Investigation of the energy deposition profile in NaCl under electron irradiation
We have proposed a new model for the calculation of the absorbed dose profile in a thick target under 0.1…3 MeV electron irradiation. The build-up phenomenon is shown to increase the maximum of the energy deposition profile in thick samples by a factor of two in comparison with thin targets as a r...
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| Cite this: | Investigation of the energy deposition profile in NaCl under electron irradiation / V.V. Gann, H.W. den Hartog, D.I. Vainshtein // Вопросы атомной науки и техники. — 2004. — № 1. — С. 197-199. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-790722015-03-26T03:01:59Z Investigation of the energy deposition profile in NaCl under electron irradiation Gann, V.V. den Hartog, H.W. Vainshtein, D.I. Применение ускоренных пучков We have proposed a new model for the calculation of the absorbed dose profile in a thick target under 0.1…3 MeV electron irradiation. The build-up phenomenon is shown to increase the maximum of the energy deposition profile in thick samples by a factor of two in comparison with thin targets as a result of backscattered and multi-scattered electrons. The absorbed dose profile in NaCl for 0.5 MeV electron irradiation has been determined by measuring the stored energy with differential scanning calorimetry. Запропоновано нову модель для розрахунку профілів поглиненої енергії в товстих мішенях, що опромінюються пучком електронів з енергіями 0.1…3 МеВ. Показано, що внаслідок ефекту накопичування дози, зв'язаного з багаторазовим і зворотним розсіюванням електронів, максимальне значення поглиненої енергії у товстих мішенях збільшується вдвічі в порівнянні з тонкими мішенями. Вивчено профіль розподілу поглиненої енергії в кристалічній пластинці NaCl, опроміненої електронами з енергією 0.5 МеВ, шляхом вимірювання запасеної енергії методом диференціальної скануємої калориметрії. Предложена новая модель для расчета профилей поглощенной энергии в толстых мишенях, облучаемых пучком электронов с энергиями 0.1…3 МэВ. Показано, что вследствие эффекта накопления дозы, связанного с многократным и обратным рассеянием электронов, максимальное значение поглощенной энергии в толстых мишенях увеличивается вдвое по сравнению с тонкими мишенями. Изучен профиль распределения поглощенной энергии в кристаллической пластинке NaCl, облученной электронами с энергией 0.5 МэВ, путем измерения запасенной энергии методом дифференциальной сканирующей калориметрии. 2004 Article Investigation of the energy deposition profile in NaCl under electron irradiation / V.V. Gann, H.W. den Hartog, D.I. Vainshtein // Вопросы атомной науки и техники. — 2004. — № 1. — С. 197-199. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 61.80.Fe, 81.40.Wx http://dspace.nbuv.gov.ua/handle/123456789/79072 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Применение ускоренных пучков Применение ускоренных пучков |
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Применение ускоренных пучков Применение ускоренных пучков Gann, V.V. den Hartog, H.W. Vainshtein, D.I. Investigation of the energy deposition profile in NaCl under electron irradiation Вопросы атомной науки и техники |
| description |
We have proposed a new model for the calculation of the absorbed dose profile in a thick target under 0.1…3 MeV electron
irradiation. The build-up phenomenon is shown to increase the maximum of the energy deposition profile in thick samples by a
factor of two in comparison with thin targets as a result of backscattered and multi-scattered electrons. The absorbed dose profile
in NaCl for 0.5 MeV electron irradiation has been determined by measuring the stored energy with differential scanning
calorimetry. |
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Article |
| author |
Gann, V.V. den Hartog, H.W. Vainshtein, D.I. |
| author_facet |
Gann, V.V. den Hartog, H.W. Vainshtein, D.I. |
| author_sort |
Gann, V.V. |
| title |
Investigation of the energy deposition profile in NaCl under electron irradiation |
| title_short |
Investigation of the energy deposition profile in NaCl under electron irradiation |
| title_full |
Investigation of the energy deposition profile in NaCl under electron irradiation |
| title_fullStr |
Investigation of the energy deposition profile in NaCl under electron irradiation |
| title_full_unstemmed |
Investigation of the energy deposition profile in NaCl under electron irradiation |
| title_sort |
investigation of the energy deposition profile in nacl under electron irradiation |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2004 |
| topic_facet |
Применение ускоренных пучков |
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http://dspace.nbuv.gov.ua/handle/123456789/79072 |
| citation_txt |
Investigation of the energy deposition profile in NaCl under electron irradiation / V.V. Gann, H.W. den Hartog, D.I. Vainshtein // Вопросы атомной науки и техники. — 2004. — № 1. — С. 197-199. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT gannvv investigationoftheenergydepositionprofileinnaclunderelectronirradiation AT denhartoghw investigationoftheenergydepositionprofileinnaclunderelectronirradiation AT vainshteindi investigationoftheenergydepositionprofileinnaclunderelectronirradiation |
| first_indexed |
2025-07-06T03:10:35Z |
| last_indexed |
2025-07-06T03:10:35Z |
| _version_ |
1836865485276184576 |
| fulltext |
INVESTIGATION OF THE ENERGY DEPOSITION PROFILE IN NaCl
UNDER ELECTRON IRRADIATION
V.V. Gann
National Science Center “Kharkov Institute of Physics and Technology”,
1, Akademicheskaya st., 61108, Kharkov, Ukraine; E-mail: gann@kipt.kharkov.ua;
H.W. den Hartog, D.I. Vainshtein
University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands;
E-mail: D.Vainshtein@phys.rug.nl
We have proposed a new model for the calculation of the absorbed dose profile in a thick target under 0.1…3 MeV electron
irradiation. The build-up phenomenon is shown to increase the maximum of the energy deposition profile in thick samples by a
factor of two in comparison with thin targets as a result of backscattered and multi-scattered electrons. The absorbed dose profile
in NaCl for 0.5 MeV electron irradiation has been determined by measuring the stored energy with differential scanning
calorimetry.
PACS: 61.80.Fe, 81.40.Wx
1. INTRODUCTION
It is necessary to distinguish two different quantities:
the energy losses and energy deposition by electrons in
a target. The energy loss is the specific energy, which is
lost by incident electrons of the beam at a given depth,
whereas the energy deposition is the specific energy dis-
sipated by primary, δ-, secondary, and other high energy
electrons absorbed by the sample at a given depth. The
energy losses of monoenergetic electrons due to ioniza-
tion and excitation processes in thin targets can be de-
scribed with the Bethe-Bloch formula [1]. The energy
loss tables, including the density correction δ and exper-
imentally derived values of mean excitation energy I,
were published by Seltzer and Berger [2] (for NaCl, the
recommended value is I = 175.3 eV).
The calculation of energy losses by electrons in a
thick target is a rather complex problem that requires a
sophisticated approach. The main difficulty arises from
the back scattering and multi-scattering of electrons in
the matter. Hence, it is necessary to take into considera-
tion the role of δ-electrons in the process of transfer of
energy, when calculating the energy deposition profile.
Spencer [3], Rao [4], and Kobetich and R. Katz [5] per-
formed extended analytical calculations of the energy
loss profiles for an incident electron beam, which is di-
rected perpendicularly to a flat surface. Many calcula-
tions have been carried out in the literature using the
Monte-Carlo method [8] for modeling the motion of
high energy electrons in matter.
2. ENERGY LOSS PROFILE
The most complete calculations of the dissipation of
energy of perpendicular electron beams in matter have
been made by Spencer [3]. Rao [4] derived a simple for-
mula for the fraction of incident electrons of energy E
transmitted by an absorber of thickness t:
)]/(exp[1
)exp(1
hRtg
gh
−+
−+=η , (1)
where 2.22.0 162.9 −− += ZZg and 27.0/63.0 += AZh .
The dependence of the transmission η on the sample
thickness t, calculated on Eq.1 for a 0.5 MeV electron
beam in NaCl is displayed in Fig.1.
The point at which the extrapolation of the linear re-
gion meets x-axis is defined as the practical (or extrap-
olated) range RP, whereas the point were the tail meets
x-axis is known as the maximum range R0 (the back-
ground is neglected).
The energy loss profile of a perpendicular incident
electron beam can be calculated as proposed in [5]:
dt
tREdS )]([ −= η
. (2)
Here Е(R) is the energy-range relation.
3. RANGE-ENERGY RELATION
The maximum range of the electrons in matter can
easily be calculated in the continuous-slowing-down-ap-
proximation (CSDA):
∫
=
E
totdx
'dE/'dE)E(R
0
0 , (3)
here totdx
dE
'
is the value of the total energy losses for
an electron with energy E'. R0 is the total path length
traveled to rest. Extended tables of CSDA ranges of
electrons in many materials and compounds were pub-
lished by Seltzer and Berger [2]. Katz and Penfold [6]
approximated the practical ranges for pure aluminum
with the following formula, which is valid in the energy
interval 0.01…3 MeV:
RAl = 0.421 E
1.265 - 0.0954 ln E , (4)
here RP is the range in g/cm
2
and E – the energy of the
electrons in MeV.
0.00 0.02 0.04 0.06 0.08 0.10
0.0
0.2
0.4
0.6
0.8
1.0
RP R0
e -> NaCl
E=0.5 MeV
Tr
an
sm
is
si
on
Thickness, cm
Fig.1. Dependence of beam transmission on the thick-
ness of NaCl samples
4. ENERGY DEPOSITION PROFILE
Some experimentally observed energy deposition
profiles for aluminum are shown in Fig.2 [7]. The ener-
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 1.
Series: Nuclear Physics Investigations (42), p.197-199. 197
gy deposition profiles as well as the energy loss profiles
show a pronounced maximum.
Depth, g/cm2
Fig.2. Energy deposition profiles in aluminum, taken
from [7]
The calculation of the electron beam energy deposi-
tion in a target is a rather complicated problem because
of multiple scattering of electrons by atoms and the ap-
pearance of δ-electrons. The Monte Carlo simulation
method is used for the evaluation of the energy deposi-
tion profile in 3D-geometry. But the Monte Carlo calcu-
lations are very time consuming. So, for a quick evalua-
tion we have developed a simple semi-empirical method
for the calculation of the electron beam energy deposi-
tion Q(x), based on dependable, measured energy depo-
sition profiles for a parallel electron beam in aluminum.
5. UNIVERSAL PROFILE APPROXIMA-
TION
It is seen from Fig. 2 that in the 100 keV…3 MeV
energy region, the energy deposition profile Q(x) can be
easily scaled in x by the value of practical range RP(E)
and expressed in terms of the universal function P(ξ)
(see Fig.3)
[ ]{ } ])295.27.2(15.0[)1295.2(95.0
065.1)( 8.1 ξξ
ξ
−+−
=
ch
P (5)
Here ξ is depth x, scaled by the extrapolated range, ξ =
x / RP(E). The values of the parameters were obtained by
fitting to the experimental data (Fig.2) Function P(ξ) is
normalized as 1)(
0
=∫
∞
ξξ dP . One can calculate the
electron range in aluminum RAl(E) by using Eq.(4). For
other materials, having an atomic number Z and an
atomic mass A, the electron range can be found in [2] or
can be evaluated using the following scaling law
( ) )(482.0)( ERZ
AER AlP = . (6)
So, the energy deposition profile for E MeV-energy
electrons can be expressed as
=
)()(
)(
ER
xP
ER
ExQ
PP
. (7)
The comparison of the profiles, calculated by
Eqs.(4-7) (labeled as PROFILE), with the experimental
data for water [7] and with some theoretical results, ob-
tained by the moment's series method for copper [8], is
shown in Fig.4 and 5, respectively.
6. CALCULATION OF THE AVERAGE
ABSORBED DOSE
Having the energy deposition profile Q(x), we can
calculate the average energy deposition Qav for the sam-
ple of given thickness t:
.')'()(
0
1 ∫=
t
tav dxxQtQ (7)
The dependence of Qav on the sample thickness t for
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
P
ξ
Fig.3. The universal profile of energy deposition
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
PROFILE
Experiment
e -> H2O
E = 3.1 MeV
E
ne
rg
y
de
po
si
tio
n,
M
eV
/c
m
Depth, cm
Fig.4. The energy deposition profiles in H2O
0,0 0,1 0,2 0,3 0
10
20
30
PROFILE
Moments method
e --> Cu
E = 4 MeV
d
E
/d
x,
M
eV
/c
m
Depth, cm
Fig.5. The energy deposition profile in Cu
NaCl irradiated with 0.5 MeV electrons is shown in
Fig.6.
The average values of the deposited energy are
plotted in Fig.6 together with energy losses, calculated
using the Bethe-Bloch formula (broken line) with
I=175.3 eV (as proposed by Seltzer-Berger).
0,00 0,02 0,04 0,06 0,08 0,10
0
2
4
6
8
10
Al - based thin-target value
e -> NaCl
E = 0.5 MeVQ
a
v ,
M
eV
/c
m
Thickness, cm
Fig.6. The average deposition profile with and without
taking in to account the effect of the back scattering and
multi-scattering electrons
198
En
er
gy
d
ep
os
iti
on MeV
One can see that taking into account the build-up of the
energy deposition due to back scattering and multi-scat-
tering of electrons results in an increase of the irradia-
tion doses of approximately 100 %.
7. COMPARISON OF THE EXPERIMEN-
TAL AND THEORETICAL RESULTS
Experimental investigations of the energy deposition
profiles in NaCl platelets under 0.5 MeV electron irradi-
ation have been performed. A set of NaCl samples,
doped with 0.1 mol% K with different values for the
thickness were irradiated by the Groningen electron ac-
celerator at 100°C up to a fluence of n=0.63 C/cm2. The
depth distribution of the absorbed dose was determined
by measuring the stored energy associated with radia-
tion damage, which was created in NaCl during electron
irradiation. The stored energy was measured for each
sample, using differential scanning calorimetry (DSC).
The experimental results are plotted in Fig.7 together
with the predicted average stored energy profile.
0,0 0,2 0,4 0,6 0,8 1,0 1,2
0,0
0,2
0,4
0,6
0,8 e -> NaCl
E = 0.5 MeV
Experiment
Fitting
St
or
ed
e
ne
rg
y,
J
/g
Thickness, mm
Fig.7. The average stored energy vs. the sample
thickness
The average stored energy W(t) is assumed to be
proportional to the average absorbed dose:
∫=
t
dxxQ
t
CntW
0
')'()(
ρ
. (8)
Here n is the electron fluence, ρ is the density of the
sample, C is a proportionality factor, which has been
obtained by fitting.
The comparison of the experimental data with the
calculated profile has shown that the proposed method
can serve as a baseline for an evaluation of the absorbed
dose in alkali halides under electron irradiation in the
MeV-energy range.
8. DISCUSSION
In the past, a point of concern has been the question
regarding the dose rate produced by the electron beam.
Until now we have employed the method published by
Berger and Seltzer, which is used extensively in the
present literature. We have concluded that this method
does not account for eventual effects associated with the
build-up phenomenon, in particular, in the presence of
the Al-target plate in which the samples are
accommodated. These effects lead to deviations in the
dose rate from the Berger and Seltzer values. In this
paper we have designed a new model for the calculation
of the dose rate in which the secondary effects are
included.
ACKNOWLEDGEMENT
This study is supported by the Dutch Ministry of
Economic Affairs.
REFERENCES
1. H.A. Bethe. Handbuch fur Physik. Springer Verlag,
Berlin, 1933, v. 24/2.
2. M.J. Berger and S. M. Seltzer. Stopping power for
electrons and positrons (ICRU-37). Washington
D.C., 1984.
3. L.V. Spencer. Natl. Bur. Std. (U.S.). Monograph 1.
1959.
4. B.N. Shubba Rao // Nucl. Instr. Methods. 1966,
v. 44, p. 155.
5. E.J. Kobetich and R. Katz // Phys. Rev. 1968,
v. 170, p. 391.
6. L. Katz and A.S. Penfold // Rev. Mod. Phys. 1952,
v. 24, p. 28.
7. Handbuch der Physik. Springer Verlag, Berlin.
1958, b. 34.
8. А.М.Colchuzhkin, V.V.Ukchaikin. Introduction
into the theory of particle passing through the mat-
ter. M.: “Atomizdat”, 1978
ИССЛЕДОВАНИЕ ПРОФИЛЕЙ ПОГЛОЩЕННОЙ ЭНЕРГИИ В КРИСТАЛЛАХ NaCl
ПРИ ЭЛЕКТРОННОМ ОБЛУЧЕНИИ
В.В. Ганн, Г.В. ден Хартог, Д.И. Вайнштейн
Предложена новая модель для расчета профилей поглощенной энергии в толстых мишенях, облучаемых
пучком электронов с энергиями 0.1…3 МэВ. Показано, что вследствие эффекта накопления дозы, связанно-
го с многократным и обратным рассеянием электронов, максимальное значение поглощенной энергии в тол-
стых мишенях увеличивается вдвое по сравнению с тонкими мишенями. Изучен профиль распределения
поглощенной энергии в кристаллической пластинке NaCl, облученной электронами с энергией 0.5 МэВ, пу-
тем измерения запасенной энергии методом дифференциальной сканирующей калориметрии.
ДОСЛІДЖЕННЯ ПРОФІЛІВ ПОГЛИНЕНОЇ ЕНЕРГІЇ В КРИСТАЛАХ NaCl
ПРИ ЕЛЕКТРОННОМУ ОПРОМІНЕННІ
В.В. Ганн, Г.В. ден Хартог, Д.І. Вайнштейн
Запропоновано нову модель для розрахунку профілів поглиненої енергії в товстих мішенях, що
опромінюються пучком електронів з енергіями 0.1…3 МеВ. Показано, що внаслідок ефекту накопичування
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 1.
Series: Nuclear Physics Investigations (42), p.197-199. 199
дози, зв'язаного з багаторазовим і зворотним розсіюванням електронів, максимальне значення поглиненої
енергії у товстих мішенях збільшується вдвічі в порівнянні з тонкими мішенями. Вивчено профіль розподілу
поглиненої енергії в кристалічній пластинці NaCl, опроміненої електронами з енергією 0.5 МеВ, шляхом
вимірювання запасеної енергії методом диференціальної скануємої калориметрії.
200
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