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

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590 Principles of Radiation Interaction in Matter and Detection

In Eq. (8.18), E is the applied electric ﬁeld, k

is the recombination factor, L is

the dimension of the box uniformly populated by the initial distribution of ions and

electrons (the ion–electron pairs are isolated), i.e., the box contains N units of each

charge at t = 0. ξ is the single parameter of the theory, ξ → 0 for perfect charge

collection and ξ → ∞ in the case of complete recombination (ξE = 470 kV/cm for

α-particles).

A slight modiﬁcation has been brought to the box model. The quantity ξE was

allowed to be a function of E and empirically found to be for α-particles [Andrieux

et al. (1999)]:

ξE = a

1 −

−bE

, (8.19)

where a = 416 ± 1.4 kV/cm and b = 0.198 ± 0.006 (kV/cm)

−1

8.2.4 Recombination with Impurities

The electrons which escape recombination (initial and columnar) move under the

inﬂuence of the applied electric ﬁeld through the liquid across the electrode spacing

to reach the anode. The electron mobility being 10

times larger than the positive ion

mobility, the total drift current is given by the drift current of electrons towards the

anode. The presence of electron attaching impurities in the gap makes it impossible

for a fraction of the electrons to reach the anode. This fraction will be converted

into negative ions, with a rate constant k

(Eq 8.6), following:

−

+ S → S

−

. (8.20)

These negative ions have much smaller mobility compared to electron and they will

not contribute to the charge collection at the anode. The number of free electrons

remaining at time t is given by:

−

(t) = n

−

(t = 0) e

−ηv

(e)t

, (8.21)

where n

−

(t=0) is the number of electrons present initially, v

(e) is the electron

drift velocity in the liquid and η is the attachment coeﬃcient of electrons to an

impurity molecule, i.e., the probability of attachment for an electron per centimeter

of drift path [Swan (1963)].

The rate constant for the attachment, k

, is given by [Bakale, Sowada and

Schmidt (1976)]:

v σ(v) f(v) dv, (8.22)

where v (= v

(e)) is the electron velocity, f(v) is the velocity distribution of the

electron, and σ(v) is the cross section, as a function of the electron velocity, of the

interaction of the electrons with the impurity S. One can express the rate constant,

, as a function of the electric ﬁeld according to:

(E) =

+∞

σ(E

) f(E

, E) dE

. (8.23)

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Ionization Chambers 591

Table 8.1 Values of the rate constant k

for dif-

ferent impurity concentrations and electric ﬁelds.

Impurity type E (V/cm) k

(mol

−1

)

30 2 × 10

50 3 × 10

100 10

5 × 10

2 × 10

Here, E

is the electron energy, σ(E

) is the capture cross section, i.e., the cross

section of the interaction between the electron and the S impurity, and f(E

, E) is

the electron energy distribution for an electron of energy E

subjected to an electric

ﬁeld E.

The rate constant for the attachment of electrons in liquid argon, k

, to SF

O, and O

has been studied and measured [Bakale, Sowada and Schmidt (1976)]

as a function of the applied electric ﬁeld. The diﬀerent values are found in Ta-

ble 8.1. As can be seen from that table, k

decreases with increasing electric ﬁeld

for SF

and O

impurities, while it increases for N

The number of electrons captured by impurities during a time dt is given by:

−

(t)

= −k

(t) n

−

(t). (8.24)

Integrating Eq. (8.24) with the assumption of a constant number of impurities, n

gives the number of free electrons remaining at time t:

−

(t) = n

−

(t = 0) e

−t/τ

, (8.25)

where n

−

(t = 0) is the number of free electrons initially present in the liquid. One

also has the electron lifetime, τ

, related to the rate constant, k

, and the numb er

of impurities via

. (8.26)

It is useful to introduce the concept of absorption length, λ, of free electron

drifting in the liquid under the inﬂuence of an electric ﬁeld E. The absorption

length varies with the electron drift velo city and its lifetime as:

λ = v

(e) τ

= µ

Eτ

, (8.27)

where the relation between the electron mobility, µ

, and the drift velocity [v

(e) =

E] has been used. The absorption length can also be expressed as:

λ = µ

. (8.28)

The current induced by N electrons collected at the anode as a function of time,

assuming a constant drift velocity (v

), is given by:

i(t) = N e

−t/τ

, (8.29)

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592 Principles of Radiation Interaction in Matter and Detection

if 0 < t < t

, with t

= D/v

, D being the spacing between the cathode and the

anode. If t > t

, the current becomes

i(t) = 0. (8.30)

The integration of the current over time gives the charge:

Q =

−t

/τ

, (8.31)

Q = Q

1 − e

−t/τ

, (8.32)

for 0 < t < t

, and

Q = Q

1 − e

−t

/τ

, (8.33)

for t ≥ t

. Using Eq. (8.27), the charge can be expressed as a function of the

absorption length:

Q = Q

1 − e

−D/λ

. (8.34)

The charge collected at the anode, taking into account the electron–ion recombina-

tions and the capture by impurities of drifting electrons on their way to the anode,

is given by combining Eqs. (8.17, 8.34):

Q(E) = Q

ln(1 + ξ)

λ(E)

1 − e

−D/λ(E)

. (8.35)

One should note the similarity between Eq. (8.35) and Eq. (6.90), the Hecht

equation (see chapter on Solid State Detectors). Indeed, the situations are quite

similar. Equation (8.35) expresses the electric charge of electrons depleted by elec-

tron recombination with ions and capture by impurities in the sensitive volume of

the chamber. Similarly, Eq. (6.90) expresses the depletion of the electric charge by

trapping and recombination with impurities and defects present in the semiconduc-

tor bulk.

8.3 Example of Ionization Chamber Application: The α-Cell

8.3.1 The α-Cell

The α-cell is a very good example of ionization chamber application and we will

present it with some details. Such a cell is used to monitor the purity of liquid

argon in high radiation environment. Example of such application can be found in

the ATLAS experiment [ATLAS Collab. (1994a)] to be performed at the CERN

LHC. High-granularity liquid argon calorimetry is a key element of the ATLAS

experiment. The liquid argon technique is used for all the ATLAS electromagnetic

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Ionization Chambers 593

calorimeters, the electromagnetic barrel and end-caps. It is also applied for the

ATLAS hadron calorimeters up to pseudorapidities

∗

η ≤ 5, the forward hadron

calorimeter (FCAL) and the hadronic end-cap (HEC). Many components of the

ATLAS calorimetry system will be located in the high radiation ﬁeld of hadrons

and gammas resulting from the interactions, with surrounding materials, of hadrons

produced by the high rate head-on collisions of 7 TeV protons at an expected peak

luminosity of 1 × 10

−2

−1

at LHC. The radiation level will depend on the

pseudorapidity. In particular, the highest radiation levels are expected to occur at

high pseudorapidity (3 ≤ η ≤ 5) in the forward calorimeter (FCAL) which will be

exposed to a neutron ﬂuence of about 10

n cm

−2

and a γ-dose of 10

Gy over ten

years of LHC operation.

The integration of the FCAL with the hadronic end-caps (HEC) also contributes

to the radiation level in the hadronic end-caps where a neutron ﬂuence of 10

–

n cm

−2

and a γ-dose of 10

–10

Gy are expected over ten years, depending on

the pseudorapidity.

The choice of liquid argon for most of ATLAS calorimeters (the hadron calorime-

ter is based on a sampling technique: plastic scintillating tile embedded in iron ab-

sorber due to ﬁnancial constraints) was largely motivated by the radiation hardness

of the technique. However, a large irradiation level can possibly inﬂict severe damage

to the liquid argon calorimeters such as mechanical damage to parts of equipment,

breakdown of electronics components or deep modiﬁcations of their characteristics

and p ollution of liquid argon with oxygen or oxygen-like impurities released from

the surface of materials and equipments immersed in liquid argon. Therefore, the

operation of the ATLAS liquid argon calorimeters requires radiation hard mate-

rials and equipment, and a limited pollution of liquid argon, below a threshold of

1–2 ppm. The latter can be achieved, if the components of the liquid argon calorime-

ters are certiﬁed against release of polluting impurities under irradiation. Therefore,

the possible outgassing, of components immersed in liquid argon and exposed to high

ﬂuences of neutrons and gammas, is being investigated in conditions similar to those

encountered in the ﬁnal detectors during LHC operation. The tested materials and

equipments are subjected to accelerated irradiation in order to receive a 10-year

dose within a short period of time.

A cold test facility has been built at the Dubna IBR-2 pulsed neutron reactor for

that purpose [Leroy et al. (1999a)]. The facility allows the irradiation of materials

and equipments immersed in liquid argon at high neutron ﬂuences (≈ 10

n cm

−2

per day) and accompanying gamma doses (≈ 10 kGy per day). With these ﬂuences

and doses, the 10-year dose to be encountered at LHC can be achieved after about

∼ 11 days. The large beam geometrical acceptance of 800 cm

oﬀered by this facility

allows the exposure of relatively large areas.

The argon is liquiﬁed at the facility in the argon vessel of the cryostat, using

liquid nitrogen, and the level of liquid argon is kept constant during the whole

∗

One can see Eq. (3.61) in Sect. 3.2.3.1 for a deﬁnition of the pseudorapidity.

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594 Principles of Radiation Interaction in Matter and Detection

Fig. 8.1 Main cryogenic scheme of the facility: (1) cryostat, (2) receiver of gaseous argon, (3)

dewar for liquid nitrogen, (4) liquid nitrogen piping, (5) automatic regulator, (6) argon con-

denser [Leroy et al. (1999b, 2000a)].

irradiation period. As can be seen on Fig. 8.1, the cryogenic system includes the

cryostat (1), the receiver of gaseous argon (2), the dewar ﬁlled with liquid nitrogen

(3), the piping for liquid nitrogen feeding to the cryostat (4), the automatic system

for maintaining constant the level of liquid argon (5), and the argon condenser

(6). The samples of materials to be tested are placed inside the argon vessel of

the cryostat. The volume of the cryostat is ab out 1 liter. An ionization chamber

(α-cell) installed in the cryostat (Fig. 8.1) is used to check for possible outgassing

under irradiation of samples immersed in liquid argon and to monitor the purity of

liquid argon. Since α particles have small range and high ionization power in liquid

argon, the α source is installed directly in the sensitive volume. An

241

Am α-source

with an activity of 7.7 kBq/4π is deposited on the cathode of the α-cell and high

voltages of 0–2 kV are applied to the anode. The gap between anode and cathode is

0.7 mm, which is an order of magnitude larger than the alpha-particle track length

(≈ 0.05 mm) in liquid argon. The α-cell with its readout scheme is illustrated in

Fig. 8.2.

8.3.2 Charge Measurement with the α-Cell

The electron charge from alpha-ionization of liquid argon in the gap is transported

across the cell gap. The collected charge induced by α-particles in liquid argon,

in the presence of low impurity concentration (≤ 10 ppm of oxygen or oxygen-like

impurities) is given by Eq. (8.35). The ratio of the charge signals after and before

irradiation is the attenuation factor, Abs(E), given as a function of the electric ﬁeld,

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Ionization Chambers 595

3.3 nF

1 pF

L = 30 m

51 Ohm

out

Cathode

Anode

Oscilloscope

ADC

DAC

Crate-controller

PC AT-386

50 MOhm

CAMAC

Purity monitor

inside the cryostat

241

Pulse Generator

Shaper

HV power supply

- cellα

Fig. 8.2 α-cell and its readout scheme. The CAMAC electronics is operated on-line by a personal

computer [Leroy et al. (1999b, 2000a)].

E (kV/cm), by

Abs(E) =

Q(E)

ln(1 + ξ)

, (8.36)

Abs(E) =

(

)

1 − e

−D/λ(E)

. (8.37)

Here Q(E) and Q

are the charge signal after and before irradiation, respectively,

where Q

= eE

/w = 37.1 fC for an alpha-particle produced in the decay of

241

(the alpha-particle mean energy, E

, in that decay is 5.48 MeV and W = 23.6 eV are

needed to create an electron–ion pair in pure liquid argon). The function

ln(1 + ξ)

in Eq. (8.36) represents the initial recombination of electron–ion pairs in pure liquid

argon [Thomas and Imel (1987)] and is assumed to be unaﬀected by low impurity

concentrations (below 10 ppm). In Thomas and Imel’s model [Thomas and Imel

(1987)], ξE = 470 kV/cm. However, as seen before, discrepancies between their

model and data have led to the use of the empirical formula [Andrieux et al. (1999);

Leroy et al. (1999a)]:

ξE = a

1 − k e

−bE

, (8.38)

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596 Principles of Radiation Interaction in Matter and Detection

Fig. 8.3 An example of the raw data. Each histogram is an ADC spectrum containing 100k

triggers recorded for two diﬀerent values of the electric ﬁeld in the liquid argon gap of the α-cell

electrodes: 5.7 kV/cm and 25.7 kV/cm. The reference pulse is also shown [Leroy et al. (1999b,

2000a)].

where a, b and k are free parameters to be ﬁtted to the data

∗

. The values of these

three parameters depend on the experimental set-up. The values

a = (720.6 ± 5.6) kV/cm, b = (0.0833 ± 0.004) (kV/cm)

−1

and k = (0.48 ± 0.01),

used to estimate the liquid argon pollution, were obtained by ﬁtting Q(E) data

measured before irradiation.

λ(E) in Eq. (8.37) is the charge carrier absorption length and D is the α-cell

gap. In the case of oxygen pollution with concentration ρ (ppm), λ is given by [Hof-

mann et al. (1976)]:

λ(E) =

αE

(8.39)

with α = 14 mm

ppm/kV.

∗

Compared to [Andrieux et al. (1999)], an additional parameter k has been introduced in [Leroy

et al. (1999a)], this explains the diﬀerent values of a and b used in Eq. (8.19).

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Ionization Chambers 597

Fig. 8.4 Calibration of the ADC scale: (a) set of calibrated pulses from (1–6) mV range are

recorded by the ADC. A Gaussian ﬁt is applied to extract each peak position; (b) generated pulse

amplitudes (in mV) are a linear function of ADC counts (the line is a linear ﬁt to the data). The

ADC has low intrinsic threshold and pedestal zero value; (c) calibration of the ADC scale for the

input capacitor C

◦

= 1.16 pF used in the experiment. The same calibration constants are used for

the data processing before and after each irradiation run [Leroy et al. (1999b, 2000a)].

In practice, for comparison between collected charge measurements performed

before and after irradiation, a normalization factor, F

, is introduced to account

for possible miscalibration of the readout charge:

Q(E)

ln(1 + ξ)

= F

Abs(E). (8.40)

Typical value for F

is (0.997±0.003) for Q(E) data measured before irradiation.

In the following, most examples of the pollution tests results will be presented in

terms of the attenuation factor [the ratio of the charge measured after irradiation to

the charge measured before irradiation, Eqs. (8.36, 8.37)] as a function of the electric

ﬁeld. These plots are easy to interpret: signiﬁcant deviation of the attenuation factor

from unity surely indicates the presence of impurities in liquid argon.

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598 Principles of Radiation Interaction in Matter and Detection

Fig. 8.5 Systematic errors estimated from diﬀerent runs of measurements: (a) uncertainty of the

ﬁt procedure; (b) variation of the reference signal around its average position; (c) uncertainty of

the ADC calibration [Leroy et al. (1999b, 2000a)].

The ADC spectra are recorded for various values of the electric ﬁeld in the range

(2–29) kV/cm. Then, one may determine the α-peak position (Fig. 8.3) and obtain

the electric ﬁeld dependence of the charge collected in the liquid argon gap. Exam-

ples of ADC-spectra are shown in Fig. 8.3 which represents the raw data collected

at two diﬀerent values of the electric ﬁeld in the liquid argon gap of the α-cell:

5.7 kV/cm and 25.7 kV/cm. The reference pulse is generated by a pulse genera-

tor feeding the test input of the preampliﬁer (Fig. 8.2) to monitor the gain of the

preampliﬁer (which is shown stable). The non-Gaussian tails of the α-peaks reveal

the contribution of pick-up signals. The ADC calibration in terms of collected

charge allows the conversion of the ADC counts into charge units (fC). The ADC

calibration procedure is shown in Fig. 8.4.

The data processing consists of three main steps: i) each recorded ADC spectra

have to be ﬁtted by some functional (usually a Gaussian) to ﬁnd the position of

the α-peak, ii) the ﬁtted positions have to be corrected assuming the reference

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Ionization Chambers 599

Evaporation & Liquefaction

Fig. 8.6 Behavior of the argon purity with time: soon after the oxygen probe injection (black

dots) and during a long period (≈ 3 days) after the full mixing of the oxygen probe and the

argon gas (open dots). Dashed lines indicate the expected levels of the oxygen concentration, see

text [Leroy et al. (1999b, 2000a)].

pulse stability and, ﬁnally, iii) the ADC counts must be translated into collected

charge units (fC) for further analysis. Each step gives a certain contribution to

the systematics which has to be summed with the statistical uncertainty from the

(Gaussian) ﬁt. These systematics contributions are: uncertainties due to the ﬁtting

procedure (±5 ADC counts), variation of the reference signal around its average

position ( ±2 ADC counts), and uncertainty of the ADC calibration (±0.01 fC).

The uncertainties due to the ﬁtting procedure can be estimated from the

variations of the peak position as determined from diﬀerent ﬁtting procedures. It

is seen from Fig. 8.3 that, at E = 5.7 kV/cm, the exponential tail of the noise

peak, which is cut by the threshold, should be taken into account. The possible

contribution of additional sources of charge at higher E values can be described by

additional Gaussian’s. On the other hand, each peak of the ADC spectra can be

ﬁtted by a single Gaussian within the ±1 σ interval around the peak position. The

diﬀerences among the results obtained from diﬀerent ﬁtting procedures are pre-

sented in Fig. 8.5(a) over an electric ﬁeld range of (5.7–28) kV/cm. The variations