode (graphite coating)Cathode (graphite coating)

PVC cellPVC cell

External read-out stripExternal read-out strip

Streamer tubesStreamer tubes

Cathode must be resistiveCathode must be resistive

The internal graphite coating of the cathode has a resistivity of about .2-.5 M /cm This also ensure a self quenching mechanism in side the tube only a portion of the wire is interested by the discharge

The internal graphite coating of the cathode has a resistivity of about .2-.5 M /cm This also ensure a self quenching mechanism in side the tube only a portion of the wire is interested by the discharge



mm12

10 mm

12

10

Streamer tubesStreamer tubes

•Analog read out on the wire•Digital readout on the strip

If he strip is perpendicular to the wire, X–Y measurement is possible

•Analog read out on the wire•Digital readout on the strip

If he strip is perpendicular to the wire, X–Y measurement is possible

Time resolution 100 ns

spatial resolution 1 cm/sqrt12

Efficiency 90% , 10 % dear area

rate capability 100 Hz/cm2

Time resolution 100 ns

spatial resolution 1 cm/sqrt12

Efficiency 90% , 10 % dear area

rate capability 100 Hz/cm2



• 10 planes of streamer tubes (total of 50000 tubes)

• Gas mixture He (73%) and n-pentane (27%)

= 0.2°

• 10 planes of streamer tubes (total of 50000 tubes)

• Gas mixture He (73%) and n-pentane (27%)

= 0.2°

Macro Search for Up going muons,

A multiple event



Used in many experiments:

calorimetry:

Charm II (CERN, SPS)

ALEPH (LEP, CERN)

DELPHI (LEP, CERN)

OPAL (LEP, CERN)

detection

UA1, (CERN)

ZEUS (HERA)

Used in many experiments:

calorimetry:

Charm II (CERN, SPS)

ALEPH (LEP, CERN)

DELPHI (LEP, CERN)

OPAL (LEP, CERN)

detection

UA1, (CERN)

ZEUS (HERA)Streamer tubes have been extensively used also for hadron calorimetric measurement

Streamer tubes have been extensively used also for hadron calorimetric measurement

Principle: numbers of hit proportional to the shower density

Principle: numbers of hit proportional to the shower density



HCAL:23 layer iron/streamer tube sandwich with total thickness of 120 cm of iron (the magnet return yoke)

HCAL:23 layer iron/streamer tube sandwich with total thickness of 120 cm of iron (the magnet return yoke)

The muon chambers are made of two layers (X-Y) of streamer tubesThe muon chambers are made of two layers (X-Y) of streamer tubes

ALEPH



Event with two muons Event with two muons Event with a muons and hadronic showers Event with a muons and hadronic showers



New challenge: improve time resolution with planar geometry

No wires, distance between electrode 1-2 mm. High electrical fied





















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Bethe-Bloch formula