characterization of bremsstrahlung radiations for 6 to 18 mev...

Chapter 3.

Characterization of bremsstrahlung radiationsfor 6 to 18 MeV electron beam from different Z

elements: experimental and simulationapproach

This chapter deals with the study of bremsstrahlung

spectra for 6 to 18 MeV electron beam from different

materials such as low to high Z elements as an e - target.

The simulation using FLUKA involves the neutron,

electron, positron and bremsstrahlung fluence

determination at various angles Moreover the thickness ofdetermination at various angles. Moreover, the thickness of

e - target has varied from thin to thick i.e from 0.1% to

150% of RCSDA. In addition, the reliability of FLUKA

simulation was confirmed by calculating the

bremsstrahlung spectrum for the setup of experiments

performed by other researchers and corresponding

validation was done. The data generated in this chapter can

be used as a right hand data for the researchers working in

the field of medical, nuclear and accelerator physics.

47

Chapter 3. Characterization of bremsstrahlung radiation 48

3.1 Importance and Objective

Radiation therapy is a clinical modality dealing with the use of high

doses of ionizing radiations in the treatment of patients mostly having malignant

tumors. The aim of radiation therapy is to deliver a sufficiently high absorbed

dose to a defined target volume resulting in the eradication of the tumor with

as minimal a damage as possible to the surrounding healthy tissues. Radiother-

apy with external high energy photon beams are the most common radiotherapy

modality [1]. Electron beams are used either as the primary mode of radiation

therapy or combined with photon beams. High energy electron and photon beams

are typically produced by linear accelerators and also by Microtrons [2]. For a

typical multi-energy medical linear accelerator, the accelerating potential spans

between 4 and 25 MV. The mean energy of the photon beams varies between

1.5 and 7 MeV [3]. In external beam therapy, to optimize the dose distribution

in a patient, the dose is typically delivered from different directions of modified

shape and intensity of the beam.

In radiation therapy with external radiation beams, the absorbed dose

at the specific point in a patient should be known with an overall uncertainty of

3.5% [4–6]. The main reason for the requirement of high accuracy in dose de-

livery is typically narrow margin between the dose needed for tumor control and

the dose causing complications for healthy tissues. The size of the dose margin

depends on the biological characteristics of tissues, size and shape of the irradi-

ated tissues, the quality of radiation as well as the dose fractionation regime. Due

to individual nature of the dose margin, 3.5% uncertainty can be regarded as a

general level accuracy requirement for dose delivery [4, 5]. Besides an individ-

ual treatments, the high accuracy in dose delivery is essential to enable a reliable

analysis and a comparison of results of different radiation therapy techniques and

modalities [6]. The knowledge of the energy spectra and angular distribution of

photon beams at the point of application is essential for accurate dose calcula-

tions [3]. Other applications requiring knowledge of the energy spectra include

design of the treatment machine head, flattening filter and collimator. It is also


important to know the variation of energy spectrum as a function of radial dis-

tance from the beam axis. The bremsstrahlung energy spectrum in the central

part of a photon beam is somewhat harder than in the region near edge of the

beam. Consequently, the relative depth dose in tissue will vary as a function of

distance from the beam axis. Variation of spectrum across the beam is also impor-

tant when calculating transmission through a block or a compensating device [3].

Knowledge of the angular distribution of photons is useful when calculating dose

near the beam boundaries. It is important to be able to evaluate reliably spectra of

bremsstrahlung from electron accelerators as functions of photon energy and an-

gle. As well as being required for fundamental reasons in photonuclear physics,

quantitative evaluations of bremsstrahlung spectra are required for purposes such

as predictions of γ ray radiation doses and dose rates, accelerator generated X-

ray radiography exposures, radioisotope production rates, and source strengths

in active γ-ray interrogation techniques [7]. Also it is necessary to know the

contamination of other particles like positron, neutron in bremsstrahlung beam,

to minimize unwanted dose to the patient body. Therefore, to generate data for

various energy and targets is very important as far as radiation therapy and radio-

graphy is concern.

3.1.1 Literature Survey

The process of bremsstrahlung has been studied theoretically and ex-

perimentally for several decades. The theoretical status of the field in 1959 was

reviewed by Koch and Motz [8], who presented a compilation of theoretical for-

mulae of various cross-sections, differentials in photon energy and photon scat-

tering angle in thin targets and for a wide range of incident electron energies.

The regimes of validity, in terms of incident energy, outgoing photon energy,

angle and radiator atomic number, etc. are discussed and evaluated for thin tar-

gets. At a depth in a thick bremsstrahlung target, the intrinsic angular photon

distribution for a thin target must be folded with the angular distribution of the

electron produced by multiple scattering [9]. For semi-thin targets, Schiff [10]


derived a formula for the angular photon distribution. A review, including exten-

sive tabulations of bremsstrahlung photon spectra, has been published by Seltzer

and Berger [11, 12]. A more recent review on various theoretical cross-sections

that have been used in Monte Carlo codes are described by Salvata [13].

Despite the relatively advanced state of the theory, few accurate, abso-

lute measurements have been made of the spectrum of bremsstrahlung photons

produced by high-energy electrons. A number of measurements have been per-

formed for electrons of energies below 30 MeV: Faddegon et al. [14, 15] and

the references therein. The thickness of the radiators generally used in these ex-

periments complicates their comparison with theory, as multiple scattering and

secondary processes become important. Monte Carlo calculations, with the the-

oretical bremsstrahlung cross-sections as input, must be employed to account for

the effects of radiator thickness and collimation on the photon spectrum and an-

gular distribution.

There has been much published on bremsstrahlung spectra over the past

few decades. A wide range of techniques have been proposed to determine the

bremsstrahlung: by early analytical modeling [10] and by elaborate Monte Carlo

simulations [16]. Additional analytical models exist in the literature which usu-

ally fit phase spaces obtained from Monte Carlo simulations [17]. Unfolding

of empirical radiation data measured by spectrometry [14, 18] has also been at-

tempted. Reconstruction from measured or calculated dosimetric data, usually

transmission measurements or depthdose curves [19–25] is yet another popular

means. While each method offers different advantages and disadvantages, it is

valuable to have an independent means to confirm the results of any given ap-

proach. Work on elementary bremsstrahlung cross sections [8, 11, 26] has been

complemented by work on the practical computation of bremsstrahlung from ra-

diators [27–33] in which different aspects of the bremsstrahlung spectrum are

treated in different ways according to the intended application.

A number of investigations on photon energy spectra have been re-

ported in literature. But, to the best of our knowledge as for angular distribu-

tions from thick targets, there are very few researcher have published their work.


Moreover, the contamination of unwanted radiations such as e−, e+, n have not

been calculated and measured very often. Therefore, keeping the importance of

bremsstrahlung in various fields mainly medical and industrial, the work on cal-

culation on bremsstrahlung yield and spectra have been carried out. The process

of bremsstrahlung production with other radiations is difficult to study theoret-

ically even on the basis of correct experiments for different cases of thickness

and materials of radiators (e− γ target). Therefore, simulations using effective

Monte Carlo based FLUKA has been carried out to generate bremsstrahlung ra-

diations by bombarding 6 to 18 MeV electrons on low to high Z target (e− γ ) of

thickness varying from 0.1% to 150% of RCS DA at various angles. RCS DA is the

range of the material for the incident electron energy. Also, the simulation using

FLUKA involves the fluence determination of neutron, positron and secondary

electrons. The data generated in this chapter will certainly help researchers work-

ing in the field of medical, nuclear and accelerator physics to take precise right

hand data of flux and energies of bremsstrahlung radiations. This can be used for

designing the various components of accelerator head of linear accelerator and

to treat desire object in radiation therapy accurately. The reliability of FLUKA

simulation was also confirmed by validating the bremsstrahlung results with the

results obtained in experiments performed by other researchers.

3.2 e− γ Target

The quality of the target to convert the electron energy into bremss-

trahlung radiation is actually given by the ratio of energy loss due to radiation

(dE/dx)rad and ionisation, (dE/dx)ion. It is therefore defined the conversion ef-

ficiency to produce bremsstrahlung radiation as the ratio between energy lost

by the electrons due to the bremsstrahlung radiation and the initial electron en-

ergy [32]. This value, in particular depends on the Z of the target material and

is proportional to energy of the electron. Basically, when high energy electrons

having kinetic energy Te passes through a target, the radiative loss results in emis-

sion of the bremsstrahlung radiation whose energy is distributed in a continuum

spectrum with end point equal to the electron energy. The energy spectrum of


bremsstrahlung can be evaluated as [8, 33, 34].

d 2Nγ

dkdΩ(Te, k,w) =

n∑i=1

ηi(k, di,w)τi(Te, di)Nidσdk

[(Te)i, k]Bi(w) (3.1)

This provides the spectrum in (photons − sr−1 − MeV−1)/electron and is calcu-

lated by dividing the whole target material thickness in n layers and evaluating

the bremss-trahlung production and diffusion in each layer. The terms appearing

in Eq. (3.1) can be estimated as explained in [33, 34] and take into account all

the parameters influencing the bremsstrahlung production such as target mate-

rial, the electron energy loss, electron scattering inside the target material Bi(w),

the electron transmission coefficient τ(Te, di) and photon mass attenuation coef-

ficient. ηi(k, di,w) is the coefficient of photon absorption in target material, Ni is

the number of atoms per unit cross section area in ith layer, dσdk [(Te)i, k] is the ele-

mentary integral bremsstrahlung spectrum in the ith layer, k is the photon energy,

w the observation angle with respect to beam axis and di is the average depth of

the ith slab.

Electron

e- target vacuum

P

d

Figure 3.1: Geometry of e− γ target for the generation of bremsstrahlung radiation.

Consider a target in a vacuum as shown in Figure 3.1, irradiated by en-

ergetic electrons which generate bremsstrahlung radiations. The bremsstrahlung

yield dS/dk is defined as the number of photons of energy k per unit energy from

a target which would reach a given point P in the vacuum per unit solid angle

per electron incident on the target. The solid angle dΩ, is defined from the point


of intersection of the beam axis with incident surface of the target to the point P.

The bremsstrahlung yield is given by the following important relation, [14]

dSdk

=1Ne

d 2Nγ

dk dΩ(3.2)

Where, (d 2Nγ/dk dΩ)dk is the number of photons with energy between k and

k + dk which exit the target and reach point P per unit solid angle and Ne is the

number of electrons incident on the target. In principle, dS/dk depends on the

distance of point P from the target, due to finite source size. The bremsstrahlung

yield is defined for a target in a vaccum, thus for an air measurements consid-

eration must be given to both attenuation and scatter in the air. The integrated

bremsstrahlung yield S k is given by the following relation, [14]

S k =

∫ kmax

k0

dSdk

dk =1Ne

(Nγ)k0

dΩ(3.3)

where,(Nγ)k0is the number of photons of energy greater than k0 which reach point

P, kmax is the maximum photon energy in the spectrum and is equal to the incident

electron beam energy and k0 is the lowest transport limit of photon.

The total bremsstrahlung yield is theoretically expressed by the Bethe-

Heitler equation and many approximation have been used to solve it for practical

calculations. Seltzer and Berger [11] published the results of electron-nucleus

and electron-electron bremsstrahlung cross section, differential in photon energy

and angle, for all elements up to 10 GeV. In FLUKA the full set of Seltzer and

Berger cross section has been tabulated in an extended form [35]. In this work,

the simulations were carried out using FLUKA code to evaluate the materials and

thicknesses to see highest bremsstrahlung yield. The bremsstrahlung fluence in

term of (photon− cm−2 −MeV−1)/electron is estimated from FLUKA is defined

by the ICRU [36] and related to the bremsstrahlung yield by

dφdk

= NedSdk

dΩ

da(3.4)


where da is the cross-sectional area of the spehere at point P as shown in Fig-

ure 3.1.

The mean energy of the bremsstrahlung beam is useful quality indica-

tor [15].

Emean =1

S E0

∫ Emax

E0

EdSdE

dE (3.5)

Strictly speaking, the whole spectrum should be used in the evaluations of the

mean energy (E0=0). This would require knowledge of the spectral shape down

to energies well below the turnover pint. In practice, this is difficult to achieve,

especially for targets of low atomic number. It is therefore useful to define Emean

with a low energy cutoff.

3.3 Validation of Bremsstrahlung production capabilities of FLUKA

The FLUKA code was used to design the e− γ targets and to simulate

the configurations for the creation of bremsstrahlung beam. The reliability of our

simulation was confirmed by calculating the spectra for the setup of the exper-

iments performed by Faddegon et al. (1991) [15]. In his study, he used a 15

MeV electron beam incident on thick targets of various materials and measured

the mean energy and energy spectrum with a sodium iodide detector placed 300

cm away from the target at different angles with respect to the incident electron

beam. The simulation geometry was designed to match the experimental arrange-

ment shown in Figure 3.2(a) as closely as possible. The 15 MeV electron beam

was focused on Titanium exit window and subsequently the beam current was

measured with silicon surface detector. Further, the beam was made to incident

on the target passing through aluminum chamber. The targets were cylinders of

Be (11.67 g/cm2 thick, 6.72 g/cm2 radius), Al (9.74 g/cm2 thick, 9.81 g/cm2

radius), Pb (9.13 g/cm2 thick, 17.95 g/cm2 radius). The height as well as radius

of the respective target cylinder was kept approximately 110% of RCS DA such

that the beam hit the target along the axis of the cylinder. Although the thickness

of 110% of RCS DA in the forward direction was kept, sufficient to achieve high-

est photon intensity with acceptable electron contamination. The exit window,


(a) (b)

Figure 3.2: Experiment arrangement (a) used by Faddegon et al. [15] (b) used byDeshmukh et al. [37] for the measurement of Bremsstrahlung Yield.

current monitor, target chamber (describe by Faddegon et al [15]), target, and the

detector with shield was modeled in FLUKA for estimation of bremsstrahlung

yield at 0°(i.e forward direction). The results measured and calculated by Fad-

degon et al [15] along with the results estimated using FLUKA are shown in

Table 3.1. It is observed that the results obtained using FLUKA are comparable

with the measured one by experimentally.

Table 3.1: Integrated bremsstrahlung yield and mean energy of 15 MeV electron inci-dent on thick Be, Al, and Pb target the measurement and EGS4 calculations by Fadde-

gaon et al. [15] and FLUKA simulation(present).

Target Bremsstrahlung Yield Mean Energy(1/Sr) (MeV)

Measured Calculated FLUKA Measured Calculated FLUKABe 2.73 2.60 2.65 2.85 2.80 2.77Al 3.42 3.27 3.35 2.75 2.76 2.72Pb 2.92 3.07 2.94 3.20 3.25 3.23

Moreover, the experimental results published by Deshmukh et al. [37]

was also validated since the results were measured using 6 MeV Race-Track


Microtron at Pune University. Experimental setup used for the measurement of

bremsstrahlung radiation is shown in Figure 3.2(b). In this study the author used

6 MeV electron beam to incident on the 0.12 cm thick lead as e− γ target and

produced bremsstrahlung radiations measured using scintillation detector. The

same setup as in experimental conditions has been modeled in FLUKA for simu-

lating the results. The theoretical and experimental Bremsstrahlung spectrum for

lead at 6 MeV electron energy is shown in Figure 3.3. From the Figure 3.3 it has

been observed that the theoretical and experimental Bremsstrahlung spectra in

the energy range 0.5 to 2 MeV show almost similar trend with marginal increase

in the experimental case. However, in the energy range 2−6 MeV experimental

value are lower than predicted, which may be due to absorption of photons in

the target and air. In general, the experimentally obtained spectra are in good

agreement with the respective theoretical spectra done by FLUKA.

0 1 2 3 4 5 6

1xe3

e4

1xe5

1xe6

1xe7

e8

1xe9

1xe10

Experimental Curve

FLUKA Curve

No

. o

f P

ho

ton

s

Photon Energy (MeV)

Figure 3.3: Comparison of relative bremsstrahlung fluence measured by Deshmukh,et al [37] and calculated using FLUKA simulation(present).


3.4 Results

The set of simulation was carried out to estimate the bremsstrahlung

yield for

(a) Electron Energy :- 6 MeV, 9 MeV, 12 MeV, 15 MeV, and 18 MeV

(b) Materials used as e− γ target (Z):- Be(4), Al(13), Si(14), Fe(26), Cu(29),

Mo(42), Ag(47), Gd(64), Ta(73), W(74), Au(79), Pb(82), U(92). (The materials

having higher melting point were chosen for bremsstrahlung study.)

(c) Target Thickness:- ranging from 0.1% to 150% of RCS DA

The inputs for FLUKA code are defined as the beam diameter 0.3 cm,

beam direction along the Z axis and beam allowed to fall on the target perpendic-

ularly. The cylindrical geometry was chosen and thickness of the cylinder was

varied. The detector was kept at 10 cm from target along the Z direction for the

measurement of bremsstrahlung fluence in term of (photon−cm−2−MeV−1/)e−.

An energy cut was set to be 100 keV for electron (Ecut) and photon (Pcut). More-

over, the 1 ×108 to 1 ×109 primary particles were used to run the system to

minimise the statistical errors in the simulation. The estimated errors were found

to be less than 0.1% in the bremsstrahlung case, it almost takes ∼ 15 − 18 Hrs to

complete the run on Xeon Quad core processor.

The geometry used for the measurement of angular distribution of in-

tegrated bremsstrahlung fluence is shown in Figure 3.4. An electron beam is

incident on the e− γ target along Z direction and the generated radiations were

estimated. Sphere of radius 100 cm has been divided by parallel planes along Z

direction such that it can form 0.2 cm thick rings of sphere at various angles of

0° to 180° with respect to the incident electron beam. The horizontal lines in the

Figure 3.4 corresponds to the 0.2 cm thick rings for the measurement of particle

fluence at various angles. The e− γ conversion performances of several mate-

rials have been accurately studied by simulating the bremsstrahlung spectrum

obtained for each material as a function of the converter thickness for different

electron energies.

When high energy electron interacts with material, it produces bremss-


Z

100

The rings are detecting

surface at various angles

e target0

Electron

beambeam

X

100

100, 100 0

Figure 3.4: A view of XZ plane geometry used for the measurement of angular distri-bution of bremsstrahlung radiation in FLUKA simulation.

trahlung radiation through the inelastic collision of electrons with nucleus. The

variation in integrated bremsstrahlung fluence with e− γ target thickness for 6,

9, 12, 15 and 18 MeV incident electron energy is shown in Figure 3.5(a), 3.5(b),

3.5(c), 3.5(d) and 3.5(e) respectively. From Figure 3.5 it is observed that as the

e− γ target thickness increases, the bremsstrahlung fluence also increases till cer-

tain thickness and then decreases with increase in the thickness of e− γ target. It

is observed from the figures that the bremsstrahlung fluence peak is shifted to-

wards the lower thickness of the target with increase in the Z of the target. For

higher density material the peak is found at lower thickness. This mainly at-

tributes to the absorption of photon in the high density material itself. Moreover,

the thickness which gives maximum bremsstrahlung fluence for e− γ target is

increases with the Z of the target and also with incident electron energy. The


0

0.5

1

1.5

2

2.5

3

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)

e-γ target thickness (cm)

BeAlSiFeCuMoAgGdTaW

AuPbU

(a) 6 MeV

0

0.5

1

1.5

2

2.5

3

3.5

4

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(b) 9 MeV

Figure 3.5: Integrated bremsstrahlung fluence versus e− γ target thickness for (a) 6MeV and (b) 9 MeV energy electron incident on different materials.

same trend is observed for 9, 12, 15 and 18 MeV electron energy case. It is also

observed that Uranium gives maximum bremsstrahlung fluence at the 0.08 cm, 1

cm, 1.2 cm, 1.4 cm and 1.5 cm thickness of target for 6, 9, 12, 15 and 18 MeV


0

1

2

3

4

5

6

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(c) 12 MeV

0

1

2

3

4

5

6

7

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(d) 15 MeV

Figure 3.5: Integrated bremsstrahlung fluence versus e− γ target thickness for (c) 12MeV and (d) 15 MeV energy electron incident on different materials.

incident electron energy respectively and beryllium gives lowest bremsstrahlung

fluence for all energies.

Typical Photon fluence distribution in XY plane (7 cm × 7 cm, 1 mm/bin)


0

1

2

3

4

5

6

7

8

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(e) 18 MeV

Figure 3.5: Integrated bremsstrahlung fluence versus e− γ target thickness for (e) 18MeV energy electron incident on different materials.

1e-07

1e-06

1e-05

0.0001

0.001

Bre

mss

trah

lung

Flu

ence

((p

hoto

n/M

eV-c

m2 )/

elec

tron

)

X (cm)

Y (

cm)

-6 -4 -2 0 2 4 6

-6

-4

-2

0

2

4

6

Figure 3.6: Photon fluence distribution in XY plane (7 cm × 7 cm, 1mm/bin) for 6MeV electron incident on 0.08 cm thick tungsten target.

is shown in Figure 3.6 for 6 MeV electron incident on 0.08 cm thick tungsten

target. Figure 3.6 shows that the maximum photon fluence is in the forward


direction which is at center and it drops radially. The photon fluence is 0.001

(photon−MeV−1−cm−2)/e− at the center and drops to 10−7 at the edge. The

angular distribution of the relative bremsstrahlung fluence for each material at

thickness equal to the range of respective energy of electron are shown in Fig-

ure 3.7(a), 3.7(b), 3.7(c), 3.7(d), and 3.7(e), respectively for 6, 9, 12, 15, and 18

MeV electrons. It is observed from Figure 3.7 that the relative bremsstrahlung

radiations produced in the forward direction i.e. at 0° is more and decreases ex-

ponentially with increase in the angle. In addition, the relative bremsstrahlung

fluence decays very slowly for low Z materials and slowly for high Z materials

with increase in angle. However, till 8 to 9° the fluence converges for all the

materials. This is because dE/dx for electrons in the initial few angstrom layers

of the target is same and further increases in angle, the electron see long path and

have observed more statistical fluctuations in the dE/dx.

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

Rel

ativ

e B

rem

sstr

ahlu

ng F

luen

ce

Angle (degree)

Be 20.8 mmAl 13.6 mmSi 15.2 mmFe 4.9 mmCu 4.4 mmMo 3.9 mmAg 3.8 mmGd 5.3 mmTa 2.5 mmW 2.2 mm

Au 2.1 mmPb 3.7 mmU 2.2 mm

(a) 6 MeV

Figure 3.7: Angular distribution of bremsstrahlung fluence for (a) 6 MeV energy elec-tron incident on e− γ target of thickness equal to the range of electrons.

The angle at which bremsstrahlung intensity drops to half of the maxi-

mum bremsstrahlung intensity is calculated for each thickness of the e− γ target.

Half and tenth value is defined as the angles where the photon intensity drops


0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

Rel

ativ

e B

rem

sstr

ahlu

ng F

luen

ce

Angle (degree)



(b) 9 MeV

0

10

20

30

40

50

60

70

80

90

100

110

0 20 40 60 80 100

Rel

ativ

e B

rem

sstr

ahlu

ng F

luen

ce

Angle (degree)



(c) 12 MeV

Figure 3.7: Angular distribution of bremsstrahlung fluence for (b) 9 MeV and (c)12 MeV energy electron incident on e− γ target of thickness equal to the range of

electrons.

to 12 and 1

10 of the maximum intensity. The half angle explains about the beam

divergence, more the half angle value more the beam spread, therefore intensity

is distributed. The variation in bremsstrahlung half angle value with thickness of


0

10

20

30

40

50

60

70

80

90

100

110

0 20 40 60 80 100

Rel

ativ

e B

rem

sstr

ahlu

ng F

luen

ce

Angle (degree)

Be 49.8 mmAl 30.8 mmSi 34.3 mmFe 10.6 mmCu 9.4 mmMo 8.0 mmAg 7.7 mm

Gd 10.3 mmTa 4.8 mmW 4.1 mm


(d) 15 MeV

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

Rel

ativ

e B

rem

sstr

ahlu

ng F

luen

ce

Angle (degree)




(e) 18 MeV

Figure 3.7: Angular distribution of bremsstrahlung fluence for (d) 15 MeV and (e)18 MeV energy electron incident on e− γ target of thickness equal to the range of

electrons.

e− γ target are shown in Figure 3.8(a), 3.8(b), 3.8(c), 3.8(d) and 3.8(e) respec-

tively for 6, 9, 12, 15 and 18 MeV electron energy. It is observed from Figure 3.8

that as the e− γ target thickness increases, the bremsstrahlung half angle value


2

4

6

8

10

12

14

16

18

20

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung h

alf

angle

val

ue

(deg

ree)


BeAlSiFeCuMoAgGdTaW

AuPbU

(a) 6 MeV

2

4

6

8

10

12

14

16

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung h

alf

angle

val

ue

(deg

ree)


BeAlSiFeCuMoAgGdTaW

AuPbU

(b) 9 MeV

Figure 3.8: Angle at which maximum bremsstrahlung intensity becomes half versusthe e− γ target thickness for (a) 6 MeV and (b) 9 MeV energy electron incident on

different materials.

increases slowly for low Z materials i.e for beryllium and increases very sharply

for high Z material i.e. uranium. This means that the bremsstrahlung radiations


3

4

5

6

7

8

9

10

11

12

13

14

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung h

alf

angle

val

ue

(deg

ree)


BeAlSiFeCuMoAgGdTaW

AuPbU

(c) 12 MeV

3

4

5

6

7

8

9

10

11

12

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung h

alf

angle

val

ue

(deg

ree)


BeAlSiFeCuMoAgGdTaW

AuPbU

(d) 15 MeV

Figure 3.8: Angle at which maximum bremsstrahlung intensity becomes half versusthe e− γ target thickness for (c) 12 MeV and (d) 15 MeV energy electron incident on


spread out more as increases in thickness and Z of the material. It is also ob-

served that the bremsstrahlung half angle value is higher for high Z materials.

Mean energy of the bremsstrahlung radiations coming out from e− γ


3

4

5

6

7

8

9

10

11

12

0.001 0.01 0.1 1 10 100

Bre

mss

trah

lung h

alf

angle

angle

(deg

ree)


BeAlSiFeCuMoAgGdTaW

AuPbU

(e) 18 MeV

Figure 3.8: Angle at which maximum bremsstrahlung intensity becomes half versusthe e− γ target thickness for (e)18 MeV energy electron incident on different materials.

target for 6, 9, 12, 15, and 18 MeV energy incident electrons are shown in Fig-

ure 3.9(a), 3.9(b), 3.9(c), 3.9(d) and 3.9(e) respectively. It is observed from Fig-

ure 3.9 that the mean energy of the bremsstrahlung spectrum decreases with an-

gle. The forward direction (0°) bremsstrahlung spectrum is found to be more

harden than the orthogonal (90°) and backward direction (180°). It is also seen

form the figure that mean energy is found to be more in case of high Z (U) ma-

terial than low Z material (Be). It is important to note in this regard that as the

energy of the electron beam increases the bremsstrahlung spectrum found to be

more harden i.e. the mean energy of bremsstrahlung increases with energy. Typi-

cally, for beryllium, it is varied from 0.9 MeV to 2 MeV with increasing electron

beam energy from 6 to 18 MeV at the forward direction (0°).

The bremsstrahlung energy spectrum generated in e− γ target of thick-

ness equal to the range of the incident electron of energy 6, 9, 12, 15 and 18 MeV

are shown in Figure 3.10(a), 3.10(b), 3.10(c), 3.10(d) and 3.10(e) respectively.

In general, for the bremsstrahlung energy spectra, the fluence increases with de-

creasing photon energy until the turnover point of the spectrum is reached. This


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 20 40 60 80 100 120 140 160 180

Mea

n e

ner

gy o

f bre

mss

trah

lung (

MeV

)

Angle (degree)



(a) 6 MeV

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120 140 160 180

Mea

n e

ner

gy o

f bre

mss

trah

lung (

MeV

)

Angle (degree)



(b) 9 MeV

Figure 3.9: Angular distribution of bremsstrahlung mean energy for (a) 6 MeV and(b) 9 MeV energy electron incident on e− γ target of thickness equal to the range of

electron.


0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100 120 140 160 180

Mea

n e

ner

gy o

f bre

mss

trah

lung (

MeV

)

Angle (degree)



(c) 12 MeV

0

0.5

1

1.5

2

2.5

3

3.5

0 20 40 60 80 100 120 140 160 180

Mea

n e

ner

gy o

f bre

mss

trah

lung (

MeV

)

Angle (degree)




(d) 15 MeV

Figure 3.9: Angular distribution of bremsstrahlung mean energy for (c) 12 MeV and(d) 15 MeV energy electron incident on e− γ target of thickness equal to the range of

electron.

is the point at which the bremsstrahlung beam begins to be strongly attenuated in

the target. Typically, the turnover point is varies between 500 to 600 keV energy

for 6 to 18 MeV incident electron on lead target.


0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120 140 160 180

Mea

n e

ner

gy o

f bre

mss

trah

lung (

MeV

)

Angle (degree)




(e) 18 MeV

Figure 3.9: Angular distribution of bremsstrahlung mean energy for (e) 18 MeV en-ergy electron incident on e− γ target of thickness equal to the range of electron.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.1 1

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

-MeV

-1)/

e_)

Bremsstrahlung Energy (MeV)



(a) 6 MeV

Figure 3.10: Energy spectra of bremsstrahlung radiations from e− γ target of thick-ness equal to the range of the electron bombarded with (a) 6 MeV electron energy for



0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.1 1 10

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

-MeV

-1)/

e_)




(b) 9 MeV

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.1 1 10

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

-MeV

-1)/

e_)




(c) 12 MeV

Figure 3.10: Energy spectra of bremsstrahlung radiations from e− γ target of thicknessequal to the range of the electron bombarded with (b) 9 MeV and (c) 12 MeV electron

energy for different materials.

Typical results for 6 MeV electron energy, the variation in transmit-

ted electron fluence as function of e− γ target thickness for different materials

is shown in Figure 3.11. Beyond the target, there is contribution of secondary


0

0.5

1

1.5

2

2.5

0.1 1 10

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

-MeV

-1)/

e_)





(d) 15 MeV

0

0.5

1

1.5

2

2.5

3

0.1 1 10

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

-MeV

-1)/

e_)





(e) 18 MeV

Figure 3.10: Energy spectra of bremsstrahlung radiations from e− γ target of thicknessequal to the range of the electron bombarded with (d) 15 MeV and (e) 18 MeV electron

energy for different materials.

and direct transmitted electrons in the photon beam. Figure 3.11 shows only

the contribution of direct transmitted electrons in photon beam. It is found that

the e− γ target thickness increases, more the electrons get absorbed in the target


0

0.5

1

1.5

2

2.5

3

3.5

4

0.001 0.01 0.1 1 10 100

Ele

ctro

n F

luen

ce (

(ele

ctro

n-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

Figure 3.11: Variation in transmitted electron fluence as a function of e− γ targetthickness of different materials for 6 MeV electron.

which results into more bremsstrahlung and less contribution of electrons beyond

the target. Larger thickness is required to stop the incident electrons inside the

e− γ target for low Z material, while smaller thickness is sufficient to stop the

incident electron in high Z material.

The variation in integrated positron fluence as a function of e− γ target

thickness for 6, 9, 12, 15 and 18 MeV incident electron energy is shown in Fig-

ure 3.12(a), 3.12(b), 3.12(c), 3.12(d) and 3.12(e) respectively.


1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.001 0.01 0.1 1 10 100

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(a) 6 MeV

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.001 0.01 0.1 1 10 100

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(b) 9 MeV

Figure 3.12: Integrated positron fluence versus e− γ target thickness for (a) 6 MeVand (b) 9 MeV incident electron energy on different materials.

The contribution of positron is also estimated in the forward direction which

found to be 3 to 4 order less than the bremsstrahlung intensity as shown in Fig-

ure 3.12. The e− γ target produces positrons through the pair production process


1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

0.001 0.01 0.1 1 10 100

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(c) 12 MeV

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

0.001 0.01 0.1 1 10 100

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(d) 15 MeV

Figure 3.12: Integrated positron fluence versus e− γ target thickness for (c) 12 MeVand (d) 15 MeV incident electron energy on different materials.

and which has more cross section for higher energy of bremsstrahlung radia-

tion. More number of positrons are produced in high Z targets since the cross

section for pair production is directly proportional to Z2 of the element. It is


1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

0.001 0.01 0.1 1 10 100

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(e) 18 MeV

Figure 3.12: Integrated positron fluence versus e− γ target thickness for (e) 18 MeVincident electron energy on different materials.

observed from the figure that as the e− γ target thickness increases the positron

contribution also increases till a certain thickness and beyond that the positron

contribution falls. This is due to the absorption of positron in the e− γ target

itself.

If the photonuclear reaction threshold of the e− γ target is less than

the incident electron energy, then neutrons can be produced in the e− γ target.

The photo nuclear reaction threshold for the Be, Al, Si, Fe, Cu, Mo, Ag, Gd, Ta,

W, Au, Pb and U is 1.67, 13.06, 17.18, 11.20, 10.85, ∼ 8 − 9, 9.54, 8.5, 7.58,

7.20, 8.07, 7.37 and 5.30 MeV respectively. (The threshold values taken from

Atlas of Giant Dipole Resonance). The mentioned threshold energies are for the

isotope which having highest abundance in nature. The other isotopes of the ele-

ment have different thresholds. For the case of 6 MeV electron energy, beryllium

and uranium produces neutrons through photo nuclear and fission process which

is shown in Figure 3.13(a). For 9 MeV electron energy, U produces highest neu-

tron fluence because of higher cross section and fission in the target which is

shown in Figure 3.13(b). Moreover, the materials such as Al, Si, Fe, Cu, Ag


1e-13

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

0.001 0.01 0.1 1 10 100

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(a) 6 MeV

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.001 0.01 0.1 1 10 100

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(b) 9 MeV

Figure 3.13: Integrated neutron fluence versus e− γ target thickness for (a) 6 MeV and(b) 9 MeV incident electron energy on different materials.

also produces negligible contribution of neurons in bremsstrahlung beam. It is

observed from the Figure 3.13(c) that the U is giving maximum neutron fluence,


1e-13

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001 0.01 0.1 1 10 100

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(c) 12 MeV

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.001 0.01 0.1 1 10 100

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(d) 15 MeV

Figure 3.13: Integrated neutron fluence versus e− γ target thickness for (c) 12 MeVand (d) 15 MeV incident electron energy on different materials.

while Al is not producing neutron in the target. However, Si is having lowest con-

tribution of neutrons seen for 12 MeV energy electrons incident on e− γ target.

Whereas, for the case of 15 MeV incident electron energy, the neutron produced


1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.001 0.01 0.1 1 10 100

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(e) 18 MeV

Figure 3.13: Integrated neutron fluence versus e− γ target thickness for (e) 18 MeVincident electron energy on different materials.

in the e− γ target is shown in Figure 3.13(d). It is observed that all the materials

having photonuclear reaction threshold lower than the 15 MeV electron energy,

shows neutrons for e− γ target. Out of this U is giving maximum neutron fluence

because of its higher cross section and fission. The neutron fluence contribution

in Al and Si material found to be negligible. Moreover, the threshold energy

for Be is lower than other materials, but it produces less neutrons because of

lower cross section value. However, the materials such as Au, Ta, W almost pro-

duces same amount of neutron fluence. Variation of neutron fluence produced

in e− γ target bombard by 18 MeV electron is shown in Figure 3.13(e), which

shows that high Z elements produces maximum neutron fluence while for low Z

electron produces minimum neutron fluence. It is also observed from all the Fig-

ure 3.13 that the neutron fluence increases till certain thickness and then further

decrease with increases in the e− γ target thickness.


Figure 3.14(a) shows the variation in bremsstrahlung fluence with atomic

number of e− γ target for 6 to 18 MeV electron energies. It is observed from the

figure that the usually bremsstrahlung fluence increases with Z of the e− γ target

except gadolinium and lead where bremsstrahlung fluence found to be less. This

attributes mainly due to the fall in the density of the respective material. Variation

in mean energy of bremsstrahlung radiation with atomic number of e− γ target

is shown in Figure 3.14(b). From this figure it is seen that for 6 MeV energy

electron the mean energy increases continuously with Z, whereas for 18 MeV in-

cident electron there is fluctuations in the mean energy of bremsstrahlung radia-

tion for Al, Si, Ta, W, Au due to there respective variations in the absorption cross

section for bremsstrahlung radiation. Variation in the contribution of positron flu-

ence with atomic number of e− γ target is shown in Figure 3.14(c). From this

figure it is also observed that the positron fluence increases with atomic number

except Gd and Pb for which it is found less. This is because of the lower density

for the respective target as compared to others. Variation in the neutron fluence

with atomic number of e− γ target for 6-18 MeV electron energy is shown in

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)

Atomic Number of e-γ target

6 MeV Electron9 MeV Electron

12 MeV Electron15 MeV Electron18 MeV Electron

(a)

Figure 3.14: (a) Variation in bremsstrahlung fluence with respect to the atomic numberof e− γ target for 6 − 18 MeV incident electron energies.


0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60 70 80 90 100

Bre

mss

trah

lung M

ean E

ner

gy (

MeV

)




(b)

Figure 3.14: (b) Variation in mean energy of bremsstrahlung with respect to the atomicnumber of e− γ target for 6 − 18 MeV incident electron energies.

0

0.005

0.01

0.015

0.02

0.025

0 10 20 30 40 50 60 70 80 90 100

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)




(c)

Figure 3.14: (c) Variation in positron fluence with respect to the atomic number ofe− γ target for 6 − 18 MeV incident electron energies.


1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0 10 20 30 40 50 60 70 80 90 100

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)




(d)

Figure 3.14: (d) Variation in neutron fluence with respect to the atomic number ofe− γ target for 6 − 18 MeV incident electron energies.

Figure 3.14(d). It is observed from figure that the neutron fluence increases with

atomic number and mainly depending on the respective cross section of the tar-

gets.

Overall, the variation of bremsstrahlung fluence, mean bremsstrahlung energy,

positron fluence and neutron fluence with incident electron energy for different

targets are shown in Figure 3.15(a), 3.15(b), 3.15(c) and 3.15(d) respectively.

In all the cases it is observed that as energy of the incident electron increases

the bremsstrahlung fluence, mean energy, positron fluence, neutron fluence in-

creases. Whereas, the contribution of each fluence of bremsstrahlung, positron,

neutron and mean energy increases with the Z of the target materials. Moreover,

it is observed that the contribution of positron and neutron is depending on the

intensity of bremsstrahlung radiations generated in the target.


0

0.5

1

1.5

2

2.5

3

3.5

4

6 8 10 12 14 16 18

Bre

mss

trah

lung F

luen

ce (

(photo

n-c

m-2

)/e_

)

Electron Energy (MeV)

BeAlSiFeCuMoAgGdTaW

AuPbU

(a)

Figure 3.15: (a) Variation in bremsstrahlung fluence with respect to the incident elec-tron energy on different atomic number of e− γ target.

0

0.5

1

1.5

2

2.5

3

6 8 10 12 14 16 18

Bre

mss

trah

lung M

ean E

ner

gy (

MeV

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(b) Mean energy of bremsstrahlung

Figure 3.15: (b) Variation in mean energy of bremsstrahlung with respect to the inci-dent electron energy on different atomic number of e− γ target.


1e-06

1e-05

0.0001

0.001

0.01

0.1

6 8 10 12 14 16 18

Posi

tron F

luen

ce (

(posi

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(c)

Figure 3.15: (c) Variation in positron fluence with respect to the incident electronenergy on different atomic number of e− γ target.

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

6 8 10 12 14 16 18

Neu

tron F

luen

ce (

(neu

tron-c

m-2

)/e_

)


BeAlSiFeCuMoAgGdTaW

AuPbU

(d) Neutron fluence

Figure 3.15: (d) Variation in neutron fluence with respect to the incident electronenergy on different atomic number of e− γ target.


3.5 Conclusion

The data of bremsstrahlung radiations generated in various target for different

energy of electron from 6 to 18 MeV are summarized and concluded below,

• Maximum bremsstrahlung fluence is obtained for high Z material (U) and

higher incident electron energy (18 MeV).

• The mean energy of bremsstrahlung radiation for high Z target is observed

more.

• The bremsstrahlung fluence is maximum in the forward direction and it

decreases sharply with angle.

• High Z targets produce higher neutron fluence for energies greater than 12

MeV electron.

• The contribution of direct transmitted electrons beyond the range of elec-

tron in the target is negligible.

• The contribution of positron in the bremsstrahlung beam is negligible.

3.6 Future Scope

The study shown here only considers the individual targets. Based on the re-

sults further studies can be carried out using multilayer targets. The multilayer

target can be formed with the combinations of materials such that the maximum

bremsstrahlung radiations can be obtained with marginal contribution of electron,

positron and neutron.

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