Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

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600 Principles of Radiation Interaction in Matter and Detection

are within the range of ±5 ADC counts.

The reference pulse position is used to correct the gain of the preampliﬁer at

each electric ﬁeld value. It is seen from Fig. 8.5(b) that the reference peak positions

are varying during the measurements within the range of ±2 ADC around the

average value. This conclusion was checked to be valid over the whole ADC scale.

The calibration of the ADC scale in terms of collected charge units (fC) is

obtained from the linear ﬁt of the calibration pulse positions. The ﬁtted parameters

are averaged over a set of measurements, and the deviations from this averaged

calibration are presented in Fig. 8.5(c). Based on this calibration method, the un-

certainty on the collected charge value is expected to be at the level of 0.01 fC.

The detailed analysis of the systematic errors was performed for all irradiation

runs. Some signiﬁcant variations of the systematics can be found due to cryostat

activation. The activation of the cryostat is at its lowest after a long stopping

perio d (3–4 months) of the reactor, due to maintenance. During normal period of

operation, frequent irradiation every three weeks increases the cryostat activation

and thus the systematic errors. In addition, this activation maintains some level of

impurities in liquid argon before irradiation. It is important to know the evolution

with time of this impurity level. A special test was dedicated to the monitoring over

a long period of time of the evolution of the impurity level of liquid argon purposely

contaminated with oxygen in the cryostat. About 6 cm

of oxygen gas were injected

into the warm argon vessel of the cryostat which was pumped out beforehand for this

test. A maximal value of about 11 ppm of oxygen concentration might be expected

in this case for the whole oxygen probe liqueﬁed in the cryostat, and about 7 ppm

for the oxygen probe mixed uniformly in the liquid and gaseous states of argon

in cryostat and receiver. The oxygen concentration values were determined using

Eqs. (8.37–8.39). The results are presented in Fig. 8.6.

The liquid argon purity improves with time after the initial liquefaction of the

oxygen probe due to the mixing of the oxygen polluted liquid argon in the cryostat

and the argon gas in the receiver. The initial value of the impurity concentration

is close to expectation (11 ppm). The “cleaning” could continue until the oxygen

concentration in the argon system becomes even. To speed up the process, the

oxygen polluted liquid argon was evaporated from the cryostat back into the receiver

and liqueﬁed once more. The liquid argon was kept in the cryostat after this full

mixing until the end of the test (6 days) and the liquid argon purity remained stable

within ±1 ppm, close to the expected level of ∼ 7 ppm. It was found that variations

of the monitor signal at the end of the test could be caused by the instability of the

high voltage power supply.

8.3.3 Examples of Pollution Tests Using the α-Cell

A very ﬁrst test consisted of a so-called “empty” run. The cryostat ﬁlled with

liquid argon (with no material for test inside, but everything else being identical to

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Ionization Chambers 601

Fig. 8.7 The attenuation factor, as a function of E (in kV/cm), measured after a purposely

injection of 2 ppm of oxygen in liquid argon. The curve is the result of ﬁtting Eqs. (8.37–8.39) to

the data [Leroy et al. (2002b)].

normal condition of operation) was exposed to a total fast neutron ﬂuence of (1.0 ±

0.1) × 10

n/cm

and a γ dose of (96 ± 10) kGy. The collected charge dependence

on the electric ﬁeld was measured before and after irradiation. Assuming that the

liquid argon was polluted by oxygen or oxygen-like impurities, Eqs. (8.37–8.39) were

ﬁtted to the collected charge measured before and after irradiation to estimate the

corresponding impurity concentrations.

It has been found that ρ = (4.4 ± 0.3) ppm and ρ = (3.7 ± 0.2) ppm before and

after irradiation, respectively. A non-zero value of the initial liquid argon purity

concentration was caused by the lack of time for a careful cleaning of the ∼ 300

litres receiver, after its preparation (about 20 hours are needed to ﬁll it with pure

argon). This non-zero value of ρ in these conditions disappears when the system is

cleaned up by multiple ﬂushing with pure argon gas. Then, the liquid argon purity

before and after irradiation were found [Leroy et al. (1999b, 2000a)] compatible

with ρ ∼ 0, showing that the cryostat and α-cell system themselves do not pollute

argon during irradiation [Leroy et al. (1999a)].

Running periods have been also devoted to various systematic studies, inclu-

ding calibration runs dedicated to check oxygen pollution concentrations, pur-

posely injected in argon by ﬁtting Eqs. (8.37–8.39) to the corresponding electric

ﬁeld curves. The attenuation factor, i.e., in the present case, the ratio between the

charge measured after an oxygen injection in liquid argon and the charge measured

with pure liquid argon, was analyzed. An example is shown in Fig. 8.7. At the

same time, the calibration runs conﬁrmed the ampliﬁer capability to recognize liquid

argon pollution at a level better than 1 ppm.

The outgassing under irradiation of PREPREG (epoxy laminate) has been stu-

died, although it is not intended to use this material in the ATLAS liquid argon

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602 Principles of Radiation Interaction in Matter and Detection

Fig. 8.8 The attenuation factor measured for PREPREG samples as a function of E (in kV/cm)

varies from 0.90 at 4.7 kV/cm up to 0.95 for 10 < E < 28.5 kV/cm, showing the eﬀect of pol-

lution. This measured attenuation factor is compared to the attenuation factor corresponding to

an oxygen pollution concentration of 2 ppm (dotted curve) and 4 ppm (dashed lower curve), see

text [Leroy et al. (2002b)].

calorimeters. PREPREG being known as a source of pollution in liquid argon, the

test was performed to check the α-cell system real capability to detect liquid ar-

gon pollution in practical situations. PREPREG samples (total area of 0.22 m

)

were immersed in liquid argon and exposed during a standard period of irradiation

of 11 days, for a total fast neutron ﬂuence of 10

n cm

−2

. The attenuation factor

for PREPREG at 10

n cm

−2

as a function of E is compared in Fig. 8.8 to the

attenuation factor curves corresponding to an oxygen pollution concentration of

2 ppm (dotted curve) and 4 ppm (dashed lower curve) as obtained from calibration

runs. This comparison shows a p ollution concentration of ρ ≈ 4 ppm, conﬁrming the

known behavior of PREPREG under irradiation as well as the system capability to

detect liquid argon pollution.

FCAL resistors, capacitors, and transformers together with capacitors and sin-

timid disks of the purity monitor have been irradiated in liquid argon to study

their possible outgassing at a neutron ﬂuence of 10

n cm

−2

at the IBR-2 reactor

of JINR, Dubna [Leroy et al. (2002a)]. The comparison of the collected charge mea-

sured before and one, two and three days after irradiation shows that no outgassing

resulting from irradiation is observable (Fig. 8.9).

The attenuation factor measured three days after irradiation shows that no

pollution resulting from irradiation is observable (see Fig. 8.10). These results also

demonstrate the good stability of the system response over a period of three days

after irradiation.

The examples shown above illustrate the utility of a ionization chamber (α-cell)

to certify materials and equipments against release of impurities polluting liquid

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Ionization Chambers 603

Fig. 8.9 The collected charge as a function of E (in kV/cm) with 72 FCAL resistors, 75 FCAL

capacitors and 47 transformers, 5 capacitors and 6 sintimid disks of the purity monitor in liquid

argon at a ﬂuence of 1.0 × 10

n cm

−2

. The charge measured before irradiation is compared to

the charge measured one, two, and three days after irradiation [Leroy et al. (2002b)].

argon in high irradiation environments such as the ones to be met at the LHC.

8.4 Proportional Counters

8.4.1 Avalanche Multiplication

Beyond the ionization region, one falls within a region of gas multiplication. When

the applied voltage is high enough, the electrons produced by primary ionization

are accelerated and gain suﬃcient energy to ionize molecules of the gas and produce

secondary electrons, themselves possibly creating a tertiary ionization. If an electron

is produced in a region of suﬃciently high uniform electric ﬁeld, after a free path-

length λ = 1/α (in standard notation), it will ionize a molecule, i.e., an electron–ion

pair will b e produced. At this stage, two electrons will derive under the applied ﬁeld,

each producing an electron–ion pair, etc. If n

−

is the number of electrons at a given

position, after a path-length dx, n

−

will increase by an amount:

−

= n

−

α dx. (8.41)

If n

−

= n

at x = 0, Eq. (8.41) can be easily integrated:

−

= n

α x

. (8.42)

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604 Principles of Radiation Interaction in Matter and Detection

Fig. 8.10 The attenuation factor measured three days after irradiation, as a function of E, for the

72 FCAL resistors, 75 FCAL capacitors, 5 capacitors and 6 sintimid disks of the purity monitor

at a ﬂuence of 10

n cm

−2

[Leroy et al. (2002a)].

The coeﬃcient α is called the ﬁrst Townsend coeﬃcient. The multiplication factor

M is deﬁned from Eq. (8.42) as

M =

−

= e

α x

. (8.43)

For non-uniform electric ﬁeld, α becomes a function of distance [α(x)] and Eq. (8.43)

has to be modifed between two points x

and x

M = exp

α(x) dx

. (8.44)

No particular geometry for the electric ﬁeld has been assumed. However, the mul-

tiplication factor can be calculated for any geometry, if one knows the Townsend

coeﬃcient dependence on the electric ﬁeld. An example of dependence of α on the

electric ﬁeld E often used is [Rose and Korﬀ (1941)]:

= A e

−Bp/E

, (8.45)

where p is the gas pressure, and A and B are two constants depending on the gas

(A and B are expressed in cm

−1

Torr

−1

and V cm

−1

Torr

−1

units, respectively). In

the E-region where Eq. (8.45) applies, one can assume a linear dependence of α on

the electron energy E

α = KNE

, (8.46)

where N is the number of molecules per units volume. The factor K depends on

the gas and is expressed in cm

−1

units. For example, for argon [Korﬀ (1946)],

A = 14 cm

−1

Torr

−1

, B = 180 V cm

−1

Torr

−1

and K = 1.81 × 10

−17

−1

The multiplication factor cannot be increased beyond some limit because beyond

some value of the electric ﬁeld, secondary processes such as emission of photons also

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Ionization Chambers 605

+ +

+ + + +

+++ +

−− −

−−−−

−−−− −

−−−−−−

− −

−

−−− −

−

++++++

+++++++

+ +

Fig. 8.11 The electrons, with faster drift velocity as compared to the ions, occupy the front of

the avalanche while the ions are left behind in the tail, with lower radial extension. The shape of

the avalanche is drop-like.

induce avalanches over the whole gas volume, leading to breakdown. The Raether

condition gives a limit for multiplication before breakdown:

α x ≈ 20, (8.47)

which gives M = 10

Because of its generation mechanism, the avalanche has a drop-like shape

(Fig. 8.11). The electrons drift velocity is much higher as compared to ions. There-

fore, the electrons occupy the front of the avalanche, while the ions are left behind in

the tail, in decreasing number and radial extension. Since they have been produced

in the last average path length, half of the ions are in the front section of the drop,

behind the electrons.

8.5 Proportional Counters: Cylindrical Coaxial Wire Chamber

The cylindrical coaxial chamber is a solution to obtain satisfactory gains while

beneﬁting from the proportional mode. Let us consider the example given in [Sauli

(1977)] of a thin layer of gas, 1 cm argon in normal conditions of temperature

and pressure, in between two parallel planar electrodes. The number of electrons

produced by a mip in a 1 cm gap is about n

−

≈ 105, [see Eq. (8.1)]. The resulting

pulse height is:

V =

−

≈ 2µV, (8.48)

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606 Principles of Radiation Interaction in Matter and Detection

for C = 10 pF (typically). This pulse height of 2 µV is below detection thresh-

old. This signal can be enhanced by avalanche multiplication by increasing the elec-

tric ﬁeld, i.e., the voltage across the electrode gap. In these conditions, one is outside

any proportionality regime, since there is no proportionality b etween the deposited

energy and the detected signal, as the signal depends on the avalanche length, and

ultimately on the location where the original charge has been produced. Consid-

erable increase of the ﬁeld can lead very rapidly to voltage breakdown (Raether

condition). A solution to this problem is the use of a cylindrical coaxial cham-

ber. The central electrode is a wire of radius r

, surrounded by a cylindric chamber

wall of radius r

(Figs. 8.12 and 8.13). The polarity is set such that the central wire

is the anode and the external cylinder is the cathode. The electric ﬁeld is of the

shape ∼ 1/r, maximum at the anode and decreasing towards the cathode.

ion

High voltage

Incoming particle

Cathode

Anode

−

ion

+−

Fig. 8.12 Schematic view of a gas ﬁlled cylindric coaxial chamber with a central electrode con-

sisting of a wire of radius r

, surrounded by a cylindric chamber wall of radius r

. The electrons

and ions created by the passage of an incoming particle are collected at the anode and cathode,

respectively.

The electric ﬁeld at a distance r from the center of the chamber (Fig. 8.14) is,

in standard notations,

E(r) =

2π²

(8.49)

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Ionization Chambers 607

and the voltage

V (r) = −

2π²

, (8.50)

with the capacitance per units of length:

C =

2π²

ln(r

)

. (8.51)

Here V

= V (r = r

) is the potential diﬀerence between cathode and anode

[V (r = r

) = 0] and ²

is the electric permittivity of the gas (typically, ²

∼

8–9 pF/m). Under the electric ﬁeld, the electrons produced by the primary intera-

ction move towards the anode while the positive ions move towards the cathode. For

gas-ﬁlled cylindrical chambers with electrodes of radii r

and r

, the electron drift

velocity is expressed as (p is the gas pressure):

(e) =

E =

r ln(r

)

. (8.52)

anode

cathode

Fig. 8.13 Cross-sectional view of a cylindric coaxial chamber; the central electrode is a wire of

radius r

, surrounded by a cylindric chamber wall of radius r

Close to the anode, the electric ﬁeld is very strong [Eq. (8.49)] and the multi-

plication can take place. As seen in the previous section, a drop-like avalanche with

electrons at the front and ions behind develops. The lateral diﬀusion, combined with

the small value of r

, allows the drop-like avalanche to surround the anode. The

electrons are rapidly collected (typically in 1 ns) and the cloud of ions is free to

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608 Principles of Radiation Interaction in Matter and Detection

r r

~ 1/r

Fig. 8.14 The electric ﬁeld as a function of the distance r to the anode (central wire of radius

move towards the cathode. As a consequence, the signal induced on the electrodes

in the proportional regime is due to the motion of the positive ions, contrary to the

case of ionization chambers where the signal was due to the electrons (very low ion

mobility compared to electron).

The multiplication factor for a proportional counter can be obtained from an

equation similar to Eq. (8.44):

M = exp

α(r) dr

, (8.53)

where α(r) is calculated from Eqs. (8.46, 8.49) in combination with the electron

mean energy obtained from the electric ﬁeld between two collisions (E

= E/α,

remind the deﬁnition of α given earlier). The distance r

is the distance where the

multiplication (through avalanche) starts. One can rewrite Eq. (8.53) as a function

of the electric ﬁeld:

ln M =

E(r

)

E(r

)

α(E)

∂r

∂E

dE. (8.54)

Combining Eqs. (8.49, 8.51, 8.54), one obtains

ln M =

ln(r

)

E(r

)

E(r

)

α(E)

. (8.55)

If α(E) is a linear function of E, one can ﬁnd [Diethorn (1956)]:

ln M =

ln (r

)

ln 2

∆V

ln(r

)

− ln K

. (8.56)

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Ionization Chambers 609

ion

Outer cylinder cathode

Central wire anode

incident

Signal

entrance

ionizing

particle

window

−

− +

−

Fig. 8.15 Schematic view of a Geiger-Mueller counter showing its operating principles (see text).

This expression is frequently used. The quantity K

is the minimal value of E/p (p is

the pressure) below which no multiplication occurs. The quantity ∆V corresponds to

the voltage gradient to which an electron is subjected during its motion in between

two successive ionizing events. The values of ∆V and K

depend on the gas. For

instance, ∆V = 36.5 (29.5) V and K

= 6.9 (10.0) 10

V/cm atm for methane

(propane) [Fischer, H. et al. (1975)].

8.6 The Geiger–Mueller Counter

The Geiger–Mueller counter [Geiger and Mueller (1928)] is a gas-ﬁlled detector built

to operate with maximum ampliﬁcation (Fig. 8.15).

The central wire (anode) is maintained at a very high potential compared to the

cylindric wall cathode. When ionization takes place in the gas volume, the electrons

are accelerated towards the anode. So, initially, one has an ampliﬁcation similar

to the one encountered in a proportional detector. However, the situation diﬀers

very rapidly as electrons strike the central wire so violently that UV photons are

emitted. A fraction of these photons reaches the cathode, where they cause emis-

sion of supplementary electrons from the cathode wall. Then, these supplementary

electrons are accelerated towards the anode where they can also cause UV gamma