F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 1 TITLE RADIATION DETECTION AND MEASUREMENT Prof. Glenn Knoll, organizer Short Courses November 10-11 2002

F. Sauli-Short Courses-IEEE-NSS 2002-PART 1

1

TITLE

RADIATION DETECTION AND MEASUREMENTProf. Glenn Knoll, organizerShort Courses November 10-112002 IEEE NSS/MICNorfolk, November 10-16, 2002


2

INTRODUCTION

PARALLELPLATE

COUTER

MULTIWIREPROPORTIONAL

CHAMBER

TIME PROJECTION

CHAMBER

DRIFTCHAMBERS

CHERENKOVRING

IMAGING

STREAMERTUBES

STRAWS

PESTOVCOUNTER

RESISTIVEPLATE

CHAMBERS

AVALANCHECHAMBERS

MICROSTRIPCHAMBERS

MICROWELL

MICROGAP

COMPTEURA

TROUS

GASELECTRONMULTIPLIER

MICROMEGAS

TRANSITIONRADIATIONTRACKER

GASEOUS DETECTORS’FAMILY TREE

PROPORTIONALCOUNTER


3

PART 1

IONIZATIONDRIFT AND DIFFUSIONCAPTURE LOSSESAVALANCHE MULTIPLICATION


4

IONIZATION

PRIMARY IONIZATION: ELECTRON-ION PAIRS

COULOMB INTERACTIONS OF CHARGED PARTICLES WITH MOLECULES

Minimum ionizing particles:

Argon DME

n (ion pairs/ cm) 25 55dE/ dx (keV/ cm)

GAS (STP)

2.4 3.9

Xenon

6.7

44

CH4

1.5

16

Pkn nk

k!e

n

Statistics of primary ionization:

Poisson: n: averagek: actual number

(Maximum) detection efficiency:

1 e n thickness

Argon

GAS (STP)

1 mm 91.82 mm 99.3

Helium

0.32

6

Helium 1 mm 452 mm 70


5

IONIZATION

SECONDARY AND TOTAL IONIZATIONCLUSTERS AND DELTA ELECTRONS:

N: total ion-electron pairs nN

~ 3_

CLUSTER SIZE DISTRIBUTION:

P(m) ~W

m2

H. Fischle et al, Nucl. Instr. and Meth. A301(1991)202

Argon DME

n (ion pairs/cm)cm) 25 55

GAS (STP) Xenon

44

CH416

N (ion pairs/cm) 90 160300 53

Helium

6

8


6

IONIZATION

CONSEQUENCES OF ENERGY LOSS STATISTICSLANDAU DISTRIBUTION OF ENERGY LOSS:

For a Gaussian distribution: N ~ 21 i.p.FWHM ~ 50 i.p.

00 500 1000

6000

4000

2000

N (i.p.)

Counts4 cm Ar-CH4 (95-5)5 bars

N = 460 i.p. PARTICLE IDENTIFICATION Requires statistical analysis of hundreds of samples

0 500 1000

6000

4000

2000

N (i.p)

Counts

0

protons electrons

15 GeV/c

I. Lehraus et al, Phys. Scripta 23(1981)727

FWHM~250 i.p.


7

IONIZATION

LOCALIZATION ACCURACY IN DRIFT CHAMBERSWORSENED BY LONG-RANGE ELECTRONS:

Drift Time

5% of events!

F. Sauli, Nucl. Instr. and Meth. 156(1978)147


8

IONIZATION

STRONG ANGULAR DEPENDENCE OF POSITION ACCURACY

G. Charpak et al, Nucl. Instr. and Meth. 167 (1979) 455

Position accuracy as a function of the track angle to the normal to the chamber:

CENTER OF GRAVITY OF INDUCED CHARGE READOUT


9

IONIZATION

F. Van den Berg et al, Nucl. Instr. and Meth. A349 (1994) 438

ANGULAR DEPENDENCE OF POSITION ACCURACY IN MICRO-STRIP CHAMBERS:


10

IONIZATION

DECLUSTERING EFFECT IN TIME PROJECTION CHAMBERS:

α

β

Data: D. Decamp et al, Nucl. Instr. and Meth. A269(1990)121 Simulation: A. Sharma, CERN

Drift

B offset

B=1.5 T


11

IONIZATION

LIMITED TIME RESOLUTION OF WIRE AND MICROPATTERN CHAMBERS:

50 ip/cm

25 ip/cm

3 ns6 ns

Time (ns)0 5 10 2015

A1n(t)

50

40

30

20

10

0

Space distribution of the cluster closer to an electrode:

Time distribution of the cluster closer to an electrode:

€

A1n(x)=ne−nx

€

A1n(t)=ne−nwt

w: drift velocity

w = 5 cm/µs


12

IONIZATION

PARALLEL PLATE CHAMBERS: SUB-NANOSECOND RESOLUTION

FAST SIGNAL INDUCTION DURING AVALANCHE DEVELOPMENT:

Useful gap

R. Arnaldi et al, Nucl. Phys. B 78(1999)84


13

DRIFT

ELECTRIC FIELD E = 0: THERMAL DIFFUSION

ELECTRIC FIELD E > 0: CHARGE TRANSPORT AND DIFFUSION

E

IONS ELECTRONS

DRIFT AND DIFFUSION OF CHARGES IN GASES


14

DRIFT

DRIFT AND DIFFUSION OF IONS (CLASSIC KINETIC THEORY OF GASES)

Ions remain thermal up to very high fieldsMaxwell energy distribution:

Average (thermal) energy:

€

εT =KT ≈0.025eV

€

F(ε)=C ε e−

εKT

Diffusion equationFraction of ions at distance x after time t:

€

dNN

=14Dt

e−

x2

4Dt dx D: diffusion coefficient

RMS of linear diffusion:

€

σ x = 2Dt

Molecules diffuse rapidly in the available volume(leaks!)


15

DRIFT

IONS DRIFT VELOCITY

(Almost) linear function of field

Mobility:

€

μ+ =w+ E

~ constant for a given gas (at fixed P and T)

IONS DIFFUSION (Einstein’s law):

€

Dμ

=KTe

€

σx=2KT

exE

€

σ x = 2Dt

Same for all ions!

E. McDaniel and E. MasonThe mobility and diffusion of ions in gases (Wiley 1973)

GAS ION µ+ (cm2 V-1 s-1) @STP

Ar Ar+ 1.51CH4 CH4

+ 2.26

Ar-CH4 80-20 CH4+ 1.61

MWPC: 1 cm gap, Ar-CH4, 5 kV/cm

Total ions drift time T+ ~ 120 µs

TPC: 1 m drift, Ar-CH4, 200 V/cm

Total ions drift time T+ ~ 300 ms


16

DRIFT

DRIFT AND DIFFUSION OF ELECTRONS IN GASES

Electron Swarm Drift

ElectricField

s, tDrift velocity:

€

w=ΔsΔ t

s

Space diffusion rms:

€

σ = 2Dt = 2Dsw

Drift velocity and diffusion are gas and field dependent:

€

w=wEP

⎛

⎝ ⎜

⎞

⎠ ⎟ P : pressure

Townsend expression:

€

w=e

2mE τ : mean collision time

€

D =gEP

⎛

⎝ ⎜

⎞

⎠ ⎟

€

σ =1P

FEP

⎛

⎝ ⎜

⎞

⎠ ⎟

€

σx =σ1 x


17

DRIFT

LARGE RANGE OF DRIFT VELOCITIES AND DIFFUSIONS

DRIFT VELOCITY: DIFFUSION:


18

DRIFT

ELECTRON TRANSPORT THEORY BALANCE BETWEEN ENERGY ACQUIRED FROM THE FIELD AND COLLISION LOSSES

Energy distribution probability:

€

Λ(ε)

€

le(ε)=1

N σ (ε)

Fractional energy loss in collisions

Mean free path between collisions

: electron-molecule cross section)

€

w=23

em

E ε∫ le(ε)∂

F0(ε)ν

∂εdε

€

v=2εm

Drift velocity:

Diffusion coefficient:

€

D =le(ε)3

∫ vF0(ε) dε Frost and Phelps, Phys. Rev. 127(1962)1621V. Palladino and B. Sadoulet, Nucl. Instr. and Meth. 128(1975)323G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413S. Biagi, Nucl. Instr. and Meth. A283(1989)716


19

DRIFT

CHARGE TRANSPORT DETERMINED BY ELECTRON-MOLECULE CROSS SECTION:

http://consult.cern.ch/writeup/magboltz/cross/

S. Biagi, Nucl. Instr. and Meth. A421 (1999) 234

http://cpa94.ups-tlse.fr/operations/operation_03/POSTERS/BOLSIG/

MAGBOLTZ


20

DRIFT

COMPUTED DRIFT VELOCITY IN MIXTURES

http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec


21

DRIFT

Lon

gitu

dina

l diff

usio

n (

µm

for

1 c

m d

rift)

Tra

nsve

rse

diff

usio

n (

µm

for

1 c

m d

rift

)

LONGITUDINAL DIFFUSION (// E)

DriftE Field

T

L

http://consult.cern.ch/writeup/garfield/examples/gas/Welcome.html

SMALLER THAN TRANSVERSE DIFFUSION:

LONGITUDINAL DIFFUSION: TRANSVERSE DIFFUSION:


22

DRIFT

DRIFT TIME ACCURACY: DEPENDS ON IONIZATION DENSITY

Drift

Anode Wire

L

Single electron Several electrons Many electrons

Detection threshold

Error on first electron electron: N=100 1~ 0.4 L

€

σ1 ~π

2 3lnNσ L

RESOLUTION LIMITS OF DRIFT TUBES:G. Scherberger et al, Nucl. Instr. and Meth. A424(1999)495W. Riegler et al, Nucl. Instr. and Meth. A443(2000)156


23

DRIFT

EFFECTS OF MAGNETIC FIELD rB

rE

θΒ

rwB

rE

rB

θΒwB

THE SWARM IS ROTATED BY AN ANGLE θB

IN THE PLANE PERPENDICULAR TO E AND B THE MAGNETIC DRIFT VELOCITY IS wB w0

THE TRANSVERSE DIFFUSION IS REDUCED

€

r E

€

r B

€

r E

€

r B

//

€

tanθB =ωτ

€

wB =EB

ωτ

1+ω2τ2

€

wB =w0

€

σL =σ0

€

σT =σ0

1+ω2τ2

: mean collision time

€

ω=eB/m Larmor frequency

rB

L

T

wB

€

r E


24

DRIFT

DRIFT IN MAGNETIC FIELD: SIMPLE MODEL:

€

τ =τ0

€

τ0 =2mw0

eE


25

DRIFT

0

100

200

300

400

500

600

700

800

102 103 104 105

Diffusion for 1 cm (µm)

E (V/cm)

P10 diffusion vs mag field log bis

T( =0)B

L

T( =2.5 )B T

T( =5 )B T

- 90-10Argon Methane

DRIFT MULTIPLICATION

0

200

400

600

800

1000

102 103 104 105

T

for 1 cm (µm)

E (V/cm)

Ar

Ar-CH4 90-10

Ar-CO2 90-10

Ar-CO2 70-30

CO2

transv diff gases bis

DRIFT MULTIPLICATION

TRANSVERSE DIFFUSION IN SEVERAL GASES

REDUCTION IN MAGNETIC FIELD // E


26

DRIFT

COMPUTED FROM TRANSPORT THEORY (MAGBOLTZ)


27

DRIFT

MAGNETIC FIELD EFFECTS:DISTORSIONS IN DRIFT CHAMBERS

W. de Boer et al, Nucl. Instr. and Meth. 156(1978)249


28

DRIFT

MAGNETIC FIELD EFFECT:COORDINATE DISTORSIONS IN MICRO-STRIP CHAMBERS

F. Angelini et al, Nucl. Instr. and Meth. A347(1994)441


29

DRIFT

TRANSVERSE DIFFUSION: SUBSTANTIALLY REDUCED IN SOME GASES

TIME PROJECTION CHAMBER: Center-of-gravity of cathode signal

B=0 B>0

€

r E

€

r B //

D. Nygren, TPC proposal (PEP4, 1976)


30

DRIFT

STABILITY OF OPERATION VOLTAGE AND PRESSURE

THE DRIFT VELOCITY IS A FUNCTION OF REDUCED FIELD E/P

€

EP

€

w=fEP

⎛

⎝ ⎜

⎞

⎠ ⎟

DRIFT VELOCITY SATURATION:INSENSITIVE TO VARIATIONS OF E AND P


31

DRIFT

STABILITY OF OPERATION TEMPERATURE

AT LOW FIELDS (THERMAL ELECTRONS):

€

Δww

=ΔTT

≅3.410−3

oC

G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413

At high fields, the thermal coefficient in some gases decreases and even becomes negative:

100 500 1000

0

-1

1

2

3

4

2000E (V/cm)

A

CO2

Methylal

C4H10

CH4

A-C4H10-Methylal 66-30-4

w/w/ºC


32

CAPTURE

ELECTRON CAPTURE LOSSES ON ELECTRONEGATIVE GASES

The attachment cross section is energy-dependent, therefore strongly depends on the gas composition and electric field

Attachmant coefficient of oxygen:

Electrons surviving after 20 cm drift (E = 200 V/cm):


33

CAPTURE

ELECTRON CAPTURE - VERY SENSITIVITE TO GAS MIXTURE

ARGON-ETHANE 50-50

DIMETHYLETHER

R. Openshaw, TRIUMF (private, 2000)

5.9 keV X-rays “Hot” gas

“Cold” gas

Energy resolution of a proportional counter with two gas fillings (and some leaks!):


34

DRIFT

USE OF CF4 AS QUENCHER REPLACING CH4 IN TPCs

- FAST DRIFT VELOCITY- SMALL DIFFUSION- NO HYDROGEN (REDUCED NEUTRON SENSITIVITY)- NON-FLAMMABLE

L. G. Christophorou et al, Nucl. Instr. and Meth.163(1979)141


35

CAPTURE

ELECTRON CROSS SECTIONS IN CF4

http://consult.cern.ch/writeup/magboltz/cross/


36

MULTIPLICATION

INCREASING THE FIELD TOWARDS CHARGE MULTIPLICATION

IONIZATION 15.7 eV

EXCITATION 11.6 eV

0 5 10 15 20 25 30

Excitation10.5 eV

Ionization15.5 eV

Electron energy (eV)

0.2 kV/cm

1 kV/cm5 kV/cm

Electrons energy distribution at increasing fields:


37

MULTIPLICATION

IONIZATION CROSS SECTIONAND TOWNSEND COEFFICIENT Mean free path for ionization

€

λ =1

NσN: molecules/cm3

Townsend coefficient

€

α =1λ

Ionizing collisions/cm

S.C. Brown, basic data of plasma physics (MIT press, 1959)


38

MULTIPLICATION

AVALANCHE MULTIPLICATION IN UNIFORM FIELD

€

n(x) =n0eα x

Multiplication factor or Gain

€

dn=nαdx

€

M(x) =nn0

=eα x

E x

Ions

Electrons

Combined cloud chamber-avalanche chamber:

H. RaetherElectron avalanches and breakdown in gases(Butterworth 1964)


39

MULTIPLICATION

MEASUREMENT OF THE TOWNSEND COEFFICIENT

Radiation

V

I

Current vs voltage for constant charge injection in a parallel plate counter:

1

M

€

α =lnM

s

s


40

MULTIPLICATION

A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420

TOWNSEND COEFFICIENT IN GAS MIXTURESARGON-CH4:

in Argon


41

MULTIPLICATION

PARALLEL PLATE COUNTERS:

+Q

-Q

-Q

+Q

-Q

-Q

A charge +Q between two conductors induces two negative charge profiles(image charge)

Moving the charge modifies the induced charge profile on the conductors and generates detectable signals

+Q towards an electrode: positive induced signal

Induced signals are equal and opposite on anode and cathode

SIGNAL DEVELOPMENT


42

MULTIPLICATION

ANODE

CATHODE

s0

s+Q

V=0

V= -V0

Charge induced on each electrode by +Q moving through the difference of potential dV:

PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE COLLECTION ONLY)

Integrating over s (or time t):

€

dq=QdVV0

=Qdss0

€

q(s)=Qs0

s q(t)=Qs0

wt w: drift velocity

Single charge +Q:

Electrons- ion pair (-Q and +Q) released at the same distance s from the cathode :

€

q(t)=Qw−ts0

+w+ts0

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ 0≤t ≤T−

€

q(t)=Qs−s0

s0+

w+ts0

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ T−≤t ≤T+

w- (w+ ) : electron (ion) drift velocity

T- (T+ ) : total electron (ion) drift time

Total signal:

€

q(T+)=Q

(+Q on cathode , -Q on anode)

€

q(t)

€

t

€

Qs0 −s

s0

€

Q

€

T−

€

T+


43

MULTIPLICATION

PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION)

During the avalanche development, the increase in the number of charges after a path ds is:

and the total after a path s:

The incremental charge induction due to electrons after a path s:

Integrating over s:

€

dn=nαds

€

n=n0eαs

€

dq−=−en0eαsds

s0

€

q−(s)=en0αs0

(eαs −1)≈en0αs0

eαs =en0αs0

eαw−t

and the corresponding current :

€

i−(t)=dq−

dt=

en0w−

s0eαw−t =

en0T− eαw−t

The current signal iduced by the ions is instead given by:

€

i+(t)=en0T+ eαw−t −eαw*t⎛

⎝ ⎜

⎞ ⎠ ⎟ 0≤t ≤T−

€

i+(t)=en0T+ eαs−eαw*t⎛

⎝ ⎜

⎞ ⎠ ⎟ T−≤t ≤T+

€

1

w* =1

w++1

w−

s0

s

-V0

0


44

MULTIPLICATION

PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION)

Fas electron signal

Slow ion tail


45

MULTIPLICATION

WIRE PROPORTIONAL COUNTERS:

+

+

-

+

-

+

+

+

+

+

+

Thin anode wire coaxial with cathode

Electric field:Cathode radius b

Anode radius a

€

E(r)=CV0

2πε0

1r

€

C =2πε0

ln b a( )

Avalanche development around a thin wire:

SIGNAL DEVELOPMENT


46

MULTIPLICATION

ln M

Voltage

Attachment

Collection

Multiplication

Streamer

PROPORTIONAL COUNTERS: GAIN CHARACTERISTICS

Breakdown

IONIZATION CHAMBER

PROPORTIONAL COUNTER

Saturation

n1

n2


47

MULTIPLICATION

PROPORTIONAL COUNTERS: SIGNAL DEVELOPMENT

€

dQ=QV0

dV=QV0

dVdr

drIncremental charge induced by Q moving through dV:

Assuming that the total charge of the avalanche Q is produced at a (small) distance from the anode, the electron and ion contributions to the induced charge are:

€

q−=QV0

dVdra

a+λ∫ dr=−

QC2πε0

lna+λ

a

€

q+=QV0

dVdra+λ

b∫ dr=−

QC2πε0

lnb

a+λand

The total induced signal is

€

q=q−+q+=−QC2πε0

lnba

=−Q on the anode ( on the cathode)

€

+Q

The ratio of electron and ion contributions:

€

q−

q+ =ln(a+λ)−lnalnb−ln(a+λ)

For a counter with a=10µm, b=10 m: q-/q+ ~1% The electron-induced signal is negligible

Neglecting electrons, and assuming all ions leave from the wire surface:

€

q(t)=q+(t)=− dq=−QC2πε00

t∫ ln

r(t)a

€

drdt

=μ+E =μ+CV0

2πε0

1r

€

r(t) = a2 +μ+CV0

2πε0t

€

i(t)=−QC2πε0

1t0 +t

Total ions drift time:

€

T+=πε0(b2 −a2)

μ+CV0

q(T+) =−Q


48

MULTIPLICATION

0 20 40 60 80 100t (ns)

i(t)

CHARGE SIGNAL:

CURRENT SIGNAL:

0 0.2 0.4 0.6 0.8 1.0t (µs)

q(t) q(t)

0 100 200 300 400 500t (µs)

Q

T+

t (ns)

AMPLIFIER TIME CONSTANT;

0 100 200 300 400 500

q(t)

300 ns

100 ns

50 ns

Documents

F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 1 TITLE RADIATION DETECTION AND MEASUREMENT Prof. Glenn Knoll, organizer Short Courses November 10-11 2002