NBS MONOGRAPH 48

Determination of Total X-Ray Beam Energy

Witii a Calibrated Ionization Chamber

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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Documents, Government Printing Office, Washington 25, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Determination of Total X-Ray Beam Energy

With a Calibrated Ionization Chamber

John S. Pruitt and Steve R. Domen

National Bureau of Standards Monograph 48

Issued June S, 1962

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. Price 20 cents
Contents

Page

1. Introduction 1

2. Description of the P2 chamber 1

3. Use of the P2 chamber 3

4. Cahbration of chamber P2-4 5

5. Sensitivity of P2-4 to monoenergetic photons . 7

6. Variations of the P2 cahbration 9

7. References 16

II
Determination of Total X-Ray Beam Energy With a Calibrated

Ionization Chamber*

John S. Pruitt and Steve R. Domen

This report describes the use of an air-filled aluminum-alloy ionization chamber to determine the energy transported by a bremsstrahlung beam with maximum photon energy in the range 6 to 170 Mev. The experimental calibrations of this chamber over this energy

range are given, as well as the results of calibration experiments made with a 250-kv constantpotential X-ray tube and with Cs^" and Co"" gamma-rays. Information is presented about

the change in calibration when the chamber is used with different experimental conditions,

and when either its dimensions or its alloy composition are changed slightly. This report can be used to construct a replica chamber and to determine its absolute calibration between

6 and 170 Mev under a variety of experimental conditions.

1. Inti

The proper evaluation of most experiments performed with a betatron or synchrotron X-ray

beam requires knowledge of the absolute number

of incident photons of each energy. This knowledge can be obtained by calculating the relative

spectral intensity distribution as a function of

photon energy, which can be predicted theoretically with reasonable accuracy [1],^ and determining the total beam energy with a calibrated

monitor. This energy is proportional to the area under the spectral distribution curve, and can be

used to assign absolute values to the distribution

at each photon energy.

The proper calibration of the beam monitor is an

important task in most radiation experiments,

where the accuracy of the results depends upon

the accuracy with which the incident energy is known. Several different techniques for performing this task have been described, relying

either upon theoretical descriptions of the interaction of X-rays with matter, or upon experimental energy measm-ements [2]. The theoretical

descriptions require knowledge of atomic parameters which are not accurately known for highenergy bremsstrahlung beams, such as average

electronic stopping powers, but the experimental

techniques of beam energy measurement have

now been developed to the point where a monitor

can be calibrated experimentally to within a few

percent.

2. Description of

Detailed shop drawings of the P2 chamber ac- company this Monograph (figs. 17, IS, 19), but its

principal features, the thick front wall and the

multicellular ionization-coUection assembly, are shown in the schematic cross section of figure 1 and the photographs of figures 2 and 3. These

chambers were designed for use in X-ray beams up

to 20 cm in diameter and with intensities ranging

*This work was supported in part by the Atomic Energy Commission.

1 Figures in brackets indicate the literature references at the end of this Monograph,

This report concerns the experimental method

used in the High Energy Radiation Section of the

National Bureau of Standards for rapid and

accurate calibration of X-ray monitors for beams

with maximum photon energy between i?inax=6 and

-E'max=l70 Mev. The method is based upon

results obtained in a series of experiments [3],

performed with two instruments which determine

the total beam energy in absolute units, a refined

version of the lead calorimeter described by

Laughlin and Beattie [4], and a large scintillation

crystal [5].

These absolute beam-energy measurements were

used to calibrate an ionization chamber of a type

labeled P2, so that a measurement of the ionization

charge collected during an X-ray exposure determines the total beam energy incident on the front

face of the chamber. This chamber has been

classified as a Standard Instrument, and its calibration is expressed as the energy in joules re- quired to produce one coulomb of ionization charge

inside the chamber when it contains dry air at

20 °C and a pressure of 760 mm of mercury. The

calibrated chamber is used in this laboratory either

to transfer the absolute calibration to special monitors used in radiation experiments, or as a con- tinuous-duty monitor in cases where its large

dimensions are not inconvenient.

the P2 Chamber

from 0.5 to 1,000 /xw/cm^ The manner in which

the design was affected by these criteria is described below.

The diameter of the chamber was choseit to be

large both to allow its use with large-diameter

X-ray beams and to reduce the dependence of the

calibration on beam diameter. The calibration

depends on the size of the beam because a part of

the radiation scattered in the tliick front wall

misses the air cavity, and the fraction escaping

increases with increasing beam diameter. Tlie

1
diameter of the internal plates is 29.2 cm, large

enough so that the calibration decreases by no

more than 0.1 percent as the beam diameter in- creases from 0 to 4 cm, and by no more than 3

percent for an increase to 20 cm.

HN CONNECTOR

6,0 cm

0.08 cm

34 cm

Collocloi ^ KEL-F

STEEL

BRASS REMAINING PARTS - 2024 DURAL Figure 1. Schematic cross section of a P2 chamber.

The front wall is made of 2024 Dural, an aluminum alloy whose composition is shown in table

1. Its thickness was chosen to minimize the

dependence of the calibration, joules/coulomb, on

the maximum photon energy of the bremsstrahlung beam. The calibration depends on the

maximum photon energy because it is a function

of the spectral distribution of the incident photons,

which changes with the maximum energy. The

spectral distribution is also a function of the

beam filtration, so although it is possible to

minimize the variation with maximum energy for a given filtration, there is no choice which will

make this variation small for all filters. The

thickness chosen is 9.4 cm, which reduces this

Table 1. Composition of £024 Dural

Element

Percentage by weight

Nominal Limits

Aluminum 93.4 90. 9-94. 7 Copper 4, .5 3. 8- 4.

Magnesium., 1. 5 1. 2- 1. 8 Manganese 0.6 0. 3- 0.

Silicon 0 - .5 Iron 0 - .5 0 - .25

0 - .10

0 - .16

Zinc .— Chromiumother

• This alloy was called 24S Dural prior to 1954.

Figure 2. External view of a P2 chamber. Figure 3. lonization-collection assembly of a P2 chamber.

2
variation to 10 percent between 6 and 170 Mev,

with a filtration of 4.5 g/cm^ of aluminum.^

The internal plate assembly, where ionization

is produced and collected, contains dry air at

atmospheric pressure. It was designed to have

high sensitivity and low leakage, so that it could

be used with low-intensity beams, and a small

probability for ion recombination, so that it could also be used with high-intensity beams.

These divergent requirements were met by using

a thick air cavity (5 cm), divided into 12 segments

by thin Dural plates. These are alternately

high-voltage and collector plates, mounted in two

interleaved stacks. Tlie two outer plates are high-voltage plates, and are considerably heavier

than the inner plates. The plates within each

stack are separated by ground steel spacers,

which serve to connect them electrically. Each

stack is mounted on Kel-F insulators, which are

in turn mounted on the grounded front cover, so that there is no direct leakage path between the

two stacks. This style of construction insures

that the total thickness of the air cavity remains

fixed, and that the calibration will not change

even if the assembly is dismantled and reas- sembled. These advantages, plus the relative

compactness of the P2 chamber, are the reasons

this design was chosen in preference to the design

of Wilson [6], where ionization is sampled at

several depths in an absorbing medium of essentially infinite thickness.

3. Use of the P2 Chamber

Figure 4 is a schematic diagram of the experimental arrangement during a typical calibration

transfer from a P2 chamber to a thin-walled

monitor used with the 180-Mev synchrotron.

X-rays incident on the P2 chamber are filtered

by one wall of the donut (the evacuated electronacceleration tube) and the monitor. The size

and shape of the direct beam in such an arrangement are determined by the aperture in the

main lead shield, but radiation scattered in the

main shield, the monitor walls, and the air adds

a second, more divergent component to the beam.

The auxiliary lead shields shown in figure 4 were

inserted to reduce the spurious effects produced

by this second component. The one in front of

the monitor reduced its response to this scattered

component, a precaution which increased the

reliability of the monitor calibration, since it has

been found that the secondary to primary intensity ratio is a function of changes in operating

conditions.^ The auxiliary shield behind the

monitor guards against backscattered radiation.

The auxiliary shield in front of the P2 chamber

served to limit the fraction of this scattered

component incident on the chamber. In this

particular experiment, it was necessary to know

the amount of radiation energy incident on an

area 9 cm in diameter and 70 cm behind the

monitor. The P2 chamber was mounted with

its front face at this position with a 9-cm-diam

hole in the lead shield in front of it. The beam

was only 4.2 cm in diameter at this position, but

this technique included a 9-cm-diam scattered2 If the chamber is used with a different filter, or at maximum energies outside this range, the variation of the calibration with peak energy may be

large in the region of interest. It can usually be reduced over a limited range by changing the front-wall thickness.

' For instance, the monitor response, per unit energy in the direct beam,

increases by about 3 percent when the synchrotron donut air pressure in- creases from 6X10-8 to 35X10-' mm of mercury. This is caused by an increase in the relative number of secondary electrons from the main shielding aperture, which is in turn caused by an increase in the size of the X-ray soui-ce. A sizable fraction of the monitor response (of the order of 50 percent) is caused by these scattered electrons, so ic will change when the relative electron- intensity changes. The P2 response is much less affected by these electrons, although it is affected by scattered photons, as discussed in the text.

P2

CHAMBER

MONITOR

MAIN LEAD

SHIELD

SYNCHROTRON

TARGET

Figure 4. Experimental arrangement during a typical monitor culibrution.

3
EXPERIMENT ROOM CONTROL ROOM

POTENTIOMETER

100 foot cable

HEAD BODY ELECTROMETER

1 = INPUT

F= FEEDBACK

G= GROUND

FiGtTBE 5. Electrical circuit used for ionization-charge

measurement.

photon beam in the energy deternimation. The

need to consider this secondary beam decreases

as the distance between P2 and tlae monitor

increases, but at the smah separation shown in

figure 4, the secondary beam may contribute as mucli as 1 percent to tlie energy incident on tlie P2 chan\ber. Although this scattered component

has been slightly degraded in energy, the chamber

calibration varies too slowly with energy to be

noticeably changed by this degradation.

The ionization charge collected in the P2

chamber during an X-ray exposure is measured

with the modified Townsend balance circuit

shown in figure 5. The required components are a high-quality polystyrene capacitor, C, a stable source of high voltage, Ej, a slide-wire

potentiometer which is used as a source of compensating voltage, Ec, and a vibrating reed

electrometer. Coaxial cables with a solid polyethylene dielectric are used to connect the P2

chamber to the power supply and to the electrometer. The electrometer cable is of the lownoise variety, with a semiconductor coating on

the dielectric.

The electrometer used in this laboratory is a three-terminal model divided into two components, which are mounted in separate rooms

and connected by a 100-ft cable. The head of the

electrometer is mounted in the experunent room

close to the P2 chamber, to reduce the length

of the input cable. The head contains two

amplifier tubes and supports a grounded metal

box covering the external capacitor, C, which

must be carefuUj^ shielded against stray radiation.

C is mounted between the input and feedback

terminals of the electrometer, in parallel with a small internal capacitor, C (about 10 pf). The

amplified signal enters the main body of the

electrometer through the 100-ft cable. This

component contains most of the electronic chcuitry, the zeroing controls, range selector, and

output meter. It is located in the accelerator

control room, where the calibration data are recorded.

The potentiometer is a commercial 1.6-v model,

constructed so that it can be periodically and

easily calibrated with a self-contained standard

cell. It is connected in series with the electrometer feedback loop by means of an external con- nector on the electrometer. It is used as a source

of accurately known voltage, which can be con- veniently varied from Ec=0 to Ec=l.Q v. The source of high voltage, Ei, is a battery power

supply consisting of 67.5-v dry cells connected in

series. They are mounted in a temperatureregulated box to reduce the electrometer drift

currents caused by changes in the ambient temperature. A total of 1,200 V is normally used with

high-intensity X-ray beams in this laboratory.

This voltage is large enough to reduce the error caused by ion recombination to about 0.1 percent

with a synchrotron beam intensity * of 400

/xw/cm^. This was determined by plotting the

measured ratio i?c/monitor-volt as a function of

the ratio relative-intensity/i?/, and making a

linear extrapolation to zero intensity [7]. Values of Er as large as 2,200 v have been used

with no evidence of gas multiplication, but the

electrometer drift currents were too large for

convenient operation. With 1,200 v, this

drift cm-rent is normally less than 10"^" amp.

Larger currents signify direct leakage between the

electrodes, which is usually caused by lint in the

air cavity. This can often be corrected by re- moving the plate assembly and blowing it out

with a high-pressure jet of nitrogen, but on oc- casion it is necessary to dismantle and clean the

components to achieve a drift current as small as

this.

When the P2 chamber is used with low-intensity

X-ray beams, recombination problems are less

severe, and Ei=800 v is usually used. This

reduces the chamber leakage, and electrometer

drift currents of the order of 10~'* amp are typical.

The electrometer is always used as a null instrument rather than as a deflection instrument,

so that accurate charge measurements can be

made without knowing the leakage capacitances

to ground or the absolute electrometer calibration.

With the compensating voltage Ec=0, C is discharged with the shorting switch before an X-ray

exposure. The electrometer is then zeroed on a

sensitive scale and the exposure begun. During

exposure, the electrometer needle may be kept

on scale either by continuously increasing Ec or by switching to a less sensitive scale.

After an exposure has been completed, the needle is returned to its initial position by adjusting

Ec. The ionization charge collected in the P2

chamber during the exposure can be calculated

from the equation

g (coulomb) = [(7 (farad) + (farad)] X^'c (volt),

(1)

where Cand C are the capacitances of the external

and internal capacitors in the electrometer head

< The synchrotron produces 60 X-ray pulses per second, and with this in- tensity, each pulse produces an ionization density of about 2 X lO-i* cou- lombs/cms.

4
and Ec is the compensating voltage required to

return the electrometer needle to its initial position. Ec can be obtained directly from the calibrated potentiometer, and (C+C) can be determined by the d-c comparison method described

below.

Absolute knowledge of (C'-fC) can be obtained

with the equipment of figure 5, plus a standard air

capacitor of known capacitance, Cs, and a second

potentiometer used as a variable soui'ce of voltage,

Eg. The comparison circuit is similar to that of

figure 5, except that the P2 chamber is replaced

by Cs and the high-voltage supply by Es, to form

a simple series loop between terminal / and ground.

The polarity of Eg must be such that an increase of

Es will move the electrometer needle in the opposite direction from that caused by an increase of

Ec. The measurement is made by first zeroing the

electrometer needle with the condensers discharged and Ec=Es=0, and then determining

the value of one (say Eg) required to return the

needle to its initial position after the other (Ec)

has been changed. Then

C+C'=^Cs (2) Ec

and {C-\-C') is known in terms of Cs-^

The P2 chamber can itself be used as a con- tinuous-duty exposure monitor, or it can be used

to calibrate a different monitor, as in the situation

shown in figure 4. The auxiliary monitors used

in this laboratory are usually transmission-ionization chambers, of the general type shown in

figure 6. This is a thin-walled chamber for use

in relatively high-intensity beams. The walls and

air gaps as shown are thin enough to prevent

BNC CONNECTOR

Figure 6. Schematic cross section of an ionizationchamber monitor.

noticeable ion recombination in the X-ray beams

used in this laboratory, but if the charge liberated

per pulse of X-rays is larger in another laboratory,

the recombination probability may increase

enough to make even smaller dimensions mandatory.^ The high voltage normally used with this

type of monitor is about 150 v. Monitor voltage measurements are always made

with the same type of circuit as that shown in

figure 5 for the P2 chamber, so that the transfer

of a P2 calibration to a transmission chamber

requires two electrometers and additional capacitors. The monitor calibration can be expressed

in joules/monitor-volt, so that there is no need for

absolute knowledge of the capacitances used with

the monitor.

4. Calibration of Chamber P2-4

The ionization charge collected in a P2 chamber

is related to the incident radiation energy by

Energy (joules) =2 (coulombs)

XCal (joules/coulomb) (3)

where g (coulombs) is the measured ionization

charge and Cal (joules/coulomb) is the chamber

calibration, a number wliich varies with maximum

photon energy. One of the NBS chambers, P2-4,

has been calibrated in bremsstrahlung beams

between 6 and 170 Mev in a series of four experiments performed with the two NBS circidar

electron accelerators, a 50-Mev betatron, and a 180-AIev synchrotron. Each experiment consisted of two measurements at a variety of

, maximum energies. The first part was a determination of the ionization charge collected in a

5 Alteinate-current measurement of (C+C) will not give the proper value

to use in eq (1) if these capacitors are not air dielectric. For polystyrene

capacitors, measurements at 1,000 c/s underestimate the capacitance by as much as several tenths of one percent. Altcrnate-curi-ent measurements are

also more cumbersome because thi-ce measurements are required to eliminate the effects of capacities to ground.

P2 chamber per unit monitor response, using an

experimental arrangement similar to that of

figure 4. The second part was a determination

of the total incident beam energy per unit monitor

response, and was performed by replacing the P2

chamber by an absolute energj^-measuring

instrument.

These four experiments are compared in table 2. The first experunent was performed with a scintillating crystal [5], covering the energy range

between 20 and 170 Mev. The next two experiments were performed with a calorimeter [3],

between 18 and 42 Mev and between 20 and 170

Mev, respectively. Experiment 4 was perl'oi'med

with a crystal [3] to investigate energies between G

and 19 Mev, a region of great importance to

nuclear physics, but one where the intensities

of the NBS accelerators were too small foi' calorimeter measurements. The data fi'om expei'imcnt

"According to the theory presented in refcreni'e 17), llie probaliilil y of

reconitiiiial ion is a function of the charge liberated per |)ulse, which can be taken as indpiji I imiid to the ratio of the time average X-ray intensity to the pulse repetition late.

5
Table 2. High-energy calibration experiments

Experiment No.

Date of experiment

Participants

Accelerator Target material Energy range Mev

Apparatus

Filtration gjcnfi Beam diameter cm

1957

J. E. Leiss R. A. SchraclfJ. S. Pruitt.-. synchrotron.-. tungsten

20-170

crystal

4. S 1.5

1958

.T. S. Pruitt—

S. R. Domen_

betatron tungsten...

18-42 calorimeter.

3.0

4.2

1959

T. S. Pruitt...

S. R. Domen.

synchrotron... tungsten

20-170 calorimeter

4.5

4.2

1959

E. G. Fuller E. Hayward

betatron tungsten

6-19

crystal7.3

5.5

1 yielded a calibration curve with an estimated

error of ± 3 percent, that from exjDeriments 2 and 3 a curve with an estimated error of dz2 percent,

and the data of experiment 4 has been assigned

an error of ±2 percent. These errors are not

maximum errors, but they are all considerably

more conservative than probable errors. In the

calorimeter experiments, for example, both the

net systematic error (the square root of the sum

of the squares of six different systematic errors)

and the standard deviation of the mean of the

calorimeter measurements at each energy were

of the order of 0.5 percent. The quoted ±2

percent error was obtained by adding the former

to three times the latter.

The calibrations of P2-4 obtained in these four

experiments are listed in table 3 and plotted in

figure 7. They are in good agreement where the

energy ranges overlap, except at high energies.

Even in this region, however, they agree to within

the stated errors except at 110 Mev. They

have all been corrected to refer to the beam size

and filtration used in experiment 3, 4.2 cm diam

and 4.5 g/cm^ of aluminum,'' using data presented

in section 6. These corrections were larger than

0.2 percent only for experiment 4, and the maximum was 1.0 percent at 6 Mev.

The solid curve in figure 7 is considered a best

fit to the experimental points (the significance of

"The filtration in each experiment included a donut wall, 4.1 g/cm^ of Pyrex for tlic synchrotron, and 1.6 g/cm-" of ceramic for the betatron. Calculations have shown that the filtration corrections are changed by less than

0.1 percent if the donut wall is treated as an equivalent g/cm^ of aluminum.

E

3.5

1 1 1 1 1 1

^—*T1 n

1 1 1 1

"CALORIMETER. N8S, 1958, 1959

• SPECTROMETER, NBS, 1957, 1959

" POHLIT, I960 i EDWARDS ond KERST. 1953

•

*

1 1 1 i

1 1 1 1 1 1

FiGUKE 7. calibration at 20 °C and 760 mm of

mercury in a 4-2-cm-diam bremsstrahlung beam filtered by 4-5 glcm^ of aluminum.

The solid curve is a best fit to the experimental data, and the dashed curves

are postulated extremes in the shape of the curve.

Table 3. Absolute calibrations of chamber P2-4 in a 4.2- cm-diam X-ray beam filtered by 4.5 g/cm^ of aluminum, at 20 °C and 760 mm of mercury

Crystal experiments Calorimeter experiments

Maximum Cal (P2-4) Maximum Gal (P2-4) energy energy

Experiment 1 Experiment 2

Mev joules1coulomb Mev joules1coulomb

19.6 4. 04X10* 18.2 4. 19X105

24.6 4. 14 19.8 4. 18 29.6 4. 10 21.7 4. 17 34.6 4. 10 25.9 4. 15 39.6 4. 07 31.3 4. 13 44.7 3. 96 36.7 4. 11 49.7 3. 86 42.

4. 14 59.7 3.82 69.8 3. 73 89.8 3. 71 Experiment 3 109.9 3.60

130.0 3.64

150.3.69 20 4. 12X105

170.2 3.71 25 4. 08

30 4.11

35 4. 10 Experiment 4 40 4. 05

45 4.02

50 3. 99 6 4. 10X105 60 3.94

8 4. 17 70 3.86

10 3. 99 90 3.80

13 4.07 110 3.84

16 4. 09 130 3. 81

19 4. 17 150 3.82

170 3. 87

the other two curves is explained in the following

section). Above 20 Mev, its shape was obtained

from a weighted average of calorimeter and crystal

points, where the weights were inversely proportional to the quoted errors. Below 20 Mev, the

shape of the curve was influenced b}' the results

of additional experimental calibrations made with

7-rays and X-rays of energy less than 1.5 Mev.

These extra calibrations were made to help

determine the sensitivity of P2-4 to monoenergetic

photons, as described in the following section.

The 34.5-Mev calibration plotted in figure 7 is based on calorimeter raeasm'ements made at the

Max Planck Institut fiir Biophj'sik in Frankfurt

[8]. They were made to calibrate P2-6, a replica

chamber belonging to this institute, and were

transferred to P2-4 by direct comparison of the

two chambers, as described in section 6. The

plotted point has been corrected to a beam

diameter of 4.2 cm and a filtration of 4.5 g/cm^

of aluminum.

The 146-Mev calibration is based on calorimeter

measurements made at the University of Illinois

6
[9]. They were transferred to P2-4 by constructing a replica of the lUinois chamber and comparing it with P2-4 at the NBS. No corrections

have been made for differences in beam filtration

and diameter, but these corrections should be

very small.

The P2-4 calibration was also determined at

low energies, in experiments using radioactive sources and a 250-kv constant potential X-ray

tube, and the results are listed in tables 4 and 5.

Table 4. Absolute calibration of chamber P2-4 in a 4.2- cm-diani y-ray beam at 20 °C and 760 mm of mercury

Source Photon energy Cal (J°2-4)

Mev joules/coulomb

0. 66 4. 59X105

Co«° 1.25 4. 14

Table 5. Absolute calibration of P2-4 in a 4-2-cni-diam

low-energy X-ray beam at 20 °C and 760 mm of mercury

Filter thickness Cal (P2-4)

Al Pb Sn Cu

Mev

0. 050

.100

. 150 .200

.250 .250

mm

3

3

3

3

3

6. 18

mm

0. 125

. 53

mm mm jouleslcoulomb

CO 72 XIO*

12.4 8.34

7. 03

6. 91

1.54 4.0

1.0 1.0

4. 15

0. 61 .59 11.850. 7 2.7

2.7

In each case, the photon-beam intensity was obtained from measurements of the exposure dose in

roentgens/min, and the calibration was taken to

be the product of intensity (watts/cm^) and beam

cross section (cm^), divided by the ionization cur- rent (amperes). The beam was 6.4 cm in diameter in each experiment, but small corrections

have been applied to the calibrations listed in

tables 4 and 5 so that they refer to a 4.2-cm beam.

In the experiments with radioactive sources,

measurements of roentgens/min were made with

a carbon cavity chamber [10], and the beam intensities were calculated using the conversion factors of 2,959 ergs/cmVroentgen for Cs'" [11] and

1.0

1 1 1 1 1

ITY ^ 0.8

UJ / w —

H

2 / 0.150 1 / 0 200 I [ 0 250 \\

0.6 w —

1-<

UJtr 0.4 1 -

XO

e

UJ

. 0.2

Ul — /

1 —

0 /

OI50

E, Mev

Figure 8. Relative speciral-intensiiy distributions for

filtered X-ray beams obtained from a 250-Kv constantpotential X-ray tube. The small peak between 0.07 Mev and the K absorption edge of lead at 0.088 Mev belongs to the lightly filtered 0.250-Mev spectrum.

3,391 ergs/cmVroentgen for Co*'° [12]. In the X-ray

tube experiments, measurements of roentgens/min

were made with a free-air ionization chamber [13],

and the beam intensities were calculated from the

equation

watts/cm^ _ 1 roentgen/min 6

xio -8 Jo

j: R(E)

(4)

where I{E,E^^^) is the differential intensity spectrum in units proportional to watts/cmVMev, and

R{E) is the conversion factor ergs/cm^/roentgen for

photons of energy E. I{E,Eaia.x) was calculated by

assuming that at these low energies, the unfiltered

intensity spectra are proportional to (Em!,x~E) [1],

and correcting for filtration with published total

attenuation coefficients [14]. The filtered spectra

are shown in figure 8. R{E) was taken from the

literature [15].

5. Sensitivity of P2-4 to IVIonoenergetic Photons

The calibration of an ionization chamber can

be calculated from the equation

Cab r I{E,E^,ME

j;

S{E)I{E,E^,ME

(5)

where I{E,E^s,:,) is the differential intensity

spectrum at the face of the chamber, and SiE)

is the chamber sensitivity for photons of energy

E, the ionization charge produced by unit incidentradiation energy. Knowledge of the sensitivity

is a prerequisite for calculation of the manner in

which the calibration depends on the X-ray

spectrum.

The sensitivity of P2-4 to monoenergetic

photons is plotted as a function of photon energy

in figure 9. The solid curve was obtained by

solving eq (5) for S{E), using the calibrations

described in the previous section. With the

data of table 5, I(E,Emax) was taken from figure 8. In this case the solution was obtained by assigning

5.570 —62-

I
>->p

mz

bJ

Mini 1 1 1 nil 1 1 1 1 III 1 1 1 1 III 1

/

"^""^

\\

\

1

/

1 IXII 1 1 1 nil 1 1 mil 1

1 Mill 1

E, Mev

Figure 9. Sensiiivity of PS-4 to a 4-^-cm-diam beam of monoenergetic photons, at 20 °C and 760 mm of mercury.

The solid curve is a best fit to the experimental data, and the dashed curves

postulated extremes in the shape of the curve.

an average photon energy to each of these spectra,

plotting 1/Cal (P2-4) at this energy, in figure 9,

drawing a smooth curve through tliese points,

and calculating Cal (P2-4) from eq (5). The

discrepancy between calculated and measured

calibrations was removed by adjustment of the

average energies.

The values of S{E) plotted at 0.66 and 1.25

Alev in figure 9 are simply the inverse of the

calibrations listed in table 4 for Cs^" and Co^°,

respectively, since the spectra are approximately

delta functions. At higher energies, eq (5) was

solved for S{E) hy the inverse-matrix technique

described in reference [16]. In this case, the

calibrations came from the solid curve in figure

7, and I(E,E^^:^) was taken from tabulations of

Schiff integrated-over-angles differential-intensity

spectra [17], corrected for a filtration of 4.5

g/cm^ of aluminum [18]. Examples of the predicted spectra are shown in figure 10. This

high-energy solution for SiE) reproduces the

solid-calibration curve of figure 7 to a few tenths

of 1 percent.

The estimated uncertainties in the sensitivity curve are indicated by vertical lines at low photon

energies. The radioactive source errors include

uncertainties of + 3 percent, —1 percent in the

determination of roentgens/min,^ and errors in

the conversion to intensitv units of ±1.5 percent

for Cs'" and ±1.2 percent for Co'°. The X-ray

tube errors include ± 1 percent for the roentgens/

min determinations, ±3 percent for the conversion to intensity units, and ±1 percent for uncertainty in the average energies. The plotted

errors are the sums of these individual errors.

* This asymmetry arises from the presence of scattered radiation, which is not completely understood at present but is under study.

Figure 10. Relative spectral-intensity distributions for

bremsstrahlung beams filtered by 4-5 g/cm- of ahminum.

The estimated errors in S{E) above 2 Mev

were obtained by maldng the trial distortions of the

calibration cm've shown b}" dashed lines in figure

7. These cmves lie -within ±2 percent of the

solid best-fit curve, but include changes in curvature winch aft'ect the sensitivit}" curve more

drastically than a simple change in absolute

magnitude does. They change the predicted

sensitivitj^ curve as sho\vn by the dashed lines in

figure 9. It is jjossible to predict values of

S{E) outside of the dashed cmwes by postulating

additional oscillations of the calibratioii curve,

but tins would be difficult to justify' because all of

the physical interactions which determine the

calibration vary slowly mth energ}'. This analysis of the uncertainty in S{E) shows that the

precise shape of the sensitivity curve is not very

well kno^vn at liigh energies, but the presence of

two maximums appears to be well established, and

this can be qualitatively explained with the following arguments.

At low photon energies, the shape of S{E) is determined by the photon-attenuation coefficients

in Dural, which decrease rapidly with increasing

E, so that an increasing fraction of the incident

energy penetrates the thick front wall of the

chamber. In the neighborhood of a few Mev,

the product of attenuation coefficient and wall

thickness is of the order of unity, and the exponential absorption is less sensitive to changes in

energy. In this region, the predominant effect

is a decrease in the efficiency of converting photon

energy into electron energy, giving rise to the lowenergy maximum in S{E).

At higher photon energies, the increasing range

of the secondary electrons means that the region

in the Dural where the electrons producing air

ionization are generated moves toward the front

of the chamber. This decreases the effective

wall attenuation and increases S(E). This increased electron range also means that a larger

volume of Dural is contributing to air ionization,

but tiiis change does not affect the calibration

because it is compensated by a decrease in the

fraction of its energy which each electron deposits

in the air cavity. At energies where the electron

8
ranges are comparable with the front-wall thick- ness (40 Mev electrons), the volume of Dural

contributing to the ionization no longer increases

with energy, but the fraction of energy deposited

by each electron continues to decrease with increasing energy. At the same time, bremsstrahlung production increases, and an increasing

fraction of the secondary electron energy is recon- verted into photons and becomes unavailable for

ionization production. These two effects in

combination cause a drop in S{E) and lead to the

high-energy maximum.

6. Variations of the P2 Calibration

The P2-4 bremsstrahlung calibration curve of

figure 7 cannot be used directly for an arbitrary

X-ray exposure, because the calibration depends

upon the value of several experimental parameters,

whicli may differ from the values used during the

calibration experiments. These are

1 . The temperature and pressure of the air in

the chamber.

2. The thickness and atomic number of the

filters in the X-ray beam.

3. The diameter and intensity distribution of

the incident beam.

The variation with air temperature and pressure

obeys the ideal gas laws, and the calibration may

be corrected for this variation by multiplying

it bv the factor

i^.„=2.592 (i+273.2)

P

(6)

where t and p are respectively the temperature

(°C) and pressure (mm of mercury) of the air in

the chamber during an exposure, t can be read

from the attached thermometer, but p must be

determined from a measurement made outside the

chamber. This factor would also include a small

humidity correction except for the use of drier in

the chamber air inlet.

The variation with filter thickness and atomic

number must be calculated with the help of eq

(5), and with I{E,E^^-^), the Schiff unfiltered spectrum [17], corrected for absorption by the materials

in the beam. These corrections multiply the unfiltered spectrum by an exponential of the form

where ti is the thickness of the ith

filter and jiiE) is its attenuation coefficient for

photons of energy E. The values of S{E) used

in this calculation may be taken directly from

figure 9. The correction for filtration multiplies

the calibration of figure 7 by a second factor:

Cal {tuZ,)

Cal (4.5 g/cm^ of Al) (7)

These calculations have been performed for the

special cases of aluminum and copper filters using

total attenuation coefficients from references [14]

and [18], which assume that no scattered photons

from the filter reach the P2 chamber. The values

of Ff obtained are shown in figures 11 and 12 as a function of filter thickness, ^(g/cm^), for a few

representative values of £'max- The variation with

energy in the aluminum curves is quite regular,

but the copper curves exhibit a maximum near

100 Mev for large t, related to the minimum in

S{E) at 14 Mev. These curves are almost independent of errors in the assumed spectra and

absorption coefficients, but they do depend on the

precise shape of S{E). If S{E) lies within the

limits shown in figure 9, figures 11 and 12 are accurate to within ±0.2 percent for i< 4.5 g/cm^

of aluminum and 2 g/cm^ of copper, respectively.

The uncertainties for thicker filters increase

approximately linearly with t and are about ±0.8

percent at 50 g/cm^, for energies less than 50 Mev.

They are smaller for high energies, and are only

about ±0.3 percent at 170 Mev, for t=5Q g/cm-.

The variation with beam diameter and intensity

distribution was investigated by observing the

1.04

0.5 I 2 5 10 20

t, g/cm^ OF ALUMINUM

FiGUEE 11. Batio of P2-Jf calibration in a beam filtered by t g/cm- of aluminum to P2-4c alibration in a beam

filtered by 4-5 g/cm"^ of aluminum.

0.5 12 5 10

t, g/cm^ OF COPPER

Figure 12. Ratio of P2-4 calibration in a beam filtered by t g/cm''' of copper to P2-4 calibration in a beam fillercd by Jf.n g/cm- of abiminum.

9
Figure 13. Relative dependence of calibration on

radius of beam incidence.

20 50

Figure 14. Energy-dependent multiplier used to calculate dependence of P2-4 calibration on radius of beam inci- dence.

1.04

Figure 15. Batio of P2-4 calibration in an X-ray beam

of diameter D to that in a 4-2-cm-diam beam, for beams of uniform intensity.

change in response when a P2 chamber was

bombarded at different radii by 1.5-cm-diam

beams of various i?max, and of unit total energy.

This change depended on the ^'max used, but it was

found that the dependence on radius, r (cm),

could be separated from the dependence on

-E'max, and the relative response could be ex- pressed as

i?(r,£'.ax) = l-/l(r)/2(£':nax). (8)

The functions /i(r) and /2(-E'max) are plotted in

figures 13 and 14, respectively. The latter has

been arbitrarily normalized to unity near 10 Mev.

The beam-size correction multiplies the calibration of figure 7 by the factor

rI{r,Era^^)R{r,Er,

771 JO

,)dr rlir,

rI{r,E^^^)R{r,E^^^)dr

r2.i

Jo

rI{r,E^^y,)dr

(9)

where R{r,E^^^ comes from eq (8) and I(r,E^^,,)

is the relative intensity of the incident beam at

radius r. These calculations have been performed

for the ideal case where the beam intensity is

uniform (for r<^y and the results are shown ^

as a function of D in figure 15 for several values

of i^maxThe corrections for beam filtration and diameter

for the calibration experiments came directly from

figures 11 and 15, respectively. The beam intensity was not uniform in these experiments, but the

corrections for beam diameter were almost negligible, and are quite insensitive to the precise

shape of /(r,£'max).

The three factors of eqs (6), (7), and (9) are enough to correct the P2-4 calibration for use in

most experimental situations, but a fourth factor

is required if a difl^erent P2 chamber is used.

This is

Cal (replica chamber)

Cal (P2-4)

(10)

a factor which is most reliably determined by

direct experimental comparison of the replica

chamber with either P2-4 itself or another chamber which has been compared with P2-4. The

comparisons are made with the experimental ar- rangement of figure 4, measuring the P2 ionization

charge collected per unit monitor response for each

of the chambers in turn. At the present time

there are eleven P2 chambers which have been

experimentally intercompared.

The first four, P2-1 to P2-4, belong to the National Bureau of Standards, and the measured

' These curves are based on measurements with a beam filtered by 4,5 g/cm2 of aluminum and may change slightly if the filtration is changed.

10
values of for these chambers are listed in table

6 for several maximum photon energies between 6

and 170 Mev. The remaining seven chambers

belong in various institutes around the world.

Their locations are shown in table 7, along with

the measured values of Fc and the energies at

which these measurements were made [19]. Their

labels, P2-?^, correspond to the order in which

they were calibrated.

Table 6. Measured calibration ratios, Fc, of NBS P2

chambers

\\

Chamber \^

6 Mev 14 Mev 32 Mev 70 Mev 170 Mev

P2-1 0. 994 0. 996 0. 996 0.994 0.998 P2-2 .994 .995 .995 .994 .996 P2-3 .996 .999 .998 .998 .998

a P2-4 1.000 1.000 1.000 1.000 1.000

a Equal to unity by definition of F,.

rr-r

Figure 16. Fractional decrease in calibration per

glcm^ increase in front-wall thickness.

In using eq (11), it is convenient to define X

and T in terms of thicknesses and densities of the

individual chamber components:

X=X(1) +.Y(4) +A^(10) + 5.5.Y(11);

XU) = pU)t(j) (12)

r=6[f(14)-T(ll)] (13)

Table 7. Measured calibration ratios of other P2 chambers

Chamber Institute

P2-5 Institut National d'llygiene, Paris, France.

Mev

18220. 994

.994

P2-6 Max Planck Institut fiir Biophysili,

Frankfurt-am-Main, Germany.

20

34.5

I. 001

0. 999

P2-7 Kantonsspital Ziirich, Ziirich, Switzerland.

31 .991

P2-8 Institut .lozef Stefan, Ljubljana,

Yugoslavia.

18 to 30 1.028

P2-9

P2-10 Tohoku University, Sendai, Japan. 3232

1.000

1.001

P2-11 University of Illinois, Urbana, Illinois, U.S.A.

38 1.008

The calibrations of these chambers differ for

several reasons. The calibration is a function of

X (g/cm-), the mass thickness of the front wall,

T (cm), the total thickness of the air cavity in the

ion collection assembly, and Z, the atomic number

of the front-wall alloy. It is a simple matter to

predict the variation with X and T. For chambers made of the same alloy, where X and T are only slightly different from the X and T iov P2-4,

the change in calibration is a linear function of

these differences:

F,^l+a{X,-X,)-h{T,-T,), (11)

where subscript i refers to the dimensions of chamber V2-i. The coeflicient a has been determined

at several values of i^max between 6 and 170 Mev

by measuring the change in the response of P2-4

when X is changed, and is plotted in figure 16.

The coefficient 6 =0.20 cm~\ tlie inverse of the

nominal value of T.

where the numbers in parentheses refer to the

corresponding pieces in the chamber plans. p{j)

and t (j) are respectively the density (g/cm^) and

thickness (cm) of piece No. j}° Note that eq (12)

includes half the total thickness of the eleven

inner plates, so that the front-wall thickness is measured to the center of the ion-collection assembly. The quantities f(14) and T(ll) in eq (13)

are, respectively, the average thicknesses of the

spacers in the high-voltage stack of plates and of

the inner plates in the collector stack.

The values of and T are known for several

of the chambers which have been intercompared,

and these are listed in table 8, along with the

values of Fc calculated from eq (11). The alloy

densities listed indicate that the alloy compositions

of these chambers are approximately the same.

It can be seen from this table that the predicted

7^/s agree with the measured values to within a few tenths of one percent, which is within the

uncertainties inherent in the measurements of Fc,

X, and T.

Table 8. Physical -parameters and calibration ratios of

several P2 chambers

F

Chamber ax X T

Calculated Measured

A/fi> g/ciri' cm

P2-1 32 27. 30 5. OBI 0. 998 0. 996 2. 786 P2-2 32 27. 30 5. 063 .997 .995 2. 786 P2-3 32 27. 43 5. 069 .999 .998 2. 790 P2-4 32 27.41 5. 062 1. 000 1.000 2. 790 P2-5 22 27. 25 5. 073 0. 995 0. 994 2. 787 P2-9 32 27. 38 5. 060 .999 1. 000 2. 793 P2-10 32 27. 39 5. 052 1. 000 1. 001 2. 794

I" /(I). <(4), and ((10) should be measured near the ceMlcrs of the corre- sponding pieces .since their faces are seldom flat.

11
The abnormally large for P2-8 (table 7) is caused by changed dhnensions, smce the inner

plates used in this chamber are 1 mm thick instead

of 0.8 mm, as specified in the chamber plans.

This change should reduce T by 0.12 cm and

increase Xhj 0.3 g/cm^, which would be expected

to increase the calibration by about 3 percent, in

reasonable agreement with the measured increase.

The dependence of the calibrations on Z is more

difficult to analyze quantitatively, since the

physical interactions which determine the calibration depend upon Z in different ways. Per

atom, the probability of a Compton interaction

varies as Z, that for pair* production varies as Z^,

and the electron stopping power varies as Z. As

an alternative approach, this effect has been

investigated at several energies by replacing the

removable plates of P2-4 (piece No. 4) by plates

made of two different alloys, 1100 Dural (99%

pure aluminum; p=2.713 g/cni^) and 7178 Dural

(2.0% copper, 2.7% magnesium, 6.8%o zinc, 0.3%

chromium; p=2.827 g/cm'), and observing the

change in calibration. The plates were machined

to have the same mass thickness as the plates

they replaced (19.82 g/cm^) to elmiinate the effects

of changes in The measured changes are listed

in table 9. They indicate that an increase in the

alloy purity will decrease the chamber calibration

below about 100 Mev and will increase it at higlier

energies. It must be remembered that pieces

Nos. 1, 10, and 11 were not changed in these tests, so that the effect of using either of these alloys

throughout the chamber will be even larger. If

each of the numbers in table 9 is expressed as

1 +e, the proper number to be used for chambers

constructed completely of these alloys should be

about 1 +1.4 e, where 1.4 is the ratio [A'(l) +A'

(4)+X(10)]/X(4).

It is tempting to use the alloy density, p, which

can be relatively easily measured, as a rough

measm-e of Z. There is no exact proportionality

between these quantities, but addition of heavy

metals usually increases both p and Z. Then an

empirical term like

c{pi-PiY (14)

could be added to eq (11) in an attempt to account

for changed alloy composition. The 32-Mev data

in table 9 indicates that c =0.13 and ^=0.95, at

least at this energy. This term would subtract

0.001 from the calculated listed for P2-1, P2-2,

and P2-.5 in table 8 and add 0.001 to the calculated

Fc for P2-9 and P2-10. These changes improve

the agreement between the calculated and measured Fc in each case, but the improvement is fortuitous. It is felt that this empirical correction

term should only be used as a rough indication of

Table 9. Effect of changing the alloy composition of the

P2-J,- front wall

Em as Oal (1100) Cal (7178) Cal (2024) Cal (2024)

Meo

6 1.000

11 0. 998

18 .995 32 .992 1.004

70 .996 90 .995

120 1.002

150 1.002

170 1.006

the change resulting from use of a different alloy,

and should be treated skeptically if it is larger

than about 0.002. The safest way to predict Fc

is to use an alloy with approximately the same

composition and density as 2024 Dural, so that

this term is negligible.

In summary of the information presented in this

section, the calibration of an arbitrary P2 chamber

is related to the P2-4 calibration by

Cal (replica) =i^,pF^i'^o^,X Cal (P2-4). (15)

The factors Ftp, Ff, and correct for changes in

experimental conditions and can be calculated

from eq (6), (7), and (9), respectively. F^ comes

from eq (10) and should be measured experimentally, but can be predicted with reasonable

accuracy from eq (11) if the composition of the

aluminum alloy is close to that of P2-4.

The authors thank the nuclear physicists of the

NBS High Energy Radiation Section for their

appreciation of the value of an absolutely calibrated ionization-chamber beam monitor, and for

their consequent interest and help in this project.

Particular thanks are extended to E. G. Frdler,

E. Hayward, J. E. Leiss, and R. A. Schrack for

permission to present the results of thek scintillation spectrometer experiments, to R. A. Schrack

for his help with the filtration computations, and

to H. W. Koch and J. E. Leiss for their help in

the preparation of this manuscript.

We also thank S. W. Smith for providing the

facilities for the low-energy sensitivity measurements, and H. O. Wyckoff for his help with their

interpretation and for his help in arranging the

replica chamber comparisons. These latter were performed with the cooperation of A. AUisy and

M. Tubiana of Paris, M. Pohlit of Frankfurt,

G. Joyet of Zurich, C. Zupancic of Ljubljana,

M. Kimura of Sendai, and N. Goldwasser, R.

Carrigan, and W. Swanson of Urbana, and we

are grateful for their interest which made these

comparisons possible.

12
13
O 5Co

ui !2 < O Q

_i w

Q. 5 =

5! (T tr . ^ Q _ Q.

J

I m

o

d

o

Q

z _

UJ C3 O o" iti

o

> _I I UJ X

o

(M

0.

Z3o

00

«

p

-1o

<

o

UJ

cr

O ir o ^ — 0.

UJX

CO

O _|Z

<Q. UJ O

CO

14
15
7. References

[1] H. W. Koch and J. W. Motz, Bremsstrahlung cross- section formulas and related data, Rev. Mod. Phys.

31, 920 (1959).

[2] A comprehensive list of references to techniques

described prior to 1954 may be found in Appendix

B of NBS Handb. 55, Protection against betatronsvnchrotron radiations up to 100 million electron

volts (1954).

[3] J. S. Pruitt and S. R. Domen, Calorimetric X-ray

monitor calibration at betatron energies. Radiation

Research 9, (1958) A; and E. G. Fuller and E. Haward, Calibration of a monitor for use in bremsstrahlung beams, J. Research NBS 65A

(Phys. and Chem.) No. 5, 401 (1961). A description of the two calorimeter experiments will be

published in 1962.

[4] J. S. Laughlin and J. W. Beattie, Calorimetric determination of the energy flux of 22.5 Mev X-rays,

Rev. Sci. Instr. 22, 572 (1951).

[5] H. W. Koch, J. E. Leiss, and J. S. Pruitt, Crystal

spectrometer calibration of a high energy X-ray

intensity monitor, Bull. APS II, 1, 199 (1956) A.

[6] R. R. Wilson, Precision quantameter for high energy

X-rays, Nuclear Instr. 1, 101 (1957).

[7] See G. J. Hine and G. L. Brownell, Radiation Dosimetry (Academic Press, Inc., New York, N.Y.,

1956) p. 172 for a treatment of ion recombination.

[8] J. S. Pruitt and W. Pohlit, Z. Naturforschung 15b,

617 (1960).

[9] P. D. Edwards and D. W. Kerst, Rev. Sci. Instr. 34,

490 (1953).

[10] F. H. Attix and V. H. Ritz, A determination of the

gamma-ray emission of radium, J. Research NBS

59, 293 (i957).

[11] P. W. Goodwin, Calorimetric measurements on a Cs'" teletherapy unit. Radiation Research 10, 6

(1959).

[12] I. T. Myers, W. H. LeBlanc, and D. M. Fleming,

unpublished data.

[13] NBS Handb. 64, Design of free-air ionization chambers (1957).

[14] G. W. Grodstein, X-ray attenuation coefficients from

10 kev to 100 Mev, NBS Circ. 583 (1957).

[15] Reference [7], p. 88. The listed values of R{E) were

increased by 33.6/32.5 on the basis of a more recent assessment "of W by W. Bay, W. B. Mann, H. H.

Seliger, and H. 0. Wyckoff, Absolute measurement

of W for sulphur-35 beta-rays. Radiation Research

7, 567 (1957).

[16] A. S. Penfold and J. E. Leiss, Phys. Rev. 114, 1332

(1959).

[17] A. S. Penfold and J. E. Leiss, Analysis of photo cross

sections. Physics Research Lab., Univ. of Illinois,

Champaign, 111. (May, 1958).

[18] For energies below 10 Mev, aluminum absorption

coefficients from reference [14] were used. At

energies between 10 and 100 Mev, the coefficients used came from J. M. Wyckofl: and H. W. Koch,

Phys. Rev. 117, 1261 (1960). These latter were

extrapolated to 170 Mev.

[19] J. S. Pruitt, A. AUisy, G. Joyet, W. Pohlit, M.

Tubiana, and C. Zupancic, Transfer of NBS High

Energy Calibrations to European Betatron Laboratories, J. Research NBS 66c, 107 (1962).

16


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Research. Antenna Research. Navigation Systems.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

RADIO STANDARDS LABORATORY

Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval

Standards. Millimeter-Wave Research.

Circuit Standards. High Frequency Electrical Standards. Microwave Circuit Standards. Electronic Calibration

Center.
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BOUND TO PLEASE

MA.Y.65

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INDIANA