A11104 3 L 1 1 L 5

NBSIR 78-1552

The Influence of Scattering

Foils on Absorbed Dose

Distributions From Electron

Beams

M. J. Berger and S. M. Seltzer

Radiation Physics Division

Center for Radiation Research

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

November 1978

Prepared for Office of Naval Research

Arlington, Virginia 22217

Department of Energy

Washington, D.C. 20545

“QC

100

, U56

478-1552

1973

National Cancer Institute

National Institutes of Health

Bethesda, Maryland 20014
r
14BcM ef SIsrKfjH#

m 1 1 19#

THE INFLUENCE OF SCATTERING

FOILS ON ABSORBED DOSE

DISTRIBUTION FROM ELECTRON

BEAMS

M. J. Berger and S. M. Seltzer

Radiation Physics Division

Center for Radiation Research

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

November 1978

Prepared for Office of Naval Research

Arlington, Virginia 22217

Department of Energy

Washington, D.C. 20545

National Cancer Institute

National Institutes of Health

Bethesda, Maryland 20014

n , . _________

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kraps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
, i\ > '
The Influence of Scattering Foils on Absorbed Dose Distributions

•k from Electron Beams

M. J. Berger and S. M. Seltzer

Center for Radiation Research

National Bureau of Standards

Washington, D.C. 20234

This paper describes a calculation of the spatial distribution of absorbed

dose in a water phantom irradiated by electron beams with energies from 5 to

40 MeV. It is assumed that the initially monoenergetic , monodirectional and

narrowly collimated electron beam passes through a lead scattering foil and

100 cm of air before reaching the water phantom. In the first part of the work

a calculation is made of the energy spread and angular diffusion of the beam

due to its passage through the scattering foil and air. In the second part of

the work, a calculation is made of the penetration of the modified beam into

the phantom. The second calculation takes into account the limitation of the

beam to finite field size at the surface of the phantom, and the contribution

of secondary bremsstrahl ung generated in the scattering foil to the absorbed

dose in the phantom.

Based on a talk presented at the Symposium "Dosimetry and Treatment Planning

Using High Energy Electrons" at the 14 ' th International Congress of Radiology,

Rio de Janeiro, Brazil, October 23-29, 1977.
1. Introduction

Various techniques are available for calculating the penetration and

diffusion of electrons in extended media. Among these, the most widely used

are the moments method^ and the Monte Carlo method^"^. The computational

schemes and computer codes based on these methods have been elaborated to the

point where they rather accurately take into account all the pertinent

processes, including the angular deflections of electrons in elastic Coulomb

collisions with atoms, angular deflections and energy losses resulting from

inelastic Coulomb collisions with atomic electrons, the setting in motion of

secondary electrons in ionization events, and the emission of secondary

bremsstrahlung quanta.

Whereas the physical processes have been treated in considerable detail,

the boundary conditions assumed in the electron transport calculations made

so far have been rather oversimplified. It has usually been assumed that

monoenergetic and monodirectional beams of electrons are incident perpendicularly onto the medium. Moreover, broad-beam conditions have often been

assumed, so the the calculations were limited to the determination of onedimensional depth-dose distributions.

The conditions of irradiation in radiation therapy and in industrial

applications are more complex. Even though the electron beams from the

accelerator may initially be highly monoenergetic and monodirectional, they

must pass through various materials (beam-spreading foils, monitors, air,

etc.) on their way to the medium (phantom, patient). Upon entry into the

medium the beams have therefore acquired a significant energy spread and

angular divergence. These beam modifications, and the collimation of the

beam to finite field size, have a considerable influence on the spatial

2
. We have attempted to

11-19

distribution of absorbed dose within the phantom

extend the electron transport calculations in order to take some of these

complications into account. In particular, we have considered the effect of

lead beam-spreading foils, and the effect of collimation to finite field size.

The arrangement of the scattering foil, collimator and water phantom assumed

in our calculations is indicated in Fig. 1. The parameters of the problem

are: the electron beam energy, the material and thickness of the foil, the

distance s between foil and phantom, the radius r

F of the (circular) field

irradiated by the beam, and the depth z and radial distance p from the

beam axis to the point where the absorbed dose is to be determined. Among

the various calculational techniques that are available, the Monte Carlo

method, i.e. the simulation of particle tracks with the use of random numbers,

has the greatest flexibility. Through the addition of complex-geometry

routines, the Monte Carlo method could be extended to treat electron transport

in the scattering foil and in the phantom in a single integrated calculation.

However, this would require a very large amount of numerical computation, and

it seems hardly practical to make lengthy Monte Carlo calculations for each of

the many foi 1 -col 1 imator configurations that may be of interest.

We therefore adopted an alternative approach, which is computationally

less demanding. The use of the Monte Carlo method was limited to the treatment of two separate restricted transport problems: (a) the transmission of

electrons through foils, and (b) the penetration of monoenergetic , pointmonodirectional electron beams into a water phantom. The results from

calculations (a) and (b) were then combined according to a superposition rule

to obtain absorbed-dose distributions for various configurations of interest.

3
2. Foil Transmission

In the foil transmission calculations, a monoenergetic, point-monodirectional beam of electrons was assumed to be incident perpendicularly on

the scattering foil. Calculations were made for eight typical cases,

involving lead scattering foils with thicknesses between 0.1 mm and 0.6 mm,

and beam energies from 5 MeV to 40 MeV. The output of the calculations

included the distribution in energy and angle of the transmitted electrons and

secondary bremsstrahl ung photons. The lateral spatial multiple scattering

deflections of electrons and photons in the foil are negligibly small so that

the radiation can be assumed to emerge from an effective focal point on the

beam axis at the exit surface of the foil.

The modification of the electron and photon beams during their passage

through the air between the lead foil and the phantom was treated by an

approximate method. Monte Carlo transmission calculations were actually done

for a two-layer medium consisting of a lead foil followed by a layer of

condensed air-equivalent material. The electrons and photons emerging from

the second layer were assumed to travel to the phantom without further

scattering. Inasmuch as the passage through the air has a strong effect only

on the spectra but not on the angular distribution of the transmitted

radiation, we expect that the error incurred by this approximate schematization is smal 1

.

For the thin foils considered here, the correlation between the energy

and direction of the transmitted radiation is quite small, expecially for

deflection angles up to 20°. Therefore the calculated distributions can be

accurately represented as the product of two one-variable functions: an energy

spectrum, and an angular distribution. These two quantities are shown in

Figs. 2 to 6, which pertain to the transmission of a 10-MeV electron beam

4
through 0.1 mm of lead. In each of these figures two sets of results are

shown, one for a lead foil only, and the other for a lead foil followed by a

layer of material equivalent to 100 cm of air. These results are representative of those obtained for other foil thicknesses and beam energies.

Energy spectra of transmitted electrons for a 10-MeV beam incident on a

0.1 -mm Pb foil are given in Fig. 2. This figure also shows the shift towards

lower energies and the broadening of the spectrum that occur when electrons

also pass through 100 cm of air after going through the foil. In Table 1, the

mean energy loss, the most probable energy loss and the full width at half

maximum of the spectrum are given for other combinations of beam energy and

lead target thickness (always with an additional 100 cm of air). Also shown

20

in Table 1 are results from Landau's theory which takes into account the

fluctuations of collision losses, but includes neither bremsstrahlung losses

nor the lengthening of the electron paths in the target due to multiple

elastic scattering. It can be seen that in spite of the omission of these

two effects the Landau theory provides a rather good estimate of the most

probable energy loss, whereas it predicts a full width at half maximum about

one third smaller than the Monte Carlo values.

Figure 3 shows a plot of the angular distribution of the transmitted

electrons (per unit solid angle) vs. the square of the deflection angle. On

this semi-logarithmic plot, the calculated points can be accurately fitted by

a straight line, which indicates that in very good approximation the angular

distribution is Gaussian, i.e. proportional to exp(- 0

2 /a 2 ). This approximation holds for 6 ^20°, but tends to break down for larger angles. Values

of the parameter a calculated for various combinations of beam energy and

lead foil thickness are given in Table 2. These results are close to the

root-mean-square angles predicted by multiple-scattering theories in the

21

small-angle approximation, as tabulated, for example, by Brahme.

5
The energy spectra and angular distributions of transmitted bremsstrahlung photons are shown in Figs. 4 and 5. The angular distribution is not

Gaussian, and is more concentrated in the forward direction than that of the

electrons. Figure 6 shows the fraction of the incident beam energy that is

transmitted through the foil and reaches the phantom, either in the form of

electrons or of secondary bremsstrahlung. These two quantities are shown as

functions of the cone half-angle 6

c which is equal to the arctangent of the

ratio of the field-size radius rp to the foil-phantom distance s. It can

be seen that the relative contribution of bremsstrahlung from the foil to the

energy deposited in the phantom is greatest when the field size is small.

3. Elementary Absorbed Dose Distributions

Assuming a water phantom occupying the region z > 0, and monoenergetic,

point-monodirectional electron beams incident along the z-axis, absorbed-dose

distributions in the phantom were calculated by the Monte Carlo method for

nine beam energies (1,5,10,15,20,30,40,50 and 60 MeV). These distributions

were obtained as functions of the depth z in the phantom and the radial

distance p from the z-axis. An illustrative set of results for a 20-MeV

beam is shown in Fig. 7. The histogram in the upper right-hand corner is the

depth-dose distribution. The other six histograms are radial distributions in

various depth intervals, and show the fractions of the energy deposited in

ring-shaped layers around the z-axis. In Fig. 7, depths and radial distances

are expressed in units of the electron range r . It has been found that

througn this scaling the explicit dependence of the absorbed-dose distribution

on the incident beam energy is greatly reduced, so that interpolation with

respect to initial beam energy is facilitated.

As a check on the validity of the method, some Monte Carlo calculations

were also made for an acrylic plastic (Lucite) medium for comparison with

experimental absorbed-dose distributions obtained without a scattering foil or

6
collimator. Figure 8 shows a comparison with depth-dose curves measured by

22 Harder and Schulz at 21.2 MeV and 62 MeV in Lucite, under broad-beam conditions (actually with a very narrow beam and a very broad detector). Figure 9

shows a comparison with radial dose distributions measured by Lillicrap,

Wilson and Boag at depths of 1 and 2 cm in a Lucite medium irradiated with a

non-divergent 10-MeV, 2.5-mm diameter beam. The quantity plotted is the

radial dose profile, i.e. the dose as a function of distance from the beam

axis, normalized to unit central-axis dose. The overall agreement between

calculated and measured results in Figs. 8 and 9 is good.

Additional Monte Carlo calculations were done in the course of the

present work to obtain absorbed-dose distributions in water from the

bremsstrahlung emitted by the scattering foil. These were done for pointmonodirectional beams, assuming photon spectra obtained in the preceeding

foil-transmission calculations.

4. Combination of Elementary Absorbed Dose Distributions

In the last stage of the calculation, the electron beam reaching the

phantom after passage through the foil (and intervening air) was considered to

be a weighted superposition of different elementary, monoenergetic , monodirectional beams with different energies, obliquities and points-of-entry

into the phantom. The weighting factors were obtained from the foiltransmission calculations. The absorbed-dose distribution from the composite

beam, as a function of depth and radial distance from the beam axis, was

correspondingly obtained by summing over the weighted elementary absorbed-dose

distributions previously obtained. By limiting the summation over obliquities

to certain cones around the beam axis, the effect of collimation to finite

field size was simulated. However, this treatment did not take into account

7
the effect of electron scattering from a collimator. A similar superposition

over obliquities and points-of-entry was also applied to the dose contribution

due to bremsstrahlung from the foil.

The application of the superposition procedure required the prior smoothing

of the Monte Carlo results for elementary absorbed dose distributions, and

extensive interpolation with respect to beam energy and the two spatial

variables. The computations were found to be moderately difficult for the

evaluation of the central-axis depth dose, and quite laborious for the

evaluation of the radial dose profile, i.e. the dependence of absorbed dose on

the distance from the beam axis. The resulting numerical uncertainties in

the latter case may have been as great as 5% in some cases, and there is a

need for improving the speed as well as the accuracy of the superposition

calculations.

5. Central -axis Depth Dose

Calculated central-axis depth-dose curves are compared in Fig. 10 for

10-MeV beams. Curves are given for a monoenergetic, non-divergent beam with a

20-cm diameter (no foil case), and for beams that have passed through a lead

foil (0.1 mm or 0.4 mm) plus 100 cm of air. The presence of a scattering foil

raises the entrance dose relative to the peak dose by several percent.

Changing the foil thickness leaves the depth-dose curves practically unchanged

near the surface, but results in a significant shift at depths beyond the

peak. Depth-dose curves for 30-MeV beams are compared in Fig. 11. Results

are given for a monoenergetic non-divergent beam with a 20-cm diameter (no

foil case), and for beams that have passed through 0.4 mm of lead and 100 cm

of air, and that have been collimated to fields with 20-cm or 5-cm diameters.

Again the presence of the foil raises the entrance dose relative to the peak

dose. The change of field size from 5 to 20 cm leaves the depth-dose curves

8
unchanged from the surface to the peak at 3.5 cm; at greater depths the

collimation to a 5-cm diameter makes the depth-dose curve fall off much more

rapidly than that for a 20-cm diameter because of increased out-scattering.

Figure 12 shows the estimated contribution to the central-axis depth-dose

made by bremsstrahlung from the scattering foil. Results are given for 10-,

20- and 30-MeV beams that have passed through 0.4 mm of lead plus 100 cm of

air. The relative bremsstrahlung contribution is small near the surface, then

rises and reaches a plateau of several percent at small and intermediate

depths; finally it becomes predominant at depths comparable with the electron

range.

Calculated central-axis depth-dose curves are compared in Fig. 13 with

experimental results of H. Svensson (private communication). The experimental

conditions for the cases selected for comparison were: (a) 41 -MeV beam,

0.125-mm aluminum window, 0.6-mm lead foil; (b) 22.5-MeV beam, 0.2-mm aluminum

window, 0.17-mm uranium foil; in both cases the field size was unlimited and

the foil-to-phantom distance in air was 100 cm. Comparison calculations are

available for the following conditions: (a) 40-Mev beam, 0.6-mm lead foil plus

100 cm of air, field diameter 20 cm; (b) 22.5-MeV beam, 0.2-mm aluminum

window, 0.17-mm uranium foil plus 100 cm of air, field diameter 40 cm. The

calculated results at 40 MeV have been adjusted to 41 MeV by "stretching" the

depth scale through multiplication by the ratio of range values at 41 and

40 MeV. The agreement between experiment and calculation is very good close

to the entrance surface and at great depths near the end of the electron

range. At intermediate depths, beyond the peak, the experimental and calculated curves appear to be shifted somewhat with respect to each other; the

direction of shift is different for the two beam energies.

9
6. Radial Dose Profiles

Radial dose profiles are shown in Fig. 14 for a 10-MeV beam that has

passed through a 0.1 -mm lead foil and 100 cm of air, and has been collimated

to a 5-cm diameter field. At the shallow depth of 0.6 cm, the radial dose

profile is rather flat out to 2.1 cm, and actually has a peak value of 1.02 at

a radial distance of 1.5 cm from the beam axis. This very small rise above

unity, appears to be the result of the angular divergence of the incident

beam. The radial profiles at the other depths shown (1.2, 2.4 and 3.2 cm)

reflect the broadening of the beam with increasing depth due to multiple

scattering. The value of the radial profile at the edge of the beam (distance

of 2.5 cm from the axis) is rather independent of the depth, and lies between

0.45 and 0.5.

In Fig. 15 calculated radial dose profiles are compared with recent

experimental results of Svensson. The cases selected for comparison were the

same as those in the central -axis depth-dose comparisons in Fig. 13. The

profiles are compared at the depths where the corresponding central -axis

depth-dose curves peak. The experimental field size was unlimited, whereas in

the calculation it was limited to a 20-cm diameter at 41 MeV and a 40-cm

diameter at 22.5 MeV. In view of this difference one must limit the

comparison to radial distances smaller than the field radius assumed in the

calculation. The agreement is very good at 41 MeV, but not as close at

22.5 MeV where the experimental profile falls off somewhat more rapidly than

the calculated profile.

7. Concluding Remarks

A method has been developed for calculating the spatial distribution of

absorbed dose from high-energy electron beams. The new aspect of the method

is that it takes into account not only the multiple scattering of the electrons

10
in the irradiated phantom, but also the effects of (a) the energy degradation

and angular diffusion of the electron beam by a scattering foil, and (b) the

limitation of the beam to finite field size. The approach used involves

separate Monte Carlo calculations of foil transmission and beam penetration

into a phantom, and the subsequent application of these Monte Carlo results,

by suitable combination, to specific scattering foil-phantom configurations.

Results are presented for some typical cases, for lead scattering foils and

electron beams with energies up to 40 MeV, in the form of central -axis

depth-dose curves, and of dose profiles as functions of the radial distance

from the beam axis. A few comparisons indicate reasonably good, but not

perfect, agreement with measured absorbed-dose distributions. In view of the

considerable amount of computational effort required, it does not yet appear

practical, in the present stage of development of the method, to treat

routinely the numerous cases that may be of interest in practice, involving

different foil materials and thicknesses, foil-to-phantom distances, field

sizes, etc. We believe that for the time being the theoretical approach may

be most valuable in providing (a) an improved understanding of the influence

of various factors on the absorbed-dose distributions, and (b) independent

confirmation of measured results.

Acknowledgements . This work was supported by the Office of Naval Research,

the Department of Energy (Division of Biomedical and Environmental Research)

and the National Cancer Institute. We are grateful to Dr. H. Svensson for

providing us with unpublished results of his recent absorbed-dose measurements.

11
REFERENCES

[1] L. V. Spencer, Phys. Rev. 98, 1597 (1955).

[2] L. V. Spencer, Energy Dissipation by Fast Electrons, Nat. Bur. Standards,

Monograph 1 (1959).

[3] N. D. Kessaris, Calculated absorbed dose for electrons, Radiat. Res. Z3,

630-640 (1964).

[4] N. D. Kessaris, Penetration of high-energy electron beams in water, Phys.

Rev. 145, 164-174 (1966).

[5] N. D. Kessaris, Spectra of high-energy electron beams in water, Radiat.

Res. 43, 281-287 (1970).

[6] M. J. Berger, Monte Carlo calculation of the penetration and diffusion of

fast charged particles, in methods in computational physics, B. Alder,

S. Fernbach and M. Rotenbert, Eds., Academic Press, N.Y. (1963).

[7] M. J. Berger and S. M. Seltzer, Ann. New York Academy of Sciences, 161,

8(1969).

[8] M. J. Berger and S. M. Seltzer, Paper presented at the 12th Int. Cong.

Radiol. Tokyo, Japan (1969).

[9] H. Sugiyana, Monte Carlo program for photon and electron transport

calculations. Bull. Electro-tech. Lab (Ministry of International Trade and

Industry, Tokyo, Japan), 3A_> 126-140 (1970).

[10] S. M. Seltzer and M. J. Berger, Nucl . Instr. Meth. 1J_9, 157 (1974).

[11] J. Rassow, Habilitationsschrift, Ruhr Universitaet (1970).

[12] H. Svensson, Acta Radiol. Ther. Phys. Biol. U), 631 (1971).

[13] M. Cohen, D. E. A. Jones and D. Green, Eds., Hospital Physicists' Assoc.

Central Axis Depth Dose Data for Use in Radiotherapy, Supplement No. 11,

Brit. J. Radiology (1972).

[14] P. R. Almond and E. E. deAlmeida, Radiation Therapy with the Electron

Beam. Course Manual, Radiological Society of North America (1973).

[15] A. Brahme, G. Hulten and H. Svensson, Phys. Med. Biol. 20, 39-46 (1975).

[16] S. Kramer, N. Suntharal ingam and G. F. Zinninger, Eds., High-Energy

Photons and Electrons: Clinical Applications in Cancer Management, Wiley,

New York (1976).

[17] A. Brahme and H. Svensson, Medical Phys. 3_, 95-102 (1976).

[18] F. Wachsmann and G. Drexler, Graphs and Tables for Use in Radiology,

Springer, Berlin Heidelberg-N.Y. (1976).

12
[19] D. Fehrentz, Habil i tationsschrift, U. of Heidelberg (1976).

[20] L. Landau, J. Phys. U.S.S.R. 8, 201 (1944).

[21] A. Brahme, Report TRITA-EPP-72-1 7, Department of Electron Physics, Roy.

Inst. Technology, Stockholm, Sweden (1972).

[22] D. Harder and H. J. Schultz, Some new Physical Data for Electron

Dosimetry, paper given at Europ. Congress of Radiology, Amsterdam (1971).

[23] S. C. Lillie ra p , P. Wilson and J. W. Boag, Phys. Med. Biol. 20, 30-38

(1975).

[24] M. J. Berger, S. M. Seltzer, S. R. Doman, and P. J. Lamperti , Stopping

power ratios for electron dosimetry with ionization chambers, pp. 589-609,

Proc. Symp. on Advances in Biomedical Dosimetry ( IAEA-SM-1 03/39 )

,

International Atomic Energy Agency, Vienna, 1975.

13

Table

1.

Parameters

characterizing

the

energy

spectra

of

electrons

transmitted

through a

composite

target

consisting

ofa

lead

foil

followed

bya

100-cm

layer

of

air.

Electrons

are

incident

perpendicularly

with

energy Tq. T

is

the

mean

energy,

and

Tp

the

most

probable

energy,

of

the

transmitted

electrons,

and W

is

the

full

width

at

half

maximum

of

the

spectrum. o CD o > co C\J n— CM r— C\J 1

CD • s: o o o o o o o u

•r—

+-> CO

fO

CDco

Q. un CO CO r^.

O r-^ CTi 1— > cn CO CO CO CO oj g O) o S O o o O O O o

CM

OJ

UDr— o co r-^ oCO r-'* O o o o o o o O

cn cn C\J CO OJ CO cn CO co OJ CO OJ o o o CD o o o

It- 00 CO cn 00 co co > CO CO O CO o CO o a) l— OJ r— •— o *

o

to

to

CD -a i— c

(Q *i

cd o o

CO'3-C\J«d-r-^j-r— o o o o o o o o o o o o o ln

•O" CO OJ OJ i— i

<D -ac

ra

to . .

a) 4-> CO CL) 00 cn o s- 1

f0

4-> CDC CL) 3 -4-J

-£C CO

fa o

s- cl

+-> E s- co O • r—

co o f0 E -—>

CL) S- CL

s- o \—

.a ci_ 1 o • to c 1

-a o — s- A"

fO +-> + -—

cn ra s_

ai e ~o •f

s_ ta cm ta CO X CD 3 •r- O r—

T3 S- -—» +

CL CL -C CL t—

a

O fO 1 fa • i

o at -n -o 1— CM i 2 <D 3 E

>i ^ II S- to II O to -—

CD <C Q. 3 -C 1—

4-> 1 . O

co to 1— - c

13O

fa •i— -a M c <_> fa CD _i r—

>+- o CD

4-> -o

cn cn c c • i

•rTM "0 s-CD o +-> CJ 4->

<_> fO

ta

O

CO “O

a> a)

+-> (

ta CL o •r— i

+-> <a r

> ZJ UJ E

fa -Q

Complete

treatment

with

computer

code

ZTRAN.
Table 2. Values of the parameter a in the Gaussian distribution

exp(- 0

2 /a 2

) used to approximate the angular distribution

of transmitted electrons

a

Lead Foil Foil Foil Plus

T

q

Thickness Only 100 cm of Air

(MeV) (mm) (Degrees)

40 0.6 9.8 9.9

30 0.4 10.0 10.4

20 0.2 10.0 10.6

20 0.4 14.6 14.9

10 0.1 13.9 15.2

10 0.4 29.6 30.2

5 0.1 24.3 26.0
FIGURE CAPTIONS

Fig. 1 Schematic arrangement of beam, foil, collimator and phantom assumed

in calculation.

Fig. 2 Energy spectra N£ (T/T

Q

) of electrons transmitted through lead

foil, or through lead foil plus 100-cm air layer. Electrons with

energy T

Q are assumed to be incident perpendicularly onto the

foil, and T is the energy with which the transmitted electrons

emerge from the foil, or from the layer of air behind the foil. The

spectra include all transmitted electrons that emerge with directions

within a cone of 20° half-angle around the direction of incidence.

The curves are normalized such that jT N (T/T ) d(T/T ) = 1.

Fig. 3 Angular distributions A (0) of electrons transmitted through a lead foil, or through a lead foil plus a 100-cm air layer. Electrons

of energy T

Q are assumed to be incident perpendicularly onto the

foil. The angle 0 is measured with respect to the direction of

incidence. The distributions include all electrons regardless of

the energy with which they are transmitted. The solid and dashed

lines are fits to the calculated points. The curves are normalized

such that sin0 A (0) de = 1

.

Fig. 4 Energy spectrum of the bremsstrahl ung intensity (k/T

Q

) N (k/T

Q

) from a composite target consisting of a lead loil and a 100-cm air

layer. k/T

Q

is the photon energy in units of the incident electron

energy T . N( k/T ) is the photon number spectrum, and includes

all photons with directions within a cone of 20° half-angle with

respect to the direction of incidence. The curve is normalized such

that fQ(k/T

Q

) N^(k/T

Q

) d(k/T

Q

) = 1. The spectral shape is quite

similar without the air layer.

Fig. 5 Angular distributions A^(0) of bremsstrahl ung intensity from a

lead foil, or from a lead foil plus a 100-cm air layer, irradiated

by electrons of energy T

Q

incident perpendicularly. The distributions include photons of all energies. The curves are normalized

such that J

n

Q

20

sine A (0) d0 = 1

.
Fig. 6 Fractions of the incident electron energy T

Q

that emerge from a lead scattering foil, or from a 100-cm layer of air behind the foil,

in the form of transmitted electrons, or in the form of bremsstrahlung

photons.

Fig. 7 Energy deposition in water from a point-monodirectional electron

beam with energy T = 20 MeV. All distances are expressed in units

0 -2

of the electron range r

Q (9.21 g cm H^O). The histogram in the

upper right hand corner shows energy deposition as a function of

scaled depth, z/r

Q

, in The form of the dimensionless scaled

quantity (r /T )D(z/r ), where D is energy deposition per

0 0 0 n electron per unit depth, in MeV/g cm . The other histograms show,

for the six indicated (shaded) depth intervals, the radial distribution of deposited energy, as function of the scaled distance p/r

Q

from the beam axis. In these histograms, the area of each bin

represents the fraction of the energy deposited in the indicated

ring around beam axis. Each histogram is normalized to unit area.

Fig. 8 Comparison of calculated broad-beam depth-dose curves with experi22

mental results of Harder and Schultz , for electron beam energies

T

q

= 21.2 and 62.0 MeV and an acrylic plastic (Lucite) medium.

The quantity plotted is the scaled distribution (ro/T

Q

)D( z /r

Q

)

,

where r is the electron range and D is the energy deposited per

0 -2

electron per unit depth, in MeV /g cm . In order to make the

comparison, we have converted the measured ionization values into

24

absorbed-dose values according to the cavity ionization theory ,

• • Luc i tc

using depth-dependent Lucite-to-air stopping power ratios S air , which we show as dashed curves.

Fig. 9 Comparison of calculated radial dose profile from beam with small

circular cross section with experimental results of Lillicrap,

23 Wilson and Boag . The profiles are expressed as functions of the

scaled distance p/r

Q

from the beam axis, and are normalized to

unit dose on the central axis.
Fig. 1

Fig. 1

Fig. 1

Fig. 1

Fig. 1

Central -axis depth-dose curves for 10-MeV beam that has passed

through a lead foil and 100 cm of air. "No foil" curve is for a monoenergetic beam. Beams are collimated to a diameter of 20 cm.

Central-axis depth-dose curves for 30-MeV beam that has passed

through a lead foil and 100 cm of air. "No foil" curve is for a monodirectional , monoenergetic beam that has been collimated to a diameter of 20 cm.

Contribution of bremsstrahlung from scattering foil to the central - axis depth dose in water. Results are for 10-, 20- and 30-MeV beams

passing through a 0.4-mm Pb foil plus 100 cm of air.

Comparison of calculated central -axis depth-dose curves in water

with experimental results of Svensson (private communication).

Calculated radial dose profiles at various depths in a water phantom.

Results are for a 10-MeV beam that has passed through a 0.1 -mm

lead foil plus 100 cm of air, and has been collimated to a diameter

of 5 cm. Dose profiles are normalized to unit dose on the central

axis.

Comparison of calculated radial dose profiles in water with experimental results of Svensson (private communication). Calculated

results are for beams collimated to finite field size, whereas

experimental results are for uncollimated beams.

ACCELERATOR

SCATTERING FOIL

'&ZZZZZZZZZZZZ

WATER

PHANTOM

Fig. 1
N€ (T/T0 ) o o ooooooooooo -ttoco^cno^oocoo-k

o

120
100

200

300

400

62,

DEGREE

2

A € (0),sr" s

-ft, o

o

10

MeV
Fig.

(k/T0

) N

y (k/T0

) poo O ^ ^ ^ ^

-J- JO oio£hb> bo b io

^

b> bo o

o

T0

=

10

MeV

0.1

mm

Pb+100

cm

AIR
Fig. 5
1

10

10

10

T0 = 10 MeV

0.1 mm Pb+IOOcmAIR

0.1 mm Pb

BREMSSTRAHLUNG

i L i I l i i i i l_l i i i ' 10

0C, DEGREES

90

Fig. 6
RELATIVE

RADIAL

DISTRIBUTION

p/rQ

Fig. 7
•o

l.l

1.0

Q

lucite

<3ir

Fig. 8
RELATIVE

DOSE

Fig. 9
DEPTH,

cm

RELATIVE CENTRAL - AXIS DEPTH DOSE

o ^ n u ^ cn co -vl oo to b
Fig. 11
BREMSTRAHLUNG CONTRIBUTION, PERCENT

H*

OQ
Fig. 13
10

MeV

0.1

mm

Pb

FOIL

FIELD

DIAM

5

cm

3Soa 3Aiivi3a

DISTANCE

FROM

BEAM

AXIS
LU

CO

o

Q

LU

>

I-<

_l

LU

cr

DISTANCE FROM BEAM AXIS, cm

Fig. 15
HBS-1 14A (rev. 7- 73 )

I

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION’ OR REPORT NO.

NBSIR 78-1552

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

The Influence of Scattering Foil § on Absorbed Dose

Distributions from Electron Beams

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

M. J. Berger and S. M. Seltzer

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project /Task/Work Unit No. 5332425

5331.43a. t- 5333432

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Office of Naval Research Division of Biomedical and

Arlington, Va. 22217 Environmental Research

(J. S. Department of Energy

13. Type of Report & Period

Covered

National Cancer Inst.-NIH

Bethesda, Md. 20014 Washington, D.C. 20545

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less [actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This paper presents results of transport calculations pertaining to the

distribution of absorbed dose in a water phantom irradiated with high-energy

electrons. The electron beam, initially monoenergetic and monodirectional

,

was assumed to pass through a lead scattering foil and 100 cm of air before

reaching the phantom. The principal aim of the calculation was to determine

the energy spread and angular divergence of the electron beam due to its

passage through the lead foil and air, and to estimate the resulting modification of the absorbed-dose distribution in the phantom. Also included in the

calculation were the effects of beam collimation to finite field size, and the

contribution to the absorbed dose from secondary bremsstrahlung generated in

the scattering foil as well as in the phantom.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Absorbed dose; central axis depth dose; collimation; electrons; radial dose profile;

scattering foil.

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1 Order From Sup. of Doc., U.S. Government Printing Office

Washington, D.C. 20402, SD Cat. No. CH

[7J Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

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UNCLASSIFIED

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