1. technology and computing

03 - Ionization chambers
Jaroslav Adam
Czech Technical University in Prague
Version 1.0
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Principle of operation
Charged particle getting through a volume of a gas or noble liquid
Interaction proceed through ionization and end excitation of the molecules, electron-ion pairs
are created
Ion can be created directly by the incident particle, or by the δ-electrons, when the energy
from the primary particle if first transferred to the electron which acquires enough energy to
make further ionization
Electric field is applied by the electrodes, electrons and ions drift to them
If the field is high enough, drifting electrons can also ionize the gas (proportional counters)
After further increase of the field strength, electrons emit UV light on the anode
(Geiger-Muller counter)
Electronic signal at the output, pulsed or current regime
Position sensitivity by segmenting one of the electrodes (xy ) and by timing measurement (z)
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Ionization detectors without amplification
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Number of ion pairs
Minimum energy W to be transferred from the incident particle to create at least one ion pair
Quantified as average energy loss to create the pair
Given by the least tightly bound shell, W = 10 - 25 eV
Non-ionizing energy loss (excitation) makes number of pairs lower
Fully stopped 1 MeV particle produces 30 000 ion pairs
Number of pairs is important for resolution
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Fano factor
Fluctuation in number of pairs affect the energy resolution
The simplest approach postulate Poisson statistics for number of ion pairs (σ =
√
N)
Fano factor makes correction to predicted variance to get observed variance
Fano factor = 0 if all incident energy converted into pairs, no statistical fluctuation
In gases Fano factor < 1, Poisson distribution valid but fluctuations are smaller than
√
N
Significant in pulse mode
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Principle of ionization chamber
Figure : Planar ionization chamber
Suppose two metallic electrodes at distance D covering volume of a gas or noble liquid
Voltage V applied to anode (thousands of kV)
Number of electrons n− given by the number of minimum-ionizing-particles (mip)
n− =
n
dE
Dρ
W
dx
(1)
ρ is the density and dE/dx is energy loss per g cm−2
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Charge carriers in gas/liquid volume
Several processes applies to the ion pairs
Drift movement by external electric field
Diffusion due to random thermal movement
Charge transfer
Recombination
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Drift movement
Electrostatic force moves the charges, positive ions opposite to electrons and negative ions
Drift of electrons characterized by drift velocity in electric field E = V /D
vd (e) =
dx
µe
V µe
=
E=
dt
p
pD
(2)
Electron mobility µe given in unit of bar cm2 V−1 s−1 , p is the gas pressure
Mobility of ions is about 1000 less than of electrons
Description with mobility provides calculation of readout times
ms for ions, µs for electrons
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Saturation of the drift velocity
Figure : Electron velocity vs. filed
No increase in drift velocity after reaching it’s maximum, only in some gases
Hydrocarbons, argon-hydrocarbon mixtures
In non-saturation gases, E/p proportionality holds up to high fields
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Diffusion
Thermal movement with mean free path of about 10−6 - 10−8 m
More important for electrons since their thermal velocity is bigger
Point-like collection of electrons form Gaussian spatial distribution widening with time
Widening in one direction x, y or z given by diffusion coefficient D
√
σ=
2Dt
(3)
D is given by kinetic gas theory or the process is described by a transport model
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Charge transfer collisions
Electron transfer from neutral gas molecule to positive ion in mutual collision
Significant in mixtures, net positive charge transfered to species with lowest ionization energy
Negative ion can be formed by capturing of free electron (oxygen)
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Recombination
Free electron captured by positive ion making ordinary neutral atom
Positive and negative ions recombine, most probable compared to electron and ion case
Original charge is lost, no contribution to final signal
Recombination rate given by density of positive and negative species n+ and n− and
recombination coefficient α
dn+
dn−
=
= −αn+ n−
dt
dt
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Initial recombination
Recombination of electron with it’s parent ion
Mainly for heavy ionizing particles (low energy α), minimal for mip
Independent of the event rate
Suppressed by applying electric field larger than Coulomb field of electron-ion system
Quantified as a ratio of charge after initial recombination Qrec to the amount of initial charge
Q0 (Onsager 1938)
"
rkT
Qrec
= exp −
1+E
Q0
r0
e3
2k 2 T 2
!#
(5)
rkT = e2 /kT is Onsager length or radius, r0 is thermalization length, k is the Boltzmann
constant, T is temperature, E is applied electric field, is electric permitivity of the medium
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Columnar recombination
Electron-ion pairs created in column along particle trajectory
Recombination may occur with neighboring ion when electrons are drifting in electric field
Depends on the angle between incident particle and electric field
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Volume recombination
Recombination during drift towards electrodes
Unlike initial/columnar recombination, this depends on irradiation rate
Suppressed by fast charge separation and collection -> high electric field
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Carrier density evolution under drift and diffusion
Initial Gaussian distribution of electrons n− and ions n+ along z in column of radius b
n± (t = 0) =
N0
exp
πb2
−
x2 + y2
b2
!
(6)
Evolution in time is given by
dn±
∂n±
= ∓µ± E sin φ
+ D± ∆n± − kr n− n+
dt
∂x
(7)
D± = µ± kT /e, φ is emission angle vs. field, kr is columnar recombination factor
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Ionization current, DC ion chamber
Constant irradiation rate creates constant formation of ion pairs
Steady-state current is measure of the rate
Supposing negligible recombination and efficient charge collection
Figure : Planar ionization chamber
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Current-voltage characteristics
Electric field by external voltage
Current in the circuit equal to ionization current at equilibrium
Increasing voltage begins to separate the charges that would recombine
High electric field makes recombination negligible
After ion saturation, all charges are collected, on increase in current when increasing the
voltage
Standard operation of ion chambers, current in the circuit is an indication of the rate of ion
pairs formation
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Saturation current
Recombination, especially columnar recombination require high voltage
Volume recombination important at high irradiation intensity
Higher voltage required to get true saturation current
More important in neutron measurement, where heavy fragments are detected
With chambers filled by ambient air, recombination depends on humidity
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Perturbations in current due to diffusion
Imbalance in steady-state situation supposing uniform production of ions within the chamber
Larger concentration of positive ions close to cathode, opposite for electrons close to anode
Gradient in concentration formed, diffusion opposite to drift
Perturbation in measured current in planar chamber given by
−
∆I
kT
=
I
eV
(8)
is ratio of average energy of charge carrier, kT /e ≈ 2.5 × 10−2 V at room temperature
close to one for ions, but several hundreds for electrons
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Losses of saturation current due to diffusion
close to one for ions, but much larger, several hundreds for electrons
Minimized by high voltage
Columnar recombination not fully eliminated
Separate measurements of ionization current as a function of voltage
1/I as a function of 1/V to determine true saturation current
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Operation of DC ion chamber
No special requirement on gas since negative charge can be collected as free electrons as
well as negative ions
Only recombination could affect the amount of charge, suppressed by high enough voltage
Few centimeters and tens of hundreds of volts sufficient to reach saturation
Air for gamma-ray exposure, denser gases like Argon to increase ionization density
Pressure about 1 atmosphere, higher to increase sensitivity
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Geometry of ionization chamber
Electric field given by geometry of electrodes
Uniform electric field with planar geometry
Cylindrical geometry with electrical field as E(r ) =
U0
r ln(ra /ri )
Figure : Cylindrical ionization chamber
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Insulators
Small values of ionization current, < 10−12 A
Resistance of insulator at least 1016 Ω to keep leakage current below 1% for U = 100 V
Leakage by moisture absorbed on surface suppressed by the guard rings and smooth surface
of insulators
Plastics or ceramic for higher irradiation
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Measurement of gamma-ray exposure with ion chambers
Amount of charge in air-filled ionization chamber
Charge is measure of exposure, ionization current gives exposure rate
Requires to measure ionization of all secondary electrons, mean free pairs several meters
compensation for secondary electrons needed
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Compensation by free-air ionization chamber
Collimated X-rays, compensation in horizontal direction
Compensation of electrons escaping the sensitive volume by electrons emerging elsewhere
Up to gamma-ray of 100 keV
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Air equivalent compensation
Reduces space requirements for higher gamma-rays energies, wall thickness less than 1 cm
Exposure rate given by saturation current Is and mass M in active volume
R=
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Is
M
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Absorbed dose
Based on average energy loss per ion pair W (joule / ion pair), relative mass stopping power
Sm and number of ion pairs per unit mass (ion pairs per kg)
Dm = W · Sm · P
(10)
Dm is then in grays (J kg−1 )
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DC chambers for radiation survey
Radiation monitoring
Saturation current in closed volume of several cm3
Dose measured by charge integration
Initial charge on the chamber, drop in voltage measures total integrated ionization charge
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Ionization dosimeter
Cylindrical air capacitor, initially charged at some voltage V0
Discharged by the radiation
Voltage reduction measures absorbed dose
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Calibration of radiation source
Saturation current depends only on geometry, long time stability
Current from unknown source compared with standard under same geometry
Chambers with thousands of cm3
Pressured gas for higher sensitivity
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Geometry for calibration of gamma-ray sources
Calibration for gamma-ray sources, ionization current for small displacement of the source
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Measurement of radioactive gases
Radioactive gas as constituent of fill gas, sampled as continuous flow
¯ and total
Ionization current I given by average energy deposition per gas disintegration E
activity α
I=
¯
Eαe
W
(11)
Principle of smoke detectors where ionization current from internal alpha source decreases
due to presence of the smoke in sampled air
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Remote sensing of ionization
Positive and negative ions in the air survive for minutes before recombination
Flow of air is transported to a chamber outside the source of radiation
LRAD - Long Range Alpha Detector:
Sample of alpha-contaminated material in container, air flowing though it
Positive and negative ions carried into an ion chamber
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Pulse mode operation
Each radiation quantum provides with distinguishable signal pulse
Application in radiation spectroscopy
Alpha spectrometry
Neutron detection
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Equivalent circuit of ion chamber
Chamber presented by it’s capacity C
Voltage V0 on load rezistor R
Drifting charges from ionization create induced charge on electrodes
Voltage drops from equilibrium V0 , giving output pulse VR
Slow return to equilibrium according time constant RC
If RC > time to collect all charges, amplitude of the pulse measures the original charge
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Equivalent circuit of ion chamber
The ion chamber behaves as parallel connection of resistor and capacity, called RC circuit
Time dependence of voltage V given by
capacity C and resistivity R
C
dV
V
=I=
dt
R
(12)
Response to initial charge giving voltage V0
is
V (t) = V0 e−t/RC
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Electron sensitive mode
Time to collect electrons ∼ µs, time for ions ∼ ms
Collection of all charges would require RC of orders of >ms
This would mean low pulse rate only and interference from microphonic signals
For electron sensitivity, RC between electron and ion collection time
Negative ions no longer allowed
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Pulse shape in planar chamber
Constant electric field E = V /d
Uniform equipotentials parallel to electrode surfaces
Ions supposed to be formed at equal distance x where electric potential is Ex
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Pulse shape of electron and ion collection
Derivation of VR (t) based on energy conservation
RC long enough to collect all charges
Energy in capacitance 1/2CV02 is energy source to move the charges
Drift velocity v − for electrons and v + for ions, n0 is number of ion pairs
1
1
2
CV02 = n0 eEv + t + n0 eEv − t + CVch
2
2
Vch
V0
V0 + Vch ' 2V0 and
'
d
d
VR =
(14)
(15)
n0 e +
(v + v − )t
dC
(16)
After collecting the electrons (time t − ≡ x/v − )
VR =
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n0 e +
(v )t
dC
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Pulse shape of electron and ion collection
After collecting the ions (time t + ≡ (d − x)/v + )
n0 e
[(d − x) + x]
dC
n0 e
VR =
C
(18)
VR =
(19)
If RC t + , maximum amplitude of the pulse is
Vmax =
n0 e
C
(20)
Independent of position of incident ionization
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Pulse shape of electron and ion collection
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Pulse shape in electron sensitive operation
Pulse shape given by electrons
Amplitude sensitive to position of incident radiation
V |elec =
n0 e x
·
C
d
(21)
Monoenergetic radiation produces a range of pulses
Removed by dividing the ion chamber by adding a grid
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Gridded ion chamber
Designed to remove amplitude position dependency
All interactions between the grid (Frisch grid) and the cathode
Grid at intermediate potential and transparent for electrons
Grid-anode voltage drops after electrons pass through the grid
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Electron signal in gridded ion chamber
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Electron signal in gridded ion chamber
With RC larger than electron collection time and grid-anode spacing d, signal on load resistor
is
VR =
n0 e −
v t
dC
(22)
Maximum voltage is
Vmax =
n0 e
C
(23)
Allows to operate at short RC
Pulse independent of position of incident radiation
But signals of order of < 10−5 V
Can not be measured directly, amplification needed
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Statistical limit to energy resolution
Number of charges n0 and fano factor F gives statistical limit
Supposing fully stopped α at energy E = 5.5 MeV in gas with W = 30 eV/ion pair and
F = 0.15
n0 =
Ed
= 1.83 × 105 ion pairs
W
(24)
Standard deviation as square root of variance
σn0 =
Jaroslav Adam (CTU, Prague)
p
Fn0 = 166
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Statistical limit to energy resolution
FWHM of Gaussian distribution for n0 and particle energy
FWHM(n0 ) = 2.35σn0 = 390
(26)
FWHM(E) = 2.35σn0 · W = 11.7 keV
(27)
Relative energy resolution to the deposited energy
R=
2.35σn0 W
= 0.123%
Ed
(28)
Good theoretical resolution can not be achieved due to electronic noise
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Charged particle spectroscopy with pulse-type ion chamber
Some advantages vs. semiconductor or scintillator detectors
Arbitrary size and geometry
Gas dielectric cable 3500 m long was used as a beam-loss monitor at SLAC
Gas pressure to adjust stopping power or effective thickness
Radiation resistant, simple design
Low level alpha particles, cross sectional area 500 cm2
Bragg curve spectroscopy: analysis of pulse shape from incident particle parallel to the field,
can distinguish particle species
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Alpha spectroscopy with ionization chamber
Fisch grid ionization chamber filled by argon allows to separate two uranium isotopes
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Measurement of purity of liquid argon by ionization chamber
α-cell ionization chamber used by ATLAS to monitor liquid argon fill of electromagnetic
calorimeters
Electron charge from α ionization
Detection of impurities in argon
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Proportional counters
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Charge multiplication in the gas
Late 1940s, effect of gas multiplication
More ion pairs compared to ionization chamber
Low energy X-rays
Neutron detection
Pulse mode most common operation
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Avalanche formation
Kinetic energy of the electron sufficient to make secondary ionization
Field at least 106 V m−1
Gas multiplication: secondary electrons also ionize after acceleration
Townsend avalanche
dn
= αdx
n
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Townsend coefficient vs. field
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Regions of operation
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Cylindrical geometry
Field with anode wire radius a, cathode inner radius b and applied voltage V is
E(r ) =
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V
r ln(b/a)
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Field as a function of radius
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Avalanche from a single electron, MC transport model
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Construction design
Figure : Cross sectional view, dimensions in cm
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2π proportional counter
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4π proportional counter
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Fill gas
Gases without significant electron attachment
Oxygen or electronegative impurities must be removed in flow-counters
Sealed counters more convenient to use, but may have limited lifetime
Polyatomic gas (methane) to prevent photon-induced effects, component called quench gas
Most common proportional gas is 90% argon + 10% methane (P-10 gas)
Penning effect - component with ionization energy lower than excitation energy of principal
gas
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Gas multiplication factor
Single electron response by avalanche created by one electron outside multiplication region
Total charge by n0 original pairs with gas multiplication factor M is
Q = n0 eM
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Gas multiplication factor vs. voltage
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Space charge effects
Reduction of the field near anode due to positive ions
Self induced effects resulting from high gas gain, does not depend on pulse rate
General space charge effect is cumulative for different avalanches, also for lower gain
M should just satisfy signal-to-noise requirement to prevent space charge effects
Simple check by varying the voltage and looking for suppression of large pulse amplitudes
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Energy resolution
Fluctuations in n0 and in multiplication
Variance of pulse amplitude given by ion pair fluctuation and single-electron multiplication
variations
Furry distribution of number of electrons in a given avalanche, probability of ionization
depends only on E
Polya distribution for higher fields, ionization depends on electron’s history, not only on E
Distribution of pulse amplitude approaches Gaussian for large n0 (more than 20)
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Energy resolution
Fractional standard deviation of the peak (FWHM/2.35), P-10 gas at 1 atm pressure
Open circles: standard tungsten anode
Full circles: improved uniformity
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Systematic variations in gas multiplication factor
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Time characteristics of the signal pulse
Output pulse is sum of drift time of free electrons to reach multiplication region and
multiplication time required for the avanlache
Drift time greater than multiplication time
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Equivalent circuit of proportional counter seen by developing signal
Derivation of pulse shape utilizes energy conservation of charge moving across the capacitor
Most of the pulse amplitude from positive ion drift
Collection time of all ions long, hundreds ms, but large fraction of signal developed early of
ion drift, fraction of µs
Spread in electron drift times (ionizations along radius) makes spread in rise time of output
pulse
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Shape of output pulse
Solid curve represents initial ionization at fixed radius (constant drift time)
Dashed line is for uniform ionization along the radius
Rise time minimized by high electric field in drift region and gases with high electron drift
velocity
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Electron drift velocity
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Variations of pulse rise time
Pulse shaping with short time constant removes slow component of rise time
Amplitude less than of full collection, effect of balistic deficit
Shape of pulse would vary with radial position of original ion pairs
Minimized by shaping time larger than variation in rise time
Can be used to separate signal α events from electron background
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Spurious pulses
Satellite afterpulses from secondary processes following desired signal
Removed by amplitude discrimination since correspond to single-electron avalanche
Effect increases with high value of gas multiplication
Optical photons by excited atoms within the avalanche, low energy electron at cathode
surface through photoeffect
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Operating voltage
Signal pulse for every particle with enough energy deposit
Sensitivity to more than one avalanche to suppress space charge effects and spurious pulses
Lower values of multiplication factor, some number of original ion pairs to create detectable
signal
Counting curve to select appropriate operating voltage (counting rate vs. voltage at same
source condition), looking for flat region
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Alpha counting
Monoenergetic charged particles of range less than dimensions of the chamber
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Beta counting
Range greater than chamber dimensions, smaller pulses compared to alpha
4π counter for absolute beta activity
Greater range advantage for mechanical source backing
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Mixed alpha and beta sources
Two readout channels for alpha and beta
Separation by amplitude
Background from cosmic rays or ambient gamma (most sources) does not affect alpha
window
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X-ray and gamma-ray sources
Fraction of incident photons absorbed in 5.08 cm of proportional gases at 1 atm pressure
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X-ray and gamma-ray sources
X-ray spectroscopy by full absorption of photoelectrons, full energy peaks in pulse spectrum
Small signal enhanced by internal gas multiplication
Gamma rays in Geiger-Muller region
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Response function for low-energy X-rays
Characteristic X-rays after photoabsorption of primary radiation may escape without
interaction
Suppressed with K-shell energy above incident X-ray energy
Requirements to entrance window, beryllium or aluminum 50 - 250 µm
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Fluorescence gating
Electronic separation of photoelectric absorption of incident photon and absorption of
consequent characteristic X-ray
Proportional counter as series of independent cells, X-ray absorbed in different cell
Two pulses in time coincidence corresponding to full absorption, escape peak avoided
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Tissue equivalent proportional counter
Dosimetry of gamma rays and neutrons
Walls and gas mixture mimic elemental composition of biological tissue
Steady flux of secondary particles from the wall
Determines quality factor for equivalent dose
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Parallel plate avalanche counters
Heavy charged particles which would impose radiation damage to solid state detectors
Parallel plate electrodes, proportional gas at low pressure
Particle species separation by specific energy loss
For gap of 1 mm, fast component from electrons in ns with high field, time resolution 160 ps
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Position-sensitive proportional counters
Avalanche occurs around small portion of anode wire length
Position of avalanche is indicator of axial position in cylindrical geometry
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Charge division method
Anode with significant resistance per unit length
Two amplifiers at the ends, sum related to conventional pulse, proportion to the position of the
interaction
Alternatively relative rise time could be analyzed, longer rise time for pulse far from amplifier
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Multiwire proportional counters (MWPC)
Field by equidistant grid of anode wires between two parallel cathode plates
High field region only in immediate vicinity of the anodes
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Two-dimensional MWPC
Cathodes divided into perpendicular strips
Centroid of discharge located by center-of-gravity technique
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Multicell proportional counter
Cylindrical independent cells
Coincidence measurement for process selection or background rejection
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Gas proportional scintillation (GPS) counters
Signal pulse from visible or UV photon emitted by excited gas atoms or molecules
Excited in inelastic collisions between drifting electrons and neutral atoms
Photons detected by photomultiplier or silicon avalanche photodiodes
Greater light yield compared to conventional scintillator
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GPS with uniform field
Avoids recombinations in low-field region
Time duration measures depth of the interaction
Depth dependence canceled by dividing the total light yield by the time duration
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Light properties in GPS
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Voltage characteristics of GPS
(1) charge gain, (2) light gain, (3) secondary light per collected electron
Secondary light at much lower voltage than the onset of charge multiplication (3 kV here)
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Microstrip gas chamber (MSGC)
Narrow anode metallic strips (10 µm) on substrate
Quick collection of ions, clearing the space charge
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Two-dimensional MSGC
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Gas electron multiplier (GEM)
Preamplification in gas to allow lower voltage readout of microstrip detector
GEM foil of insulating material, both surfaces covered by metallic cladding
Hole density 50 per mm2
Holes of 140 µm pitch and 70 µm diameter
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Electric field in GEM foil
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Cascade of GEM foils
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Micromegas (micro-mesh gaseous structure)
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Resistive Plate Chamber (RPC)
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Time Projection Chamber (TPC) of the ALICE experiment
3D position and dE/dx using volume of 90 m3 of Ne/CO2 /N2 (90/10/5) divided into two
sectors of 2.5 m
Voltage 100 kV on central electrode, drift field 400 V m−1
Electron drift velocity 2.7 cm µs−1 , maximum drift time 92 µs
Readout by MWPC with cathode pad readout mounted in trapezoidal sectors at each end
plate
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MWPC readout of ALICE TPC
Figure : Cross sectional view along the wires
Figure : Cross sectional view perpendicular to the wires
DPD_03,
Ionizationwire
chambers
Grid of anode wires above pad plane,
cathode
plane and gating grid
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MWPC readout of ALICE TPC
Grid of anode wires above pad plane, cathode wire plane and gating grid
Active area of 32.5 m2
Wire geometry and pad size dependent on radial track density
Anode to cathode distance 2 and 3 mm, gain up to 20 000
560 000 readout pads of 4 × 7.5 mm2 for inner chambers and 6 × 10 mm2 and 6 × 15 mm2 in
outer chambers
Gate opens for electrons from the drift volume by the collision trigger (6.5 µs after the
collision) for the duration of drift time, 92 µs, prevents the space charge of positive ions from
drifting back from multiplication region
Gating reduces drift of electrons by a factor more than 105
Position calibration by internal laser system, artificial straight tracks perpendicular to the
beam axis, laser trigger rate up to 10 Hz
Analog-to-digital (ADC) sampling with 6 ADC counts per fC
Position resolution 1100 - 800 µm in r φ and 1250 - 1100 µm in z
dE/dx resolution 5 % for isolated tracks, 6.8 % at high multiplicity
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TPC laser calibration seen on run monitoring
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Particle identification by dE/dx in TPC
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Upgrade of TPC
Expected rate 50 kHz of Pb-Pb, 5 interactions within maximal electron drift time, 10 events
superimposed from past+future time window
Untriggered readout without use of gating grid
Readout by GEM foils instead of MWPC, field 50 kV/cm in the hole
Suppression of back flowing ions
One side segmented to reduce total charge on the foil, segments coupled by resistors
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Simulation of GEM
Light lines - electrons, dark lines - ions, spots - ionization occurence
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Geiger-Mueller Counters
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G-M counter
Introduced in 1928, one of the oldest detectors
Higher field than in proportional counter
One avalanche can create at least one another avalanche, chain reaction
All pulses have same amplitude, 109 - 1010 ion pairs
Pulse amplitude in volts, no need for external amplification
Counting rate limited by dead time
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Geiger discharge
Excited molecules of neutral gas in Townsend avalanche, together with positive ions
They emit visible or UV light, may be absorbed by photoeffect at any place of the tube, new
free electron created
Or free electron created by absorption at cathode
New avalanche from the free electron after reaching the multiplication region around anode
Subcritical proportional tube: n00 p 1 with n00 number of excited molecules in typical
avalanche and p the probability of photoabsorption
Geiger discharge with single avalanche multiplication 106 - 100 has n00 bigger, criticality
achieved as n00 p ≥ 1
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G-M region
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Geiger discharge propagation
New avalanches created close to the original one, new electrons have to reach anode region
Spread of Geiger discharge along the anode wire with propagation velocity 2 − 4 cm µs−1
over entire length of anode, few µs after initiating event
Avalanches at random positions around anode, electrons collected by anode, secondary
positive ions around the multiplication region
Field reduced by space charge of the ions, multiplication reduced, Geiger discharge
terminated
Amount of needed space charge independent of initial ionization, the reason for same pulse
amplitude
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Amplitude of Geiger discharge
Amplitude increases with higher applied voltage
More space charge needed to reduce the field below criticality
Overvoltage defined as voltage above minimum required for Geiger discharge initiation
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Fill gases
Same requirements as for proportional counters since charge multiplication is needed (no
negative ions...)
Noble gases, helium, argon, quenching component
n00 increases with E/p (electric field to gas pressure), G-M as sealed tube with pressure less
than atmospheric
Voltage 500 - 2000 V for anode of 0.1 mm diameter
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Quenching
Slow drift of positive ions after Geiger discharge termination to the cathode, neutralization
with electron from cathode surface
Energy needed = sum of gas ionization energy and energy to extract the electron from
cathode (work function)
If (gas ionization energy) = 2 × (work function), another free electron emerges from the
cathode surface
At least one free electron from cathode with large amount of positive ions
Will drift towards anode to make new Geiger discharge
Cycle would repeat, continues output of multiple pulses
No problem for proportional counters, number of ions smaller, only spurious pulses
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External quenching
Needed any method to prevent excessive multiple pulsing
Reduction of high applied voltage for some fixed time after the pulse below gas multiplication
Time greater than transit of positive ions to the cathode (hundreds of ms) and transit time of
free electron (few µs)
Value of R selected high enough (108 Ω), so RC is of ms
Several ms for anode to return to nominal operating voltage, low counting rate
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Internal quenching
Component of quench gas added to primary fill gas, concentration 5 - 10 %
Smaller ionization potential, more complex molecular structure
Multiple pulsing prevented by charge transfer collisions, positive charge of primary gas ion
transfered to quench gas molecule, original ion neutralized before reaching cathode
Ions of quench gas at cathode with some concentration of quench component
At cathode, the excess energy dissociates the more complex molecule, emission of free
electron suppressed, no additional avalanches
Organic molecules, ethyl alcohol, ethyl formate
Limit of 109 counts due to consumption of quench gas
Problem avoided by halogens as quench gas (chorine, bromine), spontaneous recombination
after dissociation
Limit to lifetime then by contamination of reaction products from the discharge and polymer
deposition on anode surface
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Shape of the output pulse
Signal of multiple avalanches from secondary electrons
Spread in time for them to reach multiplication region
Rise time of few µs
Electric field distorted from the space charge of positive ions
Fast rise and slow rise from ions drift, time constant less than 100 µs to eliminate slow
component
Loss in amplitude tolerated due to large amount of charge
Delay in response by drift of original electrons to multiplying region, applies for timing with
G-M as time uncertainty
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Dead time
Drift of positive ions outwards, recovery of filed in multiplying region
After drift to some distance, the field permits new Geiger discharge, lower intensity in the
beginning
First pulses reduced in amplitude
Full field and full amplitude after all ions neutralized at the cathode
Dead time = time between initial pulse and second Geiger discharge, regardless of the
magnitude, 50 - 100 µs
Resolving time = time for pulse of amplitude high enough to be registered, dead time may
include also recovery time in practical application
Recovery time = time to return to the original state, pulse of full amplitude
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Dead time behavior
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Geiger counting plateau
Dependence of measured counting rate on voltage with constant rate from radiation source
Counter threshold Hd , no pulses if amplitude is below
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Onset of continues discharge
Corona discharge by irregularities on anode wire or quenching failure
Decrease of voltage needed
Operating voltage just sufficient for the flat region, reduces quench gas consumption
Low amplitude tail causes some slope of the counting curve
Hysteresis in counting curve due to charges on insulators
Linearity of the plateau measures quality of G-M
Organic quenched tubes have slope of 2 - 3 % with change in voltage by 100 V
Halogen quenched tubes have greater slope, but larger lifetime and lower operating voltage
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End-window Geiger tube
Fine anode wire, less requirements on uniformity of the wire and of the electric field
Cylindrical cathode of metal or glass with metallized inner surface
Thin window for short-range particles, differential pressure
More robust window for beta or gamma
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Other design of Geiger tube
Wire loop anode in cathode of arbitrary volume
Needle counters - sharply pointed needle, field as 1/r 2 (1/r for cylindrical geometry), used
for smaller active volume
Source in counting volume for low-energy particles
14 C
detection by gas mixture of CO2 with counter gas for high counting efficiency
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Counting electronics
R is load resistance for signal development
Cs is capacitance of the tube and wiring, parallel with R
RCs ∼ few µs for fast-rising component
Coupling capacitor Cc to block high voltage on the tube, only signal pulse transmitted, RCc
larger than pulse duration
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Counting efficiency for charged particles
100 % for any charged particle entering the active volume since a single ion pair triggers full
Geiger discharge
Effective efficiency given by the window of the tube, absorption or backscattering
For alpha counting window with 1.5 mg/cm2
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Efficiency for neutrons
Rare application for neutron detection
Low capture cross section for Geiger gases
Gamma-ray discrimination not possible, all pulses have same size
Neutron-induced reactions detected by proportional counters, large amplitude from such
reactions
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Counting efficiency for gamma rays
Interaction in solid wall of the counter, secondary electron needs just to emerge into active
volume
1 - 2 mm of innermost layer of the wall
Efficiency increased with high-Z material of the cathode (bismuth Z = 83)
Low-energy gamma may interact with fill gas, xenon and krypton (high-Z) enhance the
efficiency up to 100 % for photon energies 10 keV
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Counting efficiency for gamma rays
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Dead time correction by time-to-first-count method
Losses by dead time significant at rates of few hundred counts per second
Method based on switching two voltages on the tube
After Geiger discharge, voltage set below value for multiplication for time longer than recovery
at reduced voltage, 1 - 2 ms (waiting time)
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Dead time correction by time-to-first-count method
Series of measurements of time from end of waiting time and next true event
Average of these intervals equals to 1/r with r the true event rate
Voltage switching should be fast for reasonable timing accuracy, tens of µs
Counting rate extended up to 105 counts per second
Statistical uncertainty given by number of measured time intervals
At least 104 time intervals for 1 % statistical accuracy
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