sauli principles

F. Sauli - Gas Detectors - KEK March 14, 2009

FUNDAMENTS - 1TITLE

PRINCIPLES OF GAS DETECTORS

Fabio SauliTERA Foundation

CERNCH-1211 Geneva Switzerland

Part 1: FundamentsPart 2: Detectors

[email protected] http://fabio.home.cern.ch/fabio/

http://gdd.web.cern.ch/GDD/


FUNDAMENTS - 2BASIC BIBLIOGRAPHY

D.H. Wilkinson: Ionization Chambers and Counters (Cambridge Univ. Press, 1950) S.A. Korff: Electron and Nuclear Counters (Van Nostrand, 1955)P. Rice-Evans: Spark, Streamer, Proportional and Drift Chambers (Richelieu, 1974)F. Sauli: Principles of Operation of Multiwire Proportional and Drift Chambers (CERN 77-09, 1977)Th. Ferbel, Editor: Techniques and Concepts of High-energy Physics (Plenum, 1983)R.C. Fernow: Introduction to Experimental Particle Physics (Cambridge Univ. Press, 1986)W.R. Leo: Techniques for Nuclear and Particle Physics Experiments (Springer, 1987)C. Fabjan and J. Pilcher, ed.: Instrumentation in Elementary Particle Physics (World Scientific, 1988)C.F.G. Delaney and E.C. Finch: Radiation Detectors (Clarendon Press, 1992) R. Gilmore: Single Particle Detection and Measurement (Taylor and Francis, 1992)F. Sauli, ed.: Instrumentation in High Energy Physics (World Scientific, 1992)K. Grupen: Particle Detectors (Cambridge Monographs on Part. Phys. 1996)K. Kleinknecht: Detectors for Particle Radiation (Cambridge Univ. Press 1998)G.F. Knoll: Radiation Detection and Measurements, 3d Ed. (Wiley, 2000)W. Blum, W. Riegler and L. Rolandi: Particle Detection with Drift Chambers, 2d Ed. (Springer 2008)


FUNDAMENTS - 3ENERGY LOSS

DIFFERENTIAL ENERGY LOSS OF CHARGED PARTICES (Z=1) IN MATERIALS:

Expressed in MeV g-1 cm2, the differential energy loss is equal within a factor of two for all materials (except H2):

(gcm 2 ) (g cm 3) l(cm)

dEd ~1.5MeVg 1 cm2

: density

SEE:Review of Particle Physics Physics Letters B 667(2008)1-1340

http://pdgLive.lbl.gov

dEd

1

dEdx


FUNDAMENTS - 4PHYSICAL PROPERTIES OF GASES

DIFFERENTIAL ENERGY LOSS, PRIMARY AND TOTAL IONIZATION FOR MINIMUM IONIZING, Z=1 PARTICLESNORMAL TEMPERATURE AND PRESSURE (NTP: 20°C, 1 ATMOSPHERE)

GAS Density g cm-2

EX eV

EI eV

WI eV

dE/dx keV cm-1

NP cm-1

NT cm-1

Ne 0.839 10-3 16.7 21.6 30 1.45 13 50 Ar 1.66 10-3 11.6 15.7 25 2.65 25 106 Xe 5.495 10-3 8.4 12.1 22 6.87 41 312 CH4 0.667 10-3 8.8 12.6 30 1.61 37 54 C2H6 1.26 8.2 11.5 26 2.91 48 112 i-C4H10 2.49 10-3 10.6 26 5.67 90 220 CO2 1.84 10-3 7 13.8 34 3.35 35 100 CF4 3.78 10-3 10 16 54 6.38 63 120

Z : atomic number ; A : atomic mass; : densityEx, Ei : first excitation and ionization potentialswi: average energy per ion pairnP , nT : primary and total ion pairs per cm

(From various sources)


FUNDAMENTS - 5PRIMARY IONIZATION

Minimum ionizing particles in argon NTP (nP: 25 cm-1)s (mm) (%)1 91.8 2 99.3

Distribution of the electron closest to an electrode:

A1n (t) ne nwt

A1n (x) ne nx

Coulomb interactions between the electric field of the particle and of the molecules of the medium produce electron-ion pairs.Multiple ionizing collisions follow Poisson’s statistics:

n: averagek: actual number

Pkn

n k

k!e n

1 P0n 1 e n

Detection efficiency:

Limit in time resolution of proportional counters: arrival at anode wire of the closest electron.

ELECTRON-ION PAIR PRODUCTION

w: drift velocity (~ 5 cm µs-1)


FUNDAMENTS - 6SECONDARY AND TOTAL IONIZATION

Primary electrons can further ionize the medium producing local electron-ion clusters. Occasionally, the primary electron has enough energy to produce a long trail (delta electron).

CLUSTER SIZE PROBABILITY IN ARGON

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

Total number of ion pairs:

For minimum ionizing particles in Argon: E = 2.4 keV/cm wi = 26 eV

nT ≈ 90 ion pairs/cm

The average ionization energy is about the same in all gases and does not depend from energy and type of particles.

E: energy loss

wi : average energy per ion pair

nT Ewi

nT

nP

3


FUNDAMENTS - 7ELECTRONS RANGE IN MATERIALS

Due to multiple scattering and ionizing collisions, the penetration of electrons in materials is shorter than the integrated range along the path; the practical range is the extrapolated thickness of material absorbing all the electrons.

Practical range

Integrated path

H. Kanter, Phys. Rev. 121(1961)461

R r

R : range in cm : density in µg cm-3

r = 10 E 1.7 r : practical range in µg cm-2

E : electron energy in keV

Fit to experimental data (light elements):


FUNDAMENTS - 8APPROXIMATE EXPRESSION FOR ELECTRON RANGE

2 keV

180 µm

A 2 keV delta electron in argon STP has a practical range of ~ 200 µm.

PRACTICAL ELECTRON RANGE IN GASES AT NTP

The asymmetry in released charge affects the localization accuracy in detectors exploiting the measurement of the center of gravity (Time projection Chambers):

REAL COG


FUNDAMENTS - 9HEED

CALCULATION OF PRIMARY IONIZATION AND ELECTRON RANGE

ELECTRON RANGE IN ARGON (STP): PRIMARY CLUSTERS PER cm (STP):

I. B. Smirnov, Nucl. Instr. and Meth. A554(2005)474

2 keV

HEED

140 µm

http://consult.cern.ch/writeup/heed/HEED:


FUNDAMENTS - 10IONIZATION STASTISTICS - 1

WIDE ENERGY LOSS SPREAD (LANDAU DISTRIBUTION) The statistics of the energy loss, with wide fluctuations and a long tail (due to delta electrons) requires statistical analysis of hundreds of samples for determination of the average (as done in Time Projection Chambers)

I. B. Smirnov, Nucl. Instr. and Meth. A554(2005)474


FUNDAMENTS - 11IONIZATION STATISTICS - 2

DRIFTCoordinate deduced from drift time:

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

The presence of long range delta electrons can substantially affect the localization accuracy:

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

CENTER OF GRAVITYCoordinate from cathode induced charge

~5%


FUNDAMENTS - 12ELECTRONS DRIFT AND DIFFUSION

DRIFT VELOCITY: DIFFUSION:

Drift velocity and diffusion of electrons vary in a wide range, depending the gas mixture:

x 2KTe

xE

1.5 mm

250 µm

x 2k

exE

k : characteristic energyx: drift distanceE: electric field

Thermal limit:

The diffusion at equal E/P depends on the inverse square root of pressure:

x 2k

ePE

xP


FUNDAMENTS - 13TRANSPORT THEORY OF ELECTRON DRIFT

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

MAGBOLTZ: Montecarlo program to compute electron drift and diffusion

Charge transport processes are determined by electron-molecule cross sections:

http://rjd.web.cern.ch/rjd/cgi-bin/cross


FUNDAMENTS - 14MIXTURES

Addition to a noble gas of even small percentages of a molecular gas has dominant effect on the electron cross section:

CO2 100

CO210Ar 100

CO2 2


FUNDAMENTS - 15DRIFT VELOCITY

(Computed with MAGBOLTZ)

ELECTRON DRIFT VELOCITY IN ARGON-METHANE MIXTURES:


FUNDAMENTS - 16LONGITUDINAL AND TRANSVERSE DIFFUSION

At low electric fields, the diffusion is symmetric. At moderate to high fields however the longitudinal diffusion (in the direction of drift) is reduced.

DriftE FieldT

L

In drift chambers, the dispersive factor is the longitudinal diffusion (measured time in the direction of the electric field)In time projection chambers, the dispersive factor is the transverse diffusion (center of gravity of charge induced on pad rows)

TRANSVERSE DIFFUSION: LONGITUDINAL DIFFUSION:


FUNDAMENTS - 17MAGNETIC FIELD

B

E

wB

The drifting electrons swarm is rotated by an angle B in the plane perpendicular to E and B; the magnetic drift velocity is wB ≤ w0

E

B

wB

tanB

wB EB

1 2 2

wB w0

L 0

T 0

1 2 2

: mean collision time

eB /m Larmor frequency

Drift velocity unchangedThe transverse diffusion is reduced

E

B

w e

m

1 2 2

E

E x

B

B 2 2

B (

E

B )

B2

Friction force theory

r E

r B

rB

s L

T s

w B

E

r E

r B


FUNDAMENTS - 18TRANSVERSE DIFFUSION IN MAGNETIC FIELD

IN SOME GASES THE TRANSVERSE DIFFUSION IS STRONGLY REDUCEDImproves the precision of the projected coordinate measurement in Time Projection Chambers

200 V/cm

r E

r B

600 µm

50 µm


FUNDAMENTS - 19ELECTRON ATTACHMENT

OXYGEN ATTACHMENT COEFFICIENT:

ELECTRONS SURVIVING AFTER 20 CM DRIFT (E = 200 V/cm):

Electrons are lost by radiative or non-radiative capture to resulting in the formation of negative ions: e + a -> A- (+h). The attachment cross section is gas and energy-dependent, therefore strongly depends on the gas composition and electric field. For equal amount of oxygen contamination, capture losses are much more severe in “cold” gases. In the example, a 5% loss is observed for 20 cm drift for 15 ppm of oxygen in A-CO2 or 800 ppm in Ar-CH4.


FUNDAMENTS - 20EXCITATION AND CHARGE MULTIPLICATION

CROSS SECTIONS AT HIGH ELECTRIC FIELDS:

IONIZATION 15.7 eV

EXCITATION 11.6 eV

ELECTRONS ENERGY DISTRIBUTION IN ARGON AT INCREASING FIELDS:

Ei=15.7 eVEx=10.6 eV

Electrons on the high side of the energy distribution reach the excitation and ionization levels, inducing inelastic collisions.


FUNDAMENTS - 21INELASTIC COLLISION PROCESSES IN MIXTURES

Radiative recombination: A++ B -> AB + hRadiative capture: e + M -> M- + hDissociative capture: e + AB -> AB- -> A + B- Three-body collision: e + A = B -> A- + B Excimer formation and decay: A* + A -> A*

2 -> A + A + hPenning effect: A*+B -> A + B* + e [Ei(B) < Ex(A)]

MAJOR PROCESSES:

J.Meek and J. D. Cragg, Electrical Breakdown of Gases (Clarendon, 1953)

Radiative processes with the emission of a short wavelength photon can induce various kinds of secondary effects, as internal reconversion to charge on of molecules with low ionization potential or emission of photoelectron at cathodes. Addition to noble gases of molecular additives reduce these effects directly, quenching the emissions, or by absorption.


FUNDAMENTS - 22PHOTON EMISSION SPECTRA IN NOBLE GASES

IMAGING CHAMBERSSCINTILLATING PROPORTIONAL COUNTERS

TEATMAE

Ar

Kr

Xe

100 200 300 400 500 600Wavelength (nm)

0

0.2

0.4

0.8

0.6

1.0Relative light yield 10 5 4 3 2Energy (eV)15

The emission spectra after excitation and dimers formation of noble gases are peaked in the far ultraviolet. The low ionization potential vapors used in Cherenkov ring imaging detectors, as Triethylamine (TEA) and Tetrakis-dimethylamino ethylene (TMAE), added to noble gases, act as internal wavelength shifters and result in the emission of photons at longer wavelengths:


FUNDAMENTS - 23COLLISIONAL IONIZATION: TOWNSEND COEFFICIENT

Mean free path for ionization:

1

N N: molecules/cm3

First Townsend coefficient:

1

Ionizing collisions/cm

TOWNSEND COEFFICIENT FOR NOBLE GASES:

Electrons acquiring enough energy from the field can have ionizing collisions with molecules, resulting in with creation of an electron-ion pair.

TOWNSEND COEFFICIENT FOR Ar-CH4:

(MAGBOLTZ)


FUNDAMENTS - 24AVALANCHE MULTIPLICATION IN UNIFORM FIELD

n(x) n0e x

Multiplication factor or Gain:

dn n dx

M (x) nn0

e x

lE x

Ions

Electrons

VISUALIZATION OF AVALANCHES COMBINING A CLOUD CHAMBER WITH AN AVALANCHE CHAMBER:

H. Raether, Electron Avalanches and Breakdown in Gases (Butterworth 1964)

Maximum Avalanche size before discharge (Raether limit):

QMAX ≈ 107 e

Incremental increase of the number of electrons in the avalanche:

At each mean free path for ionization, electrons create an electron-ion pair; results an exponential increase of charge, with fast electrons on the front and slow ions left behind.


FUNDAMENTS - 25SIGNAL INDUCTION ON ELECTRODES

The multiplying and moving charges in the avalanche induce signals on the electrodes.The incremental charge induction due to electrons after a path s:

Integrating over s:

dq en0es dss0

q (s) en0s0

(es 1) en0s0

es en0s0

ew t

and the corresponding current :

i (t) dq

dt

en0w

s0

ew t en0

T ew t

The current signal induced by ions is given by:

i(t ) en0

T ew t ew*t

0 t T

i(t ) en0

T es ew*t

T t T

1w*

1w

1w

J. Townsend, Electrons in Gases (Hutchinson 1947)

Fast electron signal

Slow ion tail


FUNDAMENTS - 26AVALANCHE STATISTICS IN UNIFORM FIELDS

In constant electric field, the probability of an avalanche started by a single electron to have a size N is given by Furry’s law:

P(N ) 1N

e

NN

N e s : average multiplication factor on the gap s

H. Genz, Nucl. Instr. and Meth. 112(1973)83

The maximum probability is for N=0 (no multiplication!).

For an avalanche started by n electrons:

P(n,N ) NN

n 1 e

NN

(n 1)!

The Furry distribution has a variance equal to the average:

N

N 1

SIZE DISTRIBUTIONS FOR AVALANCHES STARTED BY 1, 2,... 10 ELECTRONS:

N N

P NN

,n


FUNDAMENTS - 27AVALANCHE SIZE DISTRIBUTION

At large gains (high fields) the avalanche distribution is described by a Polya function:

AVALANCHE SIZE DISTRIBUTIONS AT INCREASING FIELDS:

H. Sclumbohm, Zeit. Physik 151(1958)563

• The shape of the single electron avalanche distribution has a major relevance in determining the energy resolution of proportional counters• A peaked single electron pulse height distribution provides efficient detection (RICH)

The relative variance of the Polya distribution is:

N

N

2

1N

11 k

1N

b b

For k=0 the distributions reduce to a Furry law.

POLYA DISTRIBUTIONS:

P(z) (k 1)k1

(k 1)z ke (k1)z

z NN

for k integer

(k 1) (k)!


FUNDAMENTS - 28PROPORTIONAL COUNTER

Thin anode wire of radius a, coaxial with a cylindrical cathode of radius b

Electric field:

Cathode radius b

Anode radius a

E(r) CV0

20

1r

C 20

ln b a

V (r) CV0

20

ln ra

capacitance per unit length

Potential:

V (b) V0

V (a) 0

a

DRIFT AND COLLECTION REGION

AVALANCHE REGION

THRESHOLD FIELD FOR MULTIPLICATION

DISTANCE FROM CENTER

ELEC

TRIC

FIE

LD


FUNDAMENTS - 29PROPORTIONAL COUNTER: AVALANCHE DEVELOPMENT

ln M

Voltage

Attachment

Collection

Multiplication

StreamerBreakdown

IONIZATION CHAMBER

PROPORTIONAL COUNTER

Saturation

n1

n2

+

+-

+-

+

+

+

+

+

+

GAIN CHARACTERISTICS:At increasing fields, to a region of charge collection (ionization chamber) follows a region of multiplication with the detected charge proportional to the initial ionization. At higher voltage follow a region of limited proportionality, saturation (with the output charge independent from initial ionization), streamer formation and breakdown.

Electrons approach the anode; on reaching a critical value of field strength, they start an avalanche multiplication, continuing until the front reaches the wire. Ions are left behind in a characteristic drop shape. The extent by which the avalanche surrounds the wire depends on gas, geometry and gain.


FUNDAMENTS - 30PROPORTIONAL COUNTERS: INDUCED SIGNALS

For an avalanche starting at a small distance from the anode, the electron and ion contributions to the induced charge are:

q QV0

dVdra

a dr

QC20

lna

a

q QV0

dVdra

b dr

QC20

lnb

a

q(t)

0 100 200 300 400 500t (µs)

Q

T+

INDUCED CHARGE:

FAST SIGNAL DIFFERENTIATION:

0 100 200 300 400 500

q(t)

300 ns

100 ns

50 ns

t(ns)

Total induced signal on anode:

q q q QC20

lnba

Q (+Q on cathode)

Ratio of electron and ion signals:

q

q ln(a) ln alnb ln(a )

~1% for typical geometry

q(t ) QC

20ln 1

CV0

20a2 t

QC20

ln 1tt0

T 0(b2 a2)

CV0q(T) Q

Time development of the signal on anode:

Total ions drift time:


FUNDAMENTS - 31PROPORTIONAL COUNTERS: ENERGY RESOLUTION

The energy resolution is a convolution of ionization statistics, avalanche spread and electronics noise:

GAIN

RESO

LUTI

ON

%

NOISEIONIZATION

AVALANCHE

TOTAL

E

E

2

N

N

2

M

M

2

el

M

2

For soft X-rays:

N2 FN F: Fano factor

M

M

2

1N

A

A

2Gain variance:

A

ASingle electron avalanche variance

E

E

2

1N

(F b)

Ar 0.17 0.19

GAS F(calc) F(exp)

Xe <0.17

Ne+0.5%Ar 0.05

Ar-CH4 0.17 0.19

PULSE HEIGHT SPECTRUM FOR 5.9 keV X-RAYS IN P10 (Ar-CH4 90-10):

for a Polya avalanche distribution

A

Ab

fwhm 1.3 keV

1.35.9

0.22 fwhm E

E9%

For 5.9 keV X-rays (N~220):

for b=1

E

E7%


FUNDAMENTS - 32SCINTILLATING PROPORTIONAL COUNTERS

In noble gases, at moderate electric fields before multiplication, there is a large emission of scintillation photons. In proportional scintillation counters the detection of these photons eliminate the dispersion due to the avalanches and achieve the best energy resolution (close to the statistical)

SPHERICAL ANODE COUNTER:

CHARGE AND LIGHT YIELD VS VOLTAGE:

A.J.P.L. Policarpo et al, Nucl. Instr. and Meth. 102(1972)337

CHARGE

LIGHT

Xe 99.95% 1030 torr

E

E

2

FN


FUNDAMENTS - 33ENERGY RESOLUTION OF SCINTILLATION COUNTERS

Xe 99.95% 1030 torr

55Fe X-RAYS (5.898 keV):

FWHM 500 eV

R FWHME

8.5% E

E3.6%

Primary statistics limit:

E

E

FN

2.8%

A.J.P.L. Policarpo et al, Nucl. Instr. and Meth. 102(1972)337

241Am ENERGY SPECTRUM:

H. E. Palmer, IEEE Trans. Nucl. Sci.NS-22(1975)100

Fluorescence analysisX-Ray Spectroscopy


FUNDAMENTS - 34IMAGING CHAMBERS

The light emission in avalanches has been exploited to detect tracks with simple optical recorders (solid state cameras).

The UV light emission in the avalanches is converted into the visible using an internal wavelength shifter (TMAE gas) or a thin WLS on the semi-transparent anode.

DRIFT VOLUME AVALANCHEMULTIPLICATION

M. Suzuki et al, Nucl. Instr. and Meth. A263(1988)237

COSMIC RAY ACTIVITY IN A 10x10x10 cm3 SENSITIVE VOLUME:


FUNDAMENTS - 353-D OPTICAL IMAGING CHAMBER

K. Miernik et al, Nucl. Instr. and Meth. A581(2007)194

Optical imaging chamber with recording of the projected image using a CCD camera, and the time profile of the emitted light with a photomultiplier. Simultaneous recording of projection and time development of the emission permits a 3-D reconstruction of tracks.

Tested with radioactive ion beams stopping in the gas volume.

IMAGES OF NUCLEAR DECAYS:

sauli principles

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