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The Australian Primary Standard of Air K
erma for
60
Co Radiation (the Carbon Cavity C
hamber)





by




Christopher P Oliver,
John F Boas, Neville J Hargrave,
Robert B Huntley, Lew H Kotler and Keith N Wise


















Technical Report 155

619 Lower Plenty Road

ISSN 0157
-
1400

Yallambie Vic 3085

April 2011

Telephone: +61 3 9433 2211


Fax: + 61 3 9432 1835


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
i

ARPANSA Technical Report No. 155












Notice





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-
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, all other
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Requests and inquiries concerning reproduction and rights should
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addressed to:


Manager, Knowledge Management

ARPANSA

619 Lower Plenty Road

Yallambie VIC 3085

email: info@arpansa.gov.au


All care has been taken in the preparation

of this work and its conclusions.
However, where the data or results presented are utilised by third parties
,

the
Commonwealth of Australia shall not be liable for any special, indirect,
consequential or other damages whatsoever resulting from such use.
Nor will
the Commonwealth of Australia be liable for any damages arising from or in
connection with any errors or omissions that have inadvertently occurred in
this work.



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
ii

ARPANSA Technical Report No. 155

ABSTRACT


The Australian primary standard of air kerma for
60
Co radiation is
a

carbon
(graphi
te) cavity chamber maintained by

ARPANSA. It is a thick walled double
pancake chamber similar to the international refere
nce standard held at
the
Bureau
International des Poids et Mesures (
BIPM
)
. The realisation of the reference air kerma
rate relies on the calculation of a number of cor
rection factors and physical constants.
These fall into two categories
,

the first of which relate to calculating the dose to the
gas inside the chamber and are experimentally determined. The second relate to
converting the dose to the gas in the chamber to

the air kerma rate at that point in
spac
e in the absence of the chamber
.

The method of evaluation and values for all
parameters
is

presented. Monte Carl
o methods have been
recently
used to replace a
number of correction factors
.
As a result, c
hanges to th
e standard are presented.

A
new
60
Co source was
installed at ARPANSA in February 2010. This report will finali
s
e

all work done with the previous

60
Co source and air kerma primary standard.

Appendix 3 gives
preliminary
details of a comparison with the BIPM
in 2010
using
the new ARPANSA
60
Co source.



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
iv

ARPANSA Technical Report No. 155

Table of Contents

ABSTRACT

................................
................................
................................
.................

II

1.

INTRODUCTION

................................
................................
................................
...

1

2.

BASIC DOSIMETRY THEO
RY

................................
................................
.............

2

3.

DESCRIPTION OF THE A
RPANSA CARBON CAVITY

CHAMBER

...................

3

4.

THE DETERMINATION OF

THE AIR KERMA RATE

................................
..........

5

5.

DETERMINATION OF THE

CHAMBER PARAMETERS A
ND THE
PHYSICAL CONSTANTS A
S AT 2001

................................
................................

6

5.1

Determination of the chamber volume

................................
...........................

6

5.2

Ratio of the mean mass energy absorption coefficients

................................
.

6

5.3

Mean energy required to produce an ion pair

................................
................

6

5.4

Stopping power ratio

................................
................................
.......................

6

5.5

Uncertainties in the product
(W/e).s
c,a

................................
............................

7

5.6

Density of air

................................
................................
................................
....

7

5.7

Fraction of energy dissipated outside the cavity

................................
............

8

5.8

Other physical parameters relevant to the ARPANSA graphite cavity
chamber

................................
................................
................................
...........

8

6.

THE
CORRECTION FACTORS A
ND THEIR DETERMINATI
ON AS AT 2001

....

9

6.1

Correction factors and uncertainties applied to the measurement of the
current

................................
................................
................................
.............

9

6.2

Correction factors related to the physical and structural characteristics
of the chamber

................................
................................
................................

11

7.

MONTE
-
CARLO CALCULATIONS O
F THE CORRECTION FAC
TORS BY
K N WISE IN 2001

................................
................................
..............................

17

7.1

History and reasons for moving to Monte Carlo methods

............................

17

8.

MONTE CARLO MODELLIN
G IN 2009 BY C P OLI
VER.

................................
.

19

8.1

Primary standard chamber modelling

................................
..........................

20

8.2

k
wall

................................
................................
................................
.................

22

8.3

k
an

................................
................................
................................
...................

22

8.4









................................
................................
................................
................

23

8.5

(


-


)
................................
................................
................................
...............

23

8.6

(



)




................................
................................
................................
............

23

8.7

k
rn

in 2009

................................
................................
................................
.....

24

8.8

Changes to the Standard using new Monte Carlo values

.............................

25

8.9

Monte Carlo Uncertainties

................................
................................
............

26


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
v

ARPANSA Technical Report No. 155

9.

MEASUREMENTS OF THE
AIR KERMA RATE AND I
TS UNCERTAINTY
BASED ON THE ARPANSA

GRAPHITE CAVITY CHAM
BER

..........................

30

10.

REFERENCES

................................
................................
................................
....

31

APPENDIX 1:

Comparisons with the BIPM and the continuity of the
Australian standard of air kerma

................................
..............

34

A1.1

The 1988 comparison between ARL and BIPM

................................
.................

34

A1.2

The 1997 comparison between ARPANSA and BIPM
................................
........

34

A1.3

90
Sr check source results

................................
................................
.....................

35

A1.4

Uncertainties

................................
................................
................................
......

35

A1.5

Continuity of the Australian standards of air kerma

................................
........

35

APPENDIX 2:

Indirect comparisons of air kerma standards

.........................

37

A2.1

Equipment and
Radiation Sources

................................
................................
.....
37

A2.2

Transfer Chamber Measurements

................................
................................
.....

38

A2.3

Unce
rtainties

................................
................................
................................
......

40

APPENDIX 3:

2010 intercomparison of air kerma primary standards for
Co
-
60 with the BIPM

................................
................................
...

42

APPENDIX 4:

2009 Monte carlo input files

................................
......................

47

A4.1

Co
-
60 spectrum

................................
................................
................................
..

47

A4.2

k
wall



The following file was input to
cavrznrc
to calculate the
k
wall

correction.

................................
................................
................................
............

51

A4.3

k
an



The following two files were used to calculate
k
an
. File 1 uses a
parallel beam and File 2 uses the non
-
parallel beam

................................
........

57

A4.4









-

The following input file was used with sprrznrc to calculate the
stopping power ratio.

................................
................................
.........................

69

A4.5

(


-


)

-

The following input file was used with g to calculate th
e correction
for bremsstrahlung loss

................................
................................
......................

75

A4.6

(



)




The following two files were used with
dosrznrc

to calculate the
mass energy transfer coefficients

................................
................................
......

76

A4.7

k
rn



The following radial profile of the Co
-
60 beam produced using
beamdp

was used for the Monte Carlo determination of
k
rn
.

...........................

87



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
1

ARPANSA Technical Report No. 155

1.

INTRODUCTION


The Australian primary standard of exposure or air kerma for
60
Co radiation is a
thick
-
walled pancake graphite cavity chamber similar in design

to that des
cribed by
Boutillon and Niatel (1973)
.


It was designed and tested during the period 1982
-
1988
and was indirectly compared with the BIPM standard of exposure for
60
Co gamma
radiation in 1988
(Perroche and Hargrave 1989)
,

1997
(Allisy
-
Rober
t
s et

al
.

1989)

and 2010 (Allisy
-
Roberts et al. To be published)
.

As well as the comparisons with
the
BIPM, Australian standards of air kerma have been compared with a number of other
National standards e.g. those held by NRL (New Zealand), NPL (UK), NRCC Canad
a)
and INER (Taiwan).


This report describes the present status of the Australian primary standard of air
kerma for
60
Co radiation and of the correction factors as applied

to the standard as at

01/01/201
1
.


This report has the following aims:



To document
the present status of the physical constants, correction factors and
their un
certainties as of January 1, 201
1, as used in the determination of the air
kerma rate at ARPANSA
.



To indicate where these differ from the values used previously, particularly thos
e
used in the 1988 and 1997 comparisons of air kerma standards with the BIPM
.



To outline the means by which the correction factors were calculated by one of us
(NJH) during the period 1982
-
1988 and the results of a re
-
evaluation carried out
during 1997
-
200
0
, and a further re
-
evaluation in 2009
.



To indicate the implications
on the standard
for the correction factors
evaluated
using

Monte
Carlo methods in

2009.


I
t has been argued

that the
earlier
correction factor
calculations based on
the work of
Boutillon

and Niatel
(1973)

are not sufficiently rigorous
in an era of Monte
Carlo
calculations
. T
he

Monte

Carlo calculations of 2009

re
sult

in an increase of

0.
5
6
%

in
the air kerma rate

which decreases the
difference between

the ARPANSA primary
standard
and

most other
inter
n
ational primary sta
ndards
.




The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
2

ARPANSA Technical Report No. 155

2.

BASIC DOSIMETRY THEO
RY


For
a

cavity chamber
,

t
he quantity
of
air kerma,
K
, is

evaluated at ARPANSA

by the
expression






i
c
en
a
en
a
c
k
s
s
g
e
W
V
Q
K
)
/
(
)
/
(
)
1
(
1
)
)(
(






(1)


where
:


Q

is the charge produced in the volume of dry air
V

with density

ρ

W

is the average energy required to

produce an ion pair in dry air

e

is the electronic charge

g
is the fraction of energy which is dissipated outside the cavity through
bremsstrahlung ra
diation produced in the cavity.

s
c

and
s
a

are the mass stopping powers of graphite and air


en
/ρ)
a

and

en
/ρ)
c

are the mass
-
energy absorption coefficients of air and
graphite respectively

Π
k
i

is the product of all the correction factors descr
i
bed below in
S
ection
6
.




The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
3

ARPANSA Technical Report No. 155

3.

DESCRIPTION OF THE
ARPANSA CARBON CAVIT
Y
CHAMBER


The ARPANSA carbon cavity chamber was machined from homogeneous graphite
and consists of an annular ring and two end plates, forming a right circular cylinder
enclosing a cylindrical graphite disc. The disc acts as the centra
l electrode and is
supported by aluminium rods, anchored through Teflon to the annular ring. The
electrical connection also acts as a support and passes through an insulating bush
inside an aluminium stem attached to the outside of the annular ring.


The d
imensions of the components of the chamber were measured with certified
depth gauges and measuring blocks traceable to Australian measurement standards.
The results are shown in Table 1, with the dimensions of the similar chamber at
BIPM,
(Boutillon and Ni
atel 1973)

also shown for comparison. The calculations of the
chamber volume were re
-
examined in 1997, givi
ng the result in

Table 1, which is
0.11% higher than that used for the 1988 comparison with BIPM. A re
-
calculation in
2001 gave a

result
comparable
to that of 1997 when

rounding
-
off errors

are
considered
. The volume corrections for the ARPANSA chamber are estimates
accounting for the volume of the cavity taken up by the support structures of the
central electrode and the stem.

A re
-
evaluation in 2010
resulted in an increase in the
volume of
0.13% (see Appendix 3).




Figure 1
:

Front radiograph, side radiograph and photo of the carbon cavity chamber


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
4

ARPANSA Technical Report No. 155

Table

1
:

Dimensions and physical properties of the ARPANSA and BIPM
graphite

cavity chambers
.
Values for the ARPANSA chamber
given in parentheses are the
results of the re
-
calculation in
2001


BIPM (1973)

ARPANSA (1997)

Graphite density (g/cm
3
)

1.84

1.726

Annulus wall thickness
(
mm)

2.75

2.721

Mean front and rear wall thickness
(
mm)

2.829

2.821

Internal diameter
(
mm)

41.999

45.023

Internal depth
(
mm)

5.130

5.150 1

Collecting electrode diameter

(
mm)

40.982

41.013 2

Collecting electrode thickness

(
mm)

1.019 5

1.002

Collecting electrode volume (mm
3
)

1344.82

1324.95 (1323.75)

Volume corrections

(mm
3
)


-
28.49

Chamber volume (mm
3
)

6811.6

6845.7 (6847.0)



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
5

ARPANSA Technical Report No. 155

4.

THE DETERMINATION OF

THE AIR KERMA RATE


T
he air kerma rate on the beam axis at the central plane of the chamber

is given by
Eq
uation

1 w
ith
Q

replaced by
I
m
.

I
m

is the mean of the currents measured with
voltages of positive and negative polarity applied to the chamber

,
and
the
other
symbols have the meanings as described in Section
2
. The correction factors and their
uncertainties are discussed in detail in Sect
ion
6
.


The air kerma rate at ARPANSA is determined under the following conditions:



the reference distance between the effective centre of the source and the
geometric centre of the graphite cavity chamber is 993 mm



the field size in air at the reference
distance is a square, approximately 10 cm

×
10
cm



the photon fluence rate at the centre of each side of the square is approximately
50% of the photon fluence rate at the centre of the square



the polarising voltage applied to the chamber is 120 V and the c
urrent is taken as
the mean of the currents obtained when the central electrode is positive and
negative with respect to the chamber wall



o
ne of the flat walls is identified as the front wall and the chamber is always
aligned so
that this wall faces the
source



t
he measured current is converted to the conditions of 20
°
C, 101.325 kPa and
50% relative humidity by the computer associated with the ARPANSA current
integrator. The humidity correction factor is then applied to convert the current
to that at the s
tandard reference conditions for air kerma of 20
°
C, 101.325 kPa
and dry air (ie 0% RH). The uncertainties in Table 3 include those
arising from
both steps



t
he chamber stem is evacuated to less than 1 kPa with
a rotary backing pump



t
he
K

value is the mean of all sets of measurements made with the graphite cavity
chamber

since the installation of the

60
Co source in March 1995 and corrected to
the reference date of the comparison. The half life of
60
Co was taken as 1925.5 d,
σ = 0.5 d
(IAEA

1991)
.



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
6

ARPANSA Technical Report No. 155

5.

DETERMINATION OF THE

CHAMBER PARAMETERS A
ND THE
PHYSICAL CONSTANTS

AS

AT 2001


The physical constants and chamber parameters applicable to the ARPANSA graphite
cavity chamber are listed in Table 2 and are discussed together with their
uncertaintie
s

in the following sections.
1


5.1

Determination of the chamber volume


This was evaluated as described in Section
3
.


5.2

Ratio of the mean mass energy absorption coefficients


(

en
/ρ)
a,c

is the ratio of the mean mass energy absorption coefficients of air and
graphite and was obtained by the convolution of the photon energy fluence spectrum
from the
60
Co source at a distance
of 1 metre, obtained by a Monte
Carlo simulation
(Kotler 1993)

wit
h the mass
-
energy absorption coefficients of Higgins et al.
(1993).
The value
obtained

of 0.9993

is that used in the 1997 comparison of the air kerma
standards of ARPANSA and BIPM
(Allisy
-
Rober
t
s et al 1989)

and is slightly higher
than the value of 0.9987
used
earlier
(Perroche and Hargrave 1989)
.

The latter was
calculated for photon beams of energy 1.25 MeV with no scattered radiation. It should
be noted that the calculations show that approximately 25% of the photon flux at a
distance of 1 metre from the source arise from scattered radiation. The

scattered
radiation component is larger than the 1
4 % reported for the BIPM beam.


The uncertainty in the ratio arises from two components, with the Type A uncertainty
being obtained from the statistical uncertainty in the calculation and the Type B
uncer
tainty being estimated from the uncertainties in the coefficients themselves.


The estimate of the Type B uncertainty is obtained as follows. The uncertainty of the
ratio may range from zero if the uncertainties of the coefficients are completely
correlate
d to about 0.5% if they are not

(Higgins et al. 1993)
.

Since all values between
0 and 0.5% may be equally probable, we treat the distribution as rectangular which
gives an uncertainty of 0.14%.


5.3

Mean energy required to produce an ion pair


W

is the avera
ge energy spent by an electron of charge
e

to produce an ion pair in dry
air. The value of
W/e

recommended by the CCEMRI(I) is 33.97 J/C
(BIPM 1985)
.


5.4

Stopping power ratio


s
c,a

is the ratio of the mean stopping powers of graphite and air. It was obtained by
interpolation from Rogers et al.
(1985, 1986)

to the density of the graphite in the
ARPANSA cavity chamber of 1.726 g/cm
3
. This

value
, 1.000
4, was

used in the 1988



1

The uncertainties in this comparison are expressed as relative standard uncertainties where

s
i
;(v
i
)

represents the type A relative uncertainty

u
A
(x
i
)/
x
i

assessed by statistical means and with the
number of degrees of freedom in parentheses and
u
i

represents the Type B relative standard
uncertainty
u
B
(x
i
)/
x
i

assessed by other means.


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
7

ARPANSA Technical Report No. 155

(Perroche
and Hargrave 1989)

and 1997
(Allisy
-
Rober
t
s et al
.

1989)

comparisons
ofthe air kerma standards of ARPANSA and BIPM. The calculations of Rogers et al.
(1985, 1986)

used the stopping power ratios of Berger and Sel
t
zer
(1982)
.



Table 2:

Physical constants a
nd other parameters applicable to the
ARPANSA graphite cavity chamber and their relative standard
uncertainties

used in the 1997 BIPM comparison

Parameter

ARPANSA
value

Relative standard
uncertainty

100

s
i

; (v
i
)

100 u
i

V

/ cm
3

6.8470

0.02: (64)

0.05

ρ
a

/ kg.m
-
3

1.293
0
(1)

-----

0.01

)
/
(
)
/
(
)
/
(
,






en
en
en
graphite
air
c
a


0.999
3

0.05

0.14




S
air
s
graphite
a
c
s
,

1.000
4

------

0.11
(2)

W/e

(J/C)

33.97



1
-

g

0.9968

-----

0.02

Quadratic sum


0.05


.19

Combined uncertainty


0.20


(1)

For 0
°
C, 101.325 kPa

and no compressibility correction. For 20
°
C, 101.325 kPa and including the
compressibility correction, the value is 1.20447
(Davis

1992)

(2)

Uncertainty in the product
(W/e)
.
s
c,a

, see below.


5.5

Uncertainties in the product
(W/e)
.
s
c,a


The uncertainties of
W/e

and
s
c,a

are expressed as the uncertainty of the product,
(W/e)
.
s
c,a
,
where the combined uncertainty of the product is less than the
uncertainties of the components. This arises because the components are not derived
by completely independent means
(Boutillon and Perroche 1985, Niatel et al. 1985,
Rogers 1995
a
)
. The value given here of 0.11% is that proposed by the CCRI(I) at its
1999 meeting
(Allisy
-
Roberts et al.
1999)

for use by all
National Metrology Institutes
(
NMI
s
)

for the purpose of analysing

key comparison data.


5.6

Density of air


T
he quantity air kerma has very largely replaced exposure. It is defined as the kinetic
energy released per unit mass of dry air for particular reference conditions of

The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
8

ARPANSA Technical Report No. 155

temperature and pressure, not limited to STP.
Previously

the Australian primary
standard of air kerma
was

realised as being that at 0

ºC and
101.325 kPa
using the
density of air given by BIPM for these conditions, namely 1.2930 kg/m
3
. However, we
have
now suggested that it be realised for a temperatur
e of 20 ºC and a pressure of
101.325 kPa, where the density of dry air is evaluated
(Davis 1992)

as 1.20447 kg/m
3
.
This

expression

includes the air compressibility correction fac
tor.


This factor has previously been included as an explicit correction term in the
expression for
the determination of air kerma.

If the previous density of dry air is
used together with Boyle’s and Charles’ laws, but no air compressibility correction
factor,
a
dry air
density of 1.20479 kg/m
3

is obtained for 20 ºC, 101.325 kPa. The new
value of 1.20447 kg/m
3

leads to an increase in t
he air kerma rate of 0.026%.


5.7

Fraction of energy dissipated outside the cavity


The factor
g

is the fraction of the energy deposited in the air cavity which is converted
to bremsstrahlung and thus dissipated outside the air cavity. The value recommended
by the CCEMRI(I) for
60
Co is 0.003 2
(Boutillon 1985)

Although this value was
promulgated in 1
985, a more recent calculation by Borg et al.
(Borg et al. 2000)

gives
the same value, namely
0.0032 with an uncertainty of 5
% i.e. a correction factor of
0.9968 with a relati
ve standard uncertainty of 0.02
%.


5.8

Other physical parameters relevant to the ARPA
NSA graphite
cavity chamber


The following physical parameters do not e
xplicitly appear in equation 1

but are
required for the estimation of the correction factors.


The linear attenuation coefficient


was determined experimentally from the
measurement of

the chamber current as graphite discs were progressively placed in
the beam at the end of the
lead

collimator attached to the source housing. A non
-
linear
,
least squares fit to the equation



e
a
I
x




(
2
)


gave


= 0.010391 mm
-
1

with an asymptotic standard error of 0.48%. The effect of the
difference between this value and that of 0.010381 mm
-
1

used previously is not
significant.



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
9

ARPANSA Technical Report No. 155

6.

THE CORRECTION FACTO
RS AND THEIR DETERMI
NATION

AS AT

2001


Π
k
i

is the product of the correction fact
ors related to the physical characteristics of
the chamber and to the measurement of the current. It is given by



k
k
k
k
k
k
k
k
k
k
k
k
k
k
at
sc
cep
rn
an
st
blb
t
d
RH
P
T
s
i



(
3
)


These correction factors and their relative standard uncertainties are discussed below
and are listed in Tables 3 and
5
.


6.1

Correction factors and uncertainties applied to the measurement of
the current

6.1.1

Correction for incomplete charge recombination


T
he sat
uration correction factor
k
s

is applied to the measured ionisation current to
correct for the incomplete collection of charge due to recombination. For the
continuous radiation case applicable to
60
Co beams, we use the
initial recombination
model

(Kara
-
Michaelova and Lea 1940)

where
k
s

is given by



V
a
I
I
k
m
s
s



1

(
4
)


where
I
s

is the current at saturation i.e. at infinite collecting potential and
I
m

is the
measured current at the voltage applied to the chamber,
V
. The usual polarising
voltage applied to the chamber is
±
120V.

6.1.2

Temperature correction factor


T
he temperature correction factor

k
T
, corrects the measured chamber current for
changes in the mass of air enclosed in the chamber which arise from amb
ient
temperature changes. At ARPANSA

all measured currents are automatically
corrected to the reference condition of 293.15 K (20
o

Celsius) by the
computer
associated with the

current integrator. For an ideal gas, the temperature correction
factor is given by



15
.
293
)
15
.
273
(
T
k
T



(
5
)


where
T

is the measured temperature in degree Celsius. The correction is made using
Boyle’s Law, without allowing for air compressibility. Since the temperature in the
ARPANSA laboratory is usually maintained at 22 ± 1 ºC, the additional uncertainty
introduced by

neglect of this correction factor is less than 0.01%.


The ambient temperature is measured with lineari
s
ed thermistors calibrated
regularly against either certified mercury in glass thermometers or a platinum
resistance thermometer. Both are traceable to

the
s
tandards maintained at
the
National Measurement Laboratory (
NML
)
.


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6.1.3

Pressure correction factor


T
he pressure correction factor
k
P

corrects the ionisation chamber current for the
changes in the mass of air enclosed by the chamber as a result of ambient
pressure
changes. All measurements at ARPANSA

are corrected to standard atmospheric
pressure, namely 101.325 kPa, where the
pressure correction is given by



P
k
a
p
35
.
101


(
6
)


where
P
a

is the measured ambient pressure in kPa. It is assumed that the gas is ideal
and Charles’ law is followed. The uncertainty introduced by neglect of air
compressibility is assumed to be less than 0.01%
.


The value of the ambient pressure used by the comput
er associated with the
ARPANSA current integrator is measured by
a capacitance manometer which
is

regularly calibrated by a Kew p
attern mercury barometer
traceable to
n
ational
s
tandards maintained at NML.
The correc
tion of the current to that at a

pressure of
101.325 kPa is automatically applied by the AR
PANSA

computer controlled current
integrator
.

6.1.4

Humidity correction factor


The factor
k
RH

is
for
the relative humidity correction. This corrects the ionisation
chamber current for the effect of the
variation in water content of the air. A correction
to 50% relative humidity is automatically applied during the internal processing of
the ionisation current measurements (for both the carbon cavity primary standard
chamber and the transfer standard chamb
ers) by the
ARPANSA

computer controlled
current integrator. Thus the output of this device is the ionisation current corrected
to 50% relative humidity. To convert this to dry air a further correction factor of
0.9971 is applied to the carbon cavity chambe
r current for
60
Co radiation. The
correction factor for a given measured relative humidity is obtained from an
empirical formula derived by Hargrave
(1981)
. A more recent evaluation of the
humidity correction

(Rogers and Ross 1988)

also
obtains
a correctio
n factor of
0.9971.


The relative humidity is measured by means of either dial hygrometers or an
electronic humidity sensor. All hygrometers are checked on a regular basis against an
aspirated wet and dry bulb hygrometer.

6.1.5

Background, leakage and bias cur
rent correction factor


Background, leakage effects and bias currents at ARPANSA have been found t
o be
approximately

1

fA for both the primary standard graphite chamber and for
ionisation chambers when the ARPANSA current integrator is used. The
correction
factor

for these effects,

k
blb

is taken as 1.0000 with a relative standard uncertainty of
0.01%.
BIPM includes a multiplicative correction factor to account for leakage
currents observed in the absence of applied voltage
.


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6.1.6

T
he correction factor f
or air compressibility


The air compressibility correction factor
k
z

arises from the deviation of air from ideal
gas behaviour. It is included in the calculation of the air density and is mentioned
here only for completeness.


Table 3:

Correction factors a
pplied to the measurement of the current
from the ARPANSA gr
aphite cavity chamber and their relative
standard uncertainties

in the 1997 BIPM comparison

Factor

Value

100
s
i
;
(
v
i
)

100 u
i

k
s

(recombination)

1.001
2

-------

0.030

k
T

ambient to 20
°
C

20
°
C to
0
°
C

---------

1.073
2

------

0.017

k
P

(ambient pressure to 101.325 kPa)

--------

------

0.020

k
RH

ambient to 50% RH

50% RH to dry air)

---------

0.997
1

----------

----------

0.010

0.010

k
d

(distance to ref. Dist.)

993.00 mm

------

0.030

k
t

(source decay)



0.010

k
blb

(background, leakage and bias
current)

1.0000


0.010

current measurement

Calibration

Repeatability


0.053:5

0.007

Quadratic sum


0.053

0.053

Combined uncertainty


0.075


6.2

Correction factors related to the physical and
structural
characteristics of the chamber


The derivation of these correction factors closely follows the treatment of Boutillon
and Niatel
(1973)
,

for the BIPM chamber
in which the numerical values of the factors
are obtained by a combination of experiment and calculation. Some factors could be
wholly or partially determined by experiments with the ARPANSA carbon cavity
chamber similar to those described by Boutillon and

Niatel
(1973)
.
Some of the terms
in the expressions for the correction factors could be calculated using the parameters
appropriate to the ARPANSA chamber, such as dimensions and graphite density
whilst for others it was necessary to use the
original
valu
es
(Boutillon and Niatel
1973)

for the BIPM chamber. There are also a number of common terms in the
expressions for the correction factors and these are discussed under the correction
factors where they first appear.

6.2.1

T
he stem scatter correction factor


Th
e stem scatter correction factor,

k
st
,

was determined experimentally
(Boutillon and
Niatel 1973)

by attaching a dummy stem to the annular ring in a position

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ARPANSA Technical Report No. 155

diametrically opposite to the actual stem. The mean current from the cavity chamber
with the dummy
stem in place was 9.3625 nA (12 measurements; sd = 0.25%) and
with the dummy stem removed was 9.3492 nA (10 measurements; sd = 0.17%).
Assuming that the stems have no influence on each other, the scatter from a single
stem may be estimated to make a contri
bution of 0.142% to the measured current.
Thus the correction factor may be estimated as 0.9986, with a relative standard
uncertainty of 0.09%
based on an assumed rectangular distribution
.
The value of
k
st

for the BIPM chamber was 1.0000, with a relative
standard uncertainty of 0.01%.

6.2.2

T
he wall attenuation correction


The wall attenuation correction

k
at

was evaluated following the
earlier
procedure
(Boutillon and Niatel 1973)
. The expression for
k
at

is reproduced below.



2
/
)
(
)
(
2
/
)
(
1
2
1
1
1
1
]
)
1
(
)[
1
(
z
z
z
z
c
p
e
z
z
c
p
at
e
e
A
A
e
A
A
k
m
m



















(
7
)


In this equation,
A
p

and
A
c

are the cross
-
section areas of the collecting plate (central
electrode) and cavity respectively,



is the linear attenuation coefficient of the wall
material,
e

is the thickness of the collecting plate,
z

is the abscissa on the beam axis of
a plane perpendicular to
Oz

(better understood as the distance from the source (
O
) to
the point z on the beam axis) and
z
1
,
z
1m
,
z
m

and
z
2

are the distances from
O

to the
incident face of the front wall, the exit face o
f the front wall, the geometric centre of
the cavity (assumed to be the same as the mid
-
point of the electrode) and the exit face
of the rear wall. The only term in this equation unable to be evaluated independently
of
the earlier work
(Boutillon and Niate
l 1973)

is

, the fraction of the total ionisation
current due to electrons originating in the side wall of the chamber. The
ir estimated

value of


= 0.14 gives
k
at

= 1.0389 for the BIPM chamber, with an uncertainty of
0.12%. More recently, BIPM have used
k
at

= 1.0402 with an uncertainty of about
0.04%.
(Allisy
-
Roberts

et al 1989)
.


Experiments in which increasing thicknesses of side wall material were progressively
added to a chamber with an original side wall thickness of 0.5 mm could not be
performed. Figure 4
(Boutillon and Niatel 1973)

shows the relative ionisation current
as a f
unction of wall thickness, from which a value of


= 0.14 was estimated by
extrapolation to zero thickness.
It should be noted
that a

major objection to the use of
the experimental/analytical determinations of the correction factors is the doubt
about the
validity
of the extrapolation procedure.


If we use


= 0.14 and all other terms in the equation are calculated using the
chamber dimensions and linear attenuation coefficient for the ARPANSA chamber,
we obtain
k
at

= 1.0374. This value of
k
at

was used in the 1997 comparison with BIPM
and is slightly less than the value of 1.0377 used in 1988. Since the ARPANSA and
BIPM chambers have almost identical dimensions and wall thicknesses but slightly
different graphite densities, it may be argued that

the change in


is proportional to
the change in graphite density. If so, a change in


to 0.13 or 0.15 only gives a change
in
k
at

of about 0.02%.
Thus t
here would seem to be no basis at present for making a
change in the value of
k
at
.



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The uncertainty wa
s estimated as 0.15% for the 1988 and 1997 comparisons. The
major contributor to the uncertainty is the uncertainty in


arising from the
extrapolation to zero wall thickness. A change in


from 0.1 to 0.2 gives a change in
k
a
t

of 0.23%. From examining Fig
ure 4
(Boutillon and Niatel 1973)

a range in


of this
magnitude would seem to be reasonable. If we then take the range as covering 6
standard deviations (99% confidence level), we can then estimate that one standard
deviation is 0.04%. This is close to th
e present BIPM estimate, although the means by
which BIPM derived this estimate is unknown.
An alternative, more valid approach

is
to
assume a rectangular distribution of


within the range 0.1 to 0.2, an assumption
which is more consistent with the extrapolation procedure. An estimate of the
standard deviation is then approximately 0.07%
.

6.2.3

T
he correction factor for scattering from the chamber walls


This correction
factor
k
s
c

takes account of the contribution to the ionisation current
from the radiation scattered by the chamber walls and was evaluated experimentally
following the procedure of Boutillon and Niatel
(1973)

who used the method
suggested by Allisy
(Allisy 1967)
.

T
he procedure involves the measurement of the
ionisation current as a function of wall thickness, the removal of the contribution due
to attenuation in the wall and the extrapolation to zero thickness. For the front wall, a
quadratic function best fitted th
e data, whereas a linear fit was best for the back and
side walls. The contributions of the various components to the

correction are given in
Table 4
.


An estimate of the uncertainties may be made from the range of possible fits to the
experimental results
. If we again assume a rectangular distribution, we obtain a total
uncertainty of 0.013%.


Thus the value of
k
sc

is 0.9702, which is
not significantly different from

the value of
0.9703 used in 1988 and 1997

when

rounding off errors

are considered
. The BIPM
value
(Boutillon and Niatel 1973)

is 0.9735, although the result arising from the
values of thei
r components as given in Table 4

is 0.9740. The value given by BIPM in
1997 was 0.9716, with a Type A uncertainty of 0.01% and a Type B uncertainty o
f
0.07%. If we take our uncertainty calculated above as a Type A uncertainty, then
ARPANSA and BIPM are in agreement as to the magnitude of this component. It is
difficult to estimate the magnitude of the Type B uncertainties. The 1988 ARPANSA
estimate was

0.10% and it would appear reasonable to retain
this for the total
uncertainty.




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ARPANSA Technical Report No. 155

Table

4
:

The components of the scattering correction factor

Component

ARPANSA

BIPM

Correction
(%)

Correction
(%)

Fitting
Procedure

Range

Uncertainty
(%)

Front Plate

2.25

Quadratic

0.0002

0.007

1.85

Back Plate

0.14

Linear

0.00002

<0.001

0.18

Side walls

0.289

Linear

0.001

0.001

0.39

½ electrode

as front plate

0.347

Quadratic and
additional

calculations

0.0002

0.007

0.23

½ electrode

as back plate

0.21

Linear and
additional

calculations

0.0002

0.007

0.23

Total

3.067



0.013

2.67

6.2.4


The
correction factor for the mean origin of the electrons


Electrons which ionise the air in the cavity are liberated in the wall material by
photons. Therefore the mean centre of
electron production is somewhere in
side

the
wall
. Thus photons penetrate only part of the wall
before releasing an electron
and
can
therefore
be considered only partially
attenuated by the wall.
Consequently

the
photon attenuation is reduced by a correction for the change in the position of the
centre of electron production,
k
CEP

from
the inside surface of the wall
.

This correction
is evaluated following Boutillon and Niatel
(1973)
and the corrected expressio
n



1
)
)
/
(
1
(







r
x
k
pc
CEP



(
8
)


The electron range in the wall material is
r


and we define a reduced variable
r
z
z
x
m





where
z

is the position of the source of electrons which dissipate their
energy in an

volume element of wall material located at
z
m
. The energy dissipation
function
)
(
x
f
pc


allows us to calculate the energy dissipated by electrons originating
from a plane conical source at
z

in a volume element of wall material at
z
m
.
pc
x


is the
first moment of the dissipation function
)
(
x
f
pc



and is the width of the energy
spectrum of the Compton electrons generated in the wall.
r
x
pc



is the mean value of
r
x
pc



for the

Compton electron spectrum generated in the wall . The value of
r
x
pc


for
60
Co radiation calculated
(Boutillon and Niatel 1973)

for a plane conical source is

1.302 kg/m
2
. We note that this is calculated in units of mass per unit area and is
therefore independent of the mass density of the wall material. To apply this value to
a specific chamber in the formulae of Boutillon and Niatel
(1973)
requires division by
the graphi
te density (1.84 g/cm
3

for the BIPM chamber and 1.726 g/cm
3

for the
ARPANSA chamber).



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ARPANSA Technical Report No. 155

The original expression

(Boutillon and Niatel 1973)

did not include


, but is
dimensionally incorrect without it. Both


and



have been measured for the
graphite of the ARPANSA chamber and the value of
r
x
pc



used
earlier
(Boutillon and
Niatel 1973)

is 1.302 kgm
-
2
. The value of
k
CEP

then obtained for the ARPANSA
chamber is 0.9922. The value q
uoted by Boutillon and Niatel
(1973)

is 0.9925, but the
value given by BIPM in 1997 was 0.9922, with a Type B uncertainty of 0.01% (
(Allisy
-
Roberts et al.

1989)
.
The uncertainty quoted by ARPANSA in 1997 was 0.05%.
However, the major source of uncertainty
in this correction factor is in
r
x
pc


, as the
uncertainty in


gives rise to an uncertainty of only 0.003% and therefore the overall
uncertainty should be that quoted by BIPM of 0.01%.
As

the uncertainties
in

k
CEP

are
fully
correlated
they

do not contribute to the overall uncertainty

in a
ny
comparison
between ARPANSA and BIPM
.

6.2.5

The
correction factor due to the axial non
-
uniformity of the beam


The ionisation in the cavity along the beam axis deviates from the ideal
inverse
square law behaviour because of electrons originating in the cavity walls and central
electrode. This deviation is accounted for by an axial non
-
uniformity correction
factor,
k
an ,

calculated following equation (3) of Boutillon and Niatel
(1973)



1
}
)
/
(
)
0
(
[
)
1
(
2
1
{









r
e
F
F
z
u
r
x
z
k
m
pc
m
an


(
9
)


where
e

is the thickness of the central electrode (1.002 mm) and
r


is the electron
range in the wall material (graphite). Since
u
is the thickness of each half cavity
(2.074 mm) and we use Table 5 of Boutillon and Niatel
(1973)

for a distance
z
m

= 1m,
the BIPM
graphite density of 1.84 g/cm
3

and
r
x
pc



=0.1302 g/cm
2
, we find
k
an

= {1 +
0.0014 + (1


0.14)(0.0025)}
-
1

= 0.9965 for the BIPM chamber.


For the ARPANSA chamber, we can calculate the second term in the above expression
given the value of
r
x
pc


and the graphite density for the ARPANSA chamber of 1.726
g/cm
3
. The third term is also dimensionless, which means that
)]
/
(
)
0
(
[
r
e
F
F


must
be dimensionless, but dependent on
1/ρ
, where
ρ

is the graphite density. If we use the
ARPANSA graphite density of 1.726 g/cm
3

and multiply the value of the term
)]
/
(
)
0
(
[
r
e
F
F
z
u
m



b
y the ratio of the densities 1.84/1.762 with
u
= 2

mm and
z
m

= 1
metre and Table 5
(Boutillon and Niatel 1973)
, we find
k
an

= 0.9962, which is similar
to the value of 0.9963 used by ARPANSA in the 1988 and 1997 comparisons with
BIPM. The major source of uncertainty arises from that in the value of λ, where a
change from 0.13 to 0.14 gives a change in
k
an

of only 0.01%.

6.2.6

The r
ad
ial non
-
uniformity correction


T
he radial non
-
uniformity correction
k
rn

accounts for the differences between the
measured air kerma rate from the carbon cavity chamber and that at the centre of the
ion chamber due to the variation of the radiation field ov
er the front face of the cavity

The Australian Primary Standard of Air
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ARPANSA Technical Report No. 155

chamber. It is obtained

from ionisation chamber measurements at points on a grid
10mm apart in a plane perpendicular to the radiation beam
.


Table 5
:

Correction factors and their relative standard uncertainties u
j

associated with the physical characteristics of the ARPANSA
graphite cavity chamber. The values and uncertainties in this
table are those used in the 1997 comparison with BIPM. Some of
the correction factors and their uncertainties have since been
re
-
eval
u
ated, as di
scussed in the text

Correction factor

1997 Value

2001 Value

u
j

(%) 1997

u
j

(%) 2001

k
st

(stem scatter)

0.998 6

No change

0.02

0.09

k
at

(wall attenuation)

1.037 4

No change

0.15

0.07

k
cep

(mean origin of
electrons)

0.992 2

No change

0.05

0.01

k
sc

(chamber wall scatter)

0.970 3

0.9702

0.10

0.10

k
an

(axial non
-

uniformity)

0.996 3

0.9962

0.20

0.10

k
rn

(radial non
-

uniformity)

1.004 0

No change

0.03

0.03

Quadratic sum



0.28

0.18



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7.

MONTE
-
CARLO CALCULATIONS O
F THE CORRECTION
FACTORS

BY K N WISE

IN 2001


7.1

His
tory and reasons for moving to Monte C
arlo methods


The major issue being debated amongst the various NMI’s with primary standards of
air kerma is that of the means of determining the various corrections described
above. As stated
previously,
several of
these were determined initially for the
ARPANSA chamber
following Boutillon and Niatel (1973)
.

Following the 1997
comparison and the discussion during the April 1997 meeting of the CCEMRI (I)
(1997)
the question of the determination
of the correction factors and their
uncertainties was re
-
examined
and calculations based on Monte
Carlo simulations
were initiated. It became clear after 1997 and more so following the discussion during
the May 1999 CCRI(I) meeting
(CCRI 1999)

that the debate is complex and that
considerable work needs to be done to resolve the difficulties. It is clear that a major
weakness of the approach of Boutillon
and Niatel (1973)
is the extrapolation of the
wall scatter correction factor to zero wall th
ickness. Undoubtedly in the future the
correction f
actors calculated through Monte

Carlo simulation will provide what may
be regarded as a more rigorous fou
ndation for a primary standard.


There are four
principal
areas where the calculations outlined
in s
ection 6
may be
open to criticism as a result of more recent studies, principally those of

Rogers and
Treurniet
(
1999)

using Monte
Carlo methods.

7.1.1

Calculations of the correction factors
k
at
,
k
CEP

and
k
sc


The correction factors obtained above by a combinati
on of experiment and
calculation, namely
k
at
,
k
sc

and
k
CEP
, are combined to give
k
wall
.
This factor
ha
s also
been calculated by Monte
Carlo
methods
(Rogers

and Treurniet 1998, Wise 2001)
.

The Monte

Carlo calculations include
k
CEP

in the other two factors, so that a direct
comparison of
k
at

and
k
sc

with the values obtained previously for these two factors is
not meaningful. Wise
(2001)

obtains
k
wall

= 1.0003 with an uncertainty of 0.01%,
which may be compared with the value of 0.99
87 (a revised estimate of the
uncertainty of 0.13%) obtained by the methods of Boutillon and Niatel
(1973)
as
described in the previous section. The value of
k
wall

for the ARPANSA chamber
obtained
(Rogers and Treurniet 1999)

using
EGS
nrc

is 1.00100, with a
n ap
parent
uncertainty of 0.004%
.

7.1.2

The use of more recent mass
-
energy absorption coefficients and stopping
power ratios


The present formulation has used the 1992 mass
-
energy absorption coefficients but
the 1982 stopping power ratios. For consistency, the more recent stopping power
ratios should be used. The calculations of Wise
(2001)
give
s
c,a

= 1.0009
with an
uncertainty
of 0.04%.

7.1.3

Calculations of radial and axial non
-
uniformity corrections


As pointed out by Bielajew
(1990a, 1990b)

the radial and axial non
-
uniformity
corrections need to take into account the fact that the radiation emanates from what

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Page No.
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ARPANSA Technical Report No. 155

is effectively a point

source and is not a parallel beam when it strikes the incident wall
of the chamber. The analytical formulation of Bielajew
(1990b)
leads to a point source
non
-
uniformity correction factor,
k
pn
, of 1.0031 for the BIPM chamber. This may be
compared with the

value of 0.9980 given by the product
k
rn
k
an
. If the same value of
k
pn

applies to the ARPANSA chamber, it may be compared with the value of the
product
k
rn
k
an

from Table 5

of 1.0002.

7.1.4

Additional corrections obtained t
hrough Monte
Carlo simulations


These ar
e what Rogers
and Treurniet (1999)
call the “Spencer
-
Attix” correction
(electrons for which Δ < 10keV) and the corrections for non
-
graphite material in the
chamber. These corrections have been calculated for the BIPM chamber but not for
the ARPANSA chamber
.

7.1.5

Summary of effect of using
Wise’s
Monte
Carlo calculations


If the wall correction factor and the stopping power ratio as calculated by Wise
(2001)

are used, the effect is to increase the air kerma rate by 0.21%. If the point source non
-
uniformity correction factor calculated by Bielajew
(1990a, 1990b)

for the BIPM
chamber is taken to apply to the ARPANSA chamber for the radial and axial non
-
uniformit
y correction factors, the air kerma rate is increased by a further 0.29%,
giving a total increase of 0.50%. This is in agreement with the calculations of Rogers
and
Treurniet
(
1999
)

for the ARPANSA chamber.



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
19

ARPANSA Technical Report No. 155

8.

MONTE
CARLO

MODELLING

IN
2009

BY C P OLIVER


For

the recalculation of
correction factors

performed in 2009

using Monte Carlo
methods
, the approach prese
nted by Burns (2006) was followed
. This is
equivalent

to
the
formalism presented in section 2

but has a few subtle differences. It is given by














(10)

w
here

















(11)


k
rn
,
k
s
,
k
st

are the corrections for radial non
-
uniformity, recombination losses and
stem

scatter respectively.
W
,
e
,
Q
,
m

are the same as in Eq
uatio
n 1.
D
cav,exp
,
k
rn
,
k
st

and
k
s

are determined experimentally.
G
k

is evaluated usin
g Monte Carlo methods and is
given by






(



)



(





)
(


)








(12)


where:

(

tr
/

)
a,c

is the spectrum averaged ratio of mass
-
energy transfer coefficients of
air and graphite

(L/

)
c,a

is the Spencer
-
Attix spectrum averaged ratio of the mass collision
stopping powers of graphite to air

k
an

is the axial non
-
uniformity correction

k
wall

is the correction for photon scattering and attenuation in the chamber
walls
.


According to this f
ormalism, the stopping power ratio,
ratio of
mass energy transfer
coefficient
s

and correction for radiative loss are all calculated under ideal conditions.
This assumes charged particle equilibrium, a parallel photon field and no attenuation
or scattering
of the incident photon fie
ld. For more information see

Burns

(2006)
.


The first part of the Monte Carlo modelling was to simulate the ARPANSA
60
Co
source and build a phase space file at an appropriate distance from the source
position.
This was done using
BEAMnrc

(Rogers et. al 1995
b
)
. The source head
geometry
previously presented by Wise

(2001
) was used

as shown in Figure 2
. The
Cobalt source was modelled using two photons of equal probability with energies
1.175 and 1.335 MV. No bremsstrahlung splitting w
as used to avoid any occurrence of
fat photons, and electron range rejection was used with varying ECUTRR to decrease
the simulation time. A global value for ECUT of 0.7 MeV was used. The result of the
source model was a phase space file containing the ene
rgy and trajectories of al
l
particles incident on the plan
e coincident with the front face of the chamber. Analysis
of the phase space file revealed that it was a circular beam of radius 5 cm. This is
different to the experimentally measured
60
Co beam whic
h is a 10x10cm square
beam. Unfortunately no information was available to determine what collimation was
being used to produce the 10x10cm beam. Using a circular

instead of square field is
not ideal but should not make a significant difference in the subse
quent correction
factor calculations due to minimal scattering in air of
60
Co radiation. This was
tested
by recalculating
various
correction factors using different field sizes.


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
20

ARPANSA Technical Report No. 155

8.1

Primary standard chamber modelling


The chamber was modelled as the g
raphite central electrode, annular ring and the
fro
n
t and rear
plates centred on the reference point 99.3 cm from the
60
Co source.
The central electrode is a cylinder of thickness 0.1002

cm and radius 2.0507

cm. This
is surrounded by the air cavity which h
as thickness 0.515

cm and radius 0.2512

cm.
This is then enclosed by the annular ring and the front and rear face plates which
measure 1.07920

cm in thickness with

radius 2.5233

cm.
The model of
the chamber is
shown in Figure 3
.
The scoring region for the
measured dose is the air cavity region.
The central electrode supports and earthing wires of the chamber were not included
in the model. PEGS4 was used to create cros
s
section data for the graphite material
used in

the chamber. This new material was labell
ed 1726C. A density of 1.726

g/cm3
was used which had been previously measured

by Huntley (1998)
. The density
corrections used were for graphite of density

1.70

g/cm3. This may not be correct as
other studi
es have indicated that alternate

density

corrections should be used (Rogers
et. al. 2003
a
)
. The values of AE, UE, AP, UP used in generating the cross section data
for 1726C were the same as those used
for

materials in the data set 512ICRUpegs4.dat
which is distributed with
EGSnrc
.


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
21

ARPANSA Technical Report No. 155


Figure 2
:

60
Co source head geometry used for BEAMnrc simulation

as used by Wise (2001)
and Oliver in 2009.



12mm

17mm

1mm

steel

250mm

50.7mm

47.5mm

32.4mm

45mm

28.2mm

111mm

100mm

123mm

139.2mm

Lead

60
Co

Tungsten

Lead


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
22

ARPANSA Technical Report No. 155



Figure 3
:

Cross sectional view of the model of the carbon cavity chamber. The full chamber
is generated by rotating this cross section around the Z axis.


8.2

k
wall


k
wall

is calculated as the ratio of the dose to the gas in the chamber

cavity,
D
gas
, in the
case of no photon attenuation or scattering in the chamber walls, to
D
gas

with
attenuation and scattering present. This was calculated using the phase space model
of the

60
Co source
and

cavrznrc

(
Rogers et al 2000)
. The

ratio was calculated to be
1.00
09. This compares favourably with the value for the BIPM stan
dard of 1.0011
(Burns et al 2007
). The
previous

calculation of this quantity
at ARPANSA
relies on
the
determination of three correcti
on factors
k
at
,
k
s
c

and
k
cep

which are the corrections
for wall attenuation, wall scattering and the mean origin of electrons respectively.
The
wall attenuation and scatter were

calculated using the linear extrapolation
proce
dure which ha
s been shown to be incorrect

(McCaffrey et al 2004
). If the
previous

k
wall

is calculated by combining
k
at
,
k
sc
, and
k
cep
, the value is 0.9986. Thus
the new Monte Carlo value for
k
wal
l

result
s

in an increase in the
reference air kerma
rate of
0.23
%.


8.3

k
an


The axial non
-
uniformity is calculated using the following equation






(




)

(




)


(13)


where
D
gas
k
wall

is the dose to the cavity gas corrected for scattering and attenuation of
incident photons in the chamber wall. The ratio calculated w
as 1.0026. This is similar

to the value calculated by Burn
s for the BIPM

chamber of 1.0020 (Burns et. al
. 2007
).

2.821mm

25.233mm

20.507mm

22.512mm

2.074mm

1.002mm

2.074mm

2.821mm

R

Z


The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
23

ARPANSA Technical Report No. 155

This Mon
te Carlo value is +0.64
% higher than the
most
previous

value
used by
ARPANSA
which is base
d

on the work of Boutillon and Niatel

(1973
).


8.4

(


)




The stopping power ratio was calculated using
sprrznrc

(Rogers et al 2000)
. This
program calculates
Spencer
-
Attix restricted mean mass stopping

power ratios for
each region of

the chamber defined in the model. For this calculation the chamber is
modelled as a solid graphite cylinder

and photon regeneration is employed

so that
only primary photons contrib
ute to the calculation of the stopping power ratio. The
average value of the stopping power ratio in all the regions which are air in the real
chamber were used to
calculate

the stopping power ratio. The geometry of the
chamber will not alte
r the stopping
powers

due to photon regeneration being
employed. The value calculated of 1.0020 is
s
lightly higher t
han the BIPM value of
1.0010(Burns et al 2007
). No correction has been included for the change in electron
fluence due to the presence of the air cavity wh
ich has bee
n included in other studies
(Burns 2006
). The value
previously

used by ARPANSA of 1.0004 was int
erpolated
from Rogers et al.(1985, 1986
). The
new
Monte Carlo value

increase
s

the air kerma
rate
by +0.16%.


8.5

(





)

The fraction of energy lost to

bremsstrahlung in the solid graphite chamber



was
calculated using the user code
g

(Rogers et al 2000)
. The value of
(





)

calculated
was 1.0024 and is the same a
s that calculated by Burns (2006)

for the BIPM
chamber
. The
previous

value is

for air so a direct comparison is not possible.
No
correction was made for any energy re
-
absorption from the bremsstrahlung. A
correction factor for this re
-
absorption was calculated by Burns with a value of
0.99
96 reported (Burns 2006)
. The previously us
ed correction for bremsstra
h
lung
production used at ARPANSA was taken from
calculations by Borg et al (2000)
.


8.6

(



)




The
mean
mass energy transfer coefficient
ratio
was calculated using
dosrznrc

(Rogers et al 2000)
with the calculation of kerma enabled. By switching off electron
transport, the ratio of air kerma to graphite kerma results in a Monte Carlo
evaluation of the appropriate ratio of mean mass energy transport
coefficients of air
to graphite
. Photon forcing
was enabled to provide adequate statistics for this
calculation. The calculated value is 0.9995 which compares favourabl
y with Burns
value of 0.9996
for the BIPM chamber
(Burns 2006)
.
The
previous

product
(




)



(





)

used by ARPANSA
can be compare
d to the Monte Carlo calculated

product
(




)



(





)

with the new product resulting in a change of
-
0.06%.
The

mean mass energy absorption coefficients
used

previously

were obtained by
convolution of the then calculated photon energy spectrum with
the mass energy
absorption coe
fficients of
Higgins et al (1993)
.



The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
24

ARPANSA Technical Report No. 155

8.7

k
rn

in 2009





was calculated using the formalism presented by

Delaunay et

al (2007)
.
T
his
correction factor requires the profile of the radiation beam to be determined. This is
then
fitted using an easy to integrate polynomial function of the form


















(14)


The correction factor is then calculated as





















(15)


where
R

is the radius of the charge collecting cavity.


The correction factor is equal to the function at the reference point



divided by the
mean value of the profile on the surface of the charge collecting cavity of the
ioni
s
ation chamber. The radial non
-
uniformity was determined using the phase space
file

radial profile and
additionally
by experimentally measuring the radial profile
using a 0.3cc ioni
s
ation chamber. The profile of the beam was calculated from the
phase space source using
beamdp

which is included in the
BEAM
nrc

distribution. It
is known tha
t the beam shape is square and not circular as determined from the
phase space source. However for this calculation it was assumed that the variation in
the profile of the circular beam would be similar to that of the
real
square shaped
beam over the cross

section presented by the cavity chamber. The correction factor
determined using this method was 0.9993.


Radial profiles were also measured using a 0.3cc ioni
s
ation chamber. Using the
vertical profile the value of



was 1.0014. Using the horizontal pr
ofile

the value of



was 1.0016. Due to the variability involved in the calculation, a value of 1.0000
will be adopted

here with an uncertainty of 0.15
%. It has been reported that this
correction factor should be ve
ry close to unity for norm
al calibration distances
(Rogers 2003
a
)
. The val
ue of this

correction factor is 0.4% lower th
an what was

previously

used at ARPANSA. The value
for

the BIPM
chamber in their beam
is
1.0015 (Burns 2007)
. This is in very close agreem
ent with both experimental values of



calculated here. This is fortuitous as it is only a function of the radial profile of the
incident photon beam and cannot be directly compared to the ARPANSA value
.





The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
25

ARPANSA Technical Report No. 155

8.8

Changes to
the
Standard using new Monte Carl
o
values


Table 6
:

Summary of Monte Carlo results compared to
previous

values

Correction
Factor

2001 Value

2009 Value

% Change

(




)




(




)




= 0.9993

0.9995

-
0.06%

(





)

(





)

= 1.0032

1.0024

(


)




1.0004

1.0020

+0.16%




0.996
2

1.0028

+0.64
%




0.9987

1.0009

+0.22%




1.0040

1.0000

-
0.40%

Total change

+0.
56
%


It has been estimated that moving to Monte Carlo
values

would increase the average
air kerma st
andard

by approximately +0.8% (Rogers et
.

al. 2003b).

The change
reporte
d here of +0.56
% is in reasonable

agr
eem
ent with this value. Figure 4

shows
the degrees of equivalence for air kerma standards relative to ARPANSA reported for
the recent Euromet 813 comparison

(Cs
et
e

2010)
. The average variation of all
labs
relative to ARPANSA is +0.15%. If only the results that are traceable to a primary
standard other than the B
IPM are considered, see Figure 5
, the variation is +0.29%.
This variation increases to +0.42% if the two

lowest results are discarded.
Increasi
ng
the ARPANSA standard by +0.56
% giv
es a result shown in Figure
5
labelled
‘ARPANSA MC


with the current

ARPA
NSA result labelled ‘
ARPANSA current
’.




The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
26

ARPANSA Technical Report No. 155



Figure 4
:

Current
degrees of equivalence for air kerma standards relative to ARPANSA
reported for the

Eura
met no. 813 comparison

(Csete 2010).





Figure

5
:

Comparison of ‘
ARPANSA (current)’ and ‘ARPANSA (MC
)’ results with air kerma
results traceable to primary standards.

All data except ‘ARPANSA (MC)’ from
Euramet no. 813 comparison (Csete 2010).


8.9

Monte
Carlo Uncertainties


All Monte Carlo correction factors have a statistical uncertainty but these are
generally at or below 0.03% and thus the non
-
statistical uncertainties are usually
as
or
more significant. The following discussion of uncertainties
relates to these Type B
uncertainties.

-40
-30
-20
-10
0
10
20
30
LNE-LNHB
CIEMAT
CMI
LNMC-RMTC
SSM
STUK
NRPA
SMU
IAEA
HAEC-HIRCL
BIM
IRB
GUM
ITN-LMRIR
PTB
BEV
METAS
VSL
ENEA
NIST
NRC
LNMRI
VNIIM
CNEA_CAE
MKEH
-25
-20
-15
-10
-5
0
5
10
15

The Australian Primary Standard of Air
-
Kerma for
60
Co Radiation

Page No.
27

ARPANSA Technical Report No. 155

(




)






This calculation is not dependent on electron transport since
it

is
disabled in the calculation. Photon transport effects will be cancelled out in the ratio





. The major source of error is the uncertainty arising from the choice of cross
section data. The value used by
Burns (2006)

based on the work of Seltzer and
Bergstrom of 0.04% will be used here.


(





)



The value of 0.02% used by Burns
(2006)

based on t
he uncertainty in the
bremsstrahlung cross section will be used here.