Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix
By means of the Monte Carlo computer modeling technique the depth dependencies of energy deposition and concentration of radiation induced point defects have been calculated in heterogeneous assemblies of Hastelloy plates embedded into the melt of fluoride salts and irradiated by 8–10 MeV electron b...
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Bakai, A.S. Bratchenko, M.I. Dyuldya, S.V. 2015-04-18T18:49:06Z 2015-04-18T18:49:06Z 2005 Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix / A.S. Bakai, M.I. Bratchenko, S.V. Dyuldya // Вопросы атомной науки и техники. — 2005. — № 4. — С. 24-31. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 28.41.Qb, 28.50.Ft, 61.80.Fe, 61.80.Ed, 61.82.Bg, 07.05.Tp, 02.70.Uu https://nasplib.isofts.kiev.ua/handle/123456789/80539 By means of the Monte Carlo computer modeling technique the depth dependencies of energy deposition and concentration of radiation induced point defects have been calculated in heterogeneous assemblies of Hastelloy plates embedded into the melt of fluoride salts and irradiated by 8–10 MeV electron beams. For assemblies of various designs the beam penetration depth dependencies of energy spectra, angular distributions and energy fluxes of electrons and secondary gamma quanta had been studied in great details. As a result of these investigations the optimization of the target assembly design for the imitating experiment at the LUE-10 linac has been accomplished. It has been shown that for the optimized target ampoule design at the experimental conditions (700 hrs long 10 MeV electron irradiation) different surfaces of the Hastelloy plates contacting with molten fluorides are characterized by substantially different values of specific energy deposition (from ~5 keV/atom down to ~60 eV/atom) arising from inelastic ionization energy losses of primary and secondary charged particles. The concentration of point defects produced in elastic collisions of charged particles with target atoms decreases by ~500 times along the assembly thickness. Therefore the single imitating experiment opens up the possibility to study the radiation and corrosion stability of Hastelloy irradiated in the molten fluorides medium in a wide range of doses of electron beam energy deposition and radiation damage of alloy. Шляхом математичного моделювання методом Монте-Карло розраховані профілі енерговиділення та концентрацій точкових дефектів, що утворюються в гетерогенних збірках тонких платівок сплаву хастелой, занурених у розплав фторидних солей, під опроміненням пучками електронів с енергіями 8…10 МеВ. Детально досліджена еволюція енергетичних спектрів, кутових розподілів та густин потоку енергії електронів та вторинних гамма-квантів з глибиною проникнення пучка у збірки різних конструкцій. На цій основі виконана оптимізація конструкції збірки-мішені для імітаційного експерименту на електроннім прискорювачі ЛПЕ-10. Показано, що для оптимізованої конструкції ампули мішені за умов експерименту (700-годинне опромінювання електронами з енергією 10 МеВ) на різних поверхнях платівок хастелою, що контактують з розплавом, досягаються суттєво різні значення питомого енерговиділення (від ~5 кеВ/атом до ~60 еВ/атом), пов’язаного з непружними іонізаційними втратами енергії первинних та вторинних заряджених частинок. Концентрації точкових дефектів, що утворюються у пружних зіткненнях заряджених частинок з атомами, на товщині збірки спадають приблизно у 500 разів. Таким чином, єдиний імітаційний експеримент відкриває можливість дослідити радіаційну та корозійну стійкість хастелою, опроміненого у середовищі розплавлених фторидів, в широкому інтервалі доз енерговиділення електронного пучка та радіаційного пошкодження сплаву. Путем математического моделирования методом Монте-Карло рассчитаны профили энерговыделения и концентраций образуемых точечных дефектов в гетерогенных сборках тонких пластинок сплава хастеллой, погруженных в расплав фторидных солей, под облучением пучками электронов с энергиями 8…10 МэВ. Детально исследована эволюция энергетических спектров, угловых распределений и плотностей потока энергии электронов и вторичных гамма-квантов по глубине проникновения пучка в сборки различных конструкций. На этой основе выполнена оптимизация конструкции сборки-мишени для имитационного эксперимента на электронном ускорителе ЛУЭ-10. Показано, что для оптимизированной конструкции ампулы мишени в условиях эксперимента (700-часовое облучение электронами с энергией 10 МэВ) на различных поверхностях пластинок хастеллоя, контактирующих с расплавом, достигаются существенно различные значения удельного энерговыделения (от ~5 кэВ/атом до ~60 эВ/атом), связанного с неупругими ионизационными потерями энергии первичных и вторичных заряженных частиц. Концентрации точечных дефектов, образуемых в упругих столкновениях заряженных частиц с атомами, на толщине сборки спадают приблизительно в 500 раз. Таким образом, единственный имитационный эксперимент открывает возможность исследовать радиационную и коррозионную стойкость хастеллоя, облученного в среде расплавленных фторидов, в широком интервале доз энерговыделения электронного пучка и радиационного повреждения сплава. The work is partially supported by the STCU Project #294. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix Транспорт та поглинання енергії електронних пучків в гетерогенних збірках зразків хастелоя, занурених у суміш розплавлених фторидів Транспорт и поглощение энергии электронных пучков в гетерогенных сборках образцов хастеллоя, погруженных в смесь расплавленных фторидов Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix |
| spellingShingle |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix Bakai, A.S. Bratchenko, M.I. Dyuldya, S.V. |
| title_short |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix |
| title_full |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix |
| title_fullStr |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix |
| title_full_unstemmed |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix |
| title_sort |
electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix |
| author |
Bakai, A.S. Bratchenko, M.I. Dyuldya, S.V. |
| author_facet |
Bakai, A.S. Bratchenko, M.I. Dyuldya, S.V. |
| publishDate |
2005 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Транспорт та поглинання енергії електронних пучків в гетерогенних збірках зразків хастелоя, занурених у суміш розплавлених фторидів Транспорт и поглощение энергии электронных пучков в гетерогенных сборках образцов хастеллоя, погруженных в смесь расплавленных фторидов |
| description |
By means of the Monte Carlo computer modeling technique the depth dependencies of energy deposition and concentration of radiation induced point defects have been calculated in heterogeneous assemblies of Hastelloy plates embedded into the melt of fluoride salts and irradiated by 8–10 MeV electron beams. For assemblies of various designs the beam penetration depth dependencies of energy spectra, angular distributions and energy fluxes of electrons and secondary gamma quanta had been studied in great details. As a result of these investigations the optimization of the target assembly design for the imitating experiment at the LUE-10 linac has been accomplished. It has been shown that for the optimized target ampoule design at the experimental conditions (700 hrs long 10 MeV electron irradiation) different surfaces of the Hastelloy plates contacting with molten fluorides are characterized by substantially different values of specific energy deposition (from ~5 keV/atom down to ~60 eV/atom) arising from inelastic ionization energy losses of primary and secondary charged particles. The concentration of point defects produced in elastic collisions of charged particles with target atoms decreases by ~500 times along the assembly thickness. Therefore the single imitating experiment opens up the possibility to study the radiation and corrosion stability of Hastelloy irradiated in the molten fluorides medium in a wide range of doses of electron beam energy deposition and radiation damage of alloy.
Шляхом математичного моделювання методом Монте-Карло розраховані профілі енерговиділення та концентрацій точкових дефектів, що утворюються в гетерогенних збірках тонких платівок сплаву хастелой, занурених у розплав фторидних солей, під опроміненням пучками електронів с енергіями 8…10 МеВ. Детально досліджена еволюція енергетичних спектрів, кутових розподілів та густин потоку енергії електронів та вторинних гамма-квантів з глибиною проникнення пучка у збірки різних конструкцій. На цій основі виконана оптимізація конструкції збірки-мішені для імітаційного експерименту на електроннім прискорювачі ЛПЕ-10. Показано, що для оптимізованої конструкції ампули мішені за умов експерименту (700-годинне опромінювання електронами з енергією 10 МеВ) на різних поверхнях платівок хастелою, що контактують з розплавом, досягаються суттєво різні значення питомого енерговиділення (від ~5 кеВ/атом до ~60 еВ/атом), пов’язаного з непружними іонізаційними втратами енергії первинних та вторинних заряджених частинок. Концентрації точкових дефектів, що утворюються у пружних зіткненнях заряджених частинок з атомами, на товщині збірки спадають приблизно у 500 разів. Таким чином, єдиний імітаційний експеримент відкриває можливість дослідити радіаційну та корозійну стійкість хастелою, опроміненого у середовищі розплавлених фторидів, в широкому інтервалі доз енерговиділення електронного пучка та радіаційного пошкодження сплаву.
Путем математического моделирования методом Монте-Карло рассчитаны профили энерговыделения и концентраций образуемых точечных дефектов в гетерогенных сборках тонких пластинок сплава хастеллой, погруженных в расплав фторидных солей, под облучением пучками электронов с энергиями 8…10 МэВ. Детально исследована эволюция энергетических спектров, угловых распределений и плотностей потока энергии электронов и вторичных гамма-квантов по глубине проникновения пучка в сборки различных конструкций. На этой основе выполнена оптимизация конструкции сборки-мишени для имитационного эксперимента на электронном ускорителе ЛУЭ-10. Показано, что для оптимизированной конструкции ампулы мишени в условиях эксперимента (700-часовое облучение электронами с энергией 10 МэВ) на различных поверхностях пластинок хастеллоя, контактирующих с расплавом, достигаются существенно различные значения удельного энерговыделения (от ~5 кэВ/атом до ~60 эВ/атом), связанного с неупругими ионизационными потерями энергии первичных и вторичных заряженных частиц. Концентрации точечных дефектов, образуемых в упругих столкновениях заряженных частиц с атомами, на толщине сборки спадают приблизительно в 500 раз. Таким образом, единственный имитационный эксперимент открывает возможность исследовать радиационную и коррозионную стойкость хастеллоя, облученного в среде расплавленных фторидов, в широком интервале доз энерговыделения электронного пучка и радиационного повреждения сплава.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/80539 |
| citation_txt |
Electron beam transport and energy deposition in heterogeneous assemblies of the hastelloy samples embedded into the molten fluorides mix / A.S. Bakai, M.I. Bratchenko, S.V. Dyuldya // Вопросы атомной науки и техники. — 2005. — № 4. — С. 24-31. — Бібліогр.: 4 назв. — англ. |
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2025-11-24T11:37:30Z |
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PACS: 28.41.Qb, 28.50.Ft, 61.80.Fe, 61.80.Ed, 61.82.Bg, 07.05.Tp, 02.70.Uu
ELECTRON BEAMS TRANSPORT AND ENERGY DEPOSITION
IN HETEROGENEOUS ASSEMBLIES OF THE HASTELLOY SAMPLES
EMBEDDED INTO THE MOLTEN FLUORIDES MIX
O.S. Bakai, M.I. Bratchenko, S.V. Dyuldya
National Science Center “Kharkiv Institute for Physics and Technology”
Kharkiv, Ukraine, sdul@kipt.kharkov.ua
By means of the Monte Carlo computer modeling technique the depth dependencies of energy deposition and concentration
of radiation induced point defects have been calculated in heterogeneous assemblies of Hastelloy plates embedded into the melt
of fluoride salts and irradiated by 8–10 MeV electron beams. For assemblies of various designs the beam penetration depth de
pendencies of energy spectra, angular distributions and energy fluxes of electrons and secondary gamma quanta had been studied
in great details. As a result of these investigations the optimization of the target assembly design for the imitating experiment at
the LUE-10 linac has been accomplished. It has been shown that for the optimized target ampoule design at the experimental
conditions (700 hrs long 10 MeV electron irradiation) different surfaces of the Hastelloy plates contacting with molten fluorides
are characterized by substantially different values of specific energy deposition (from ~5 keV/atom down to ~60 eV/atom) aris
ing from inelastic ionization energy losses of primary and secondary charged particles. The concentration of point defects pro
duced in elastic collisions of charged particles with target atoms decreases by ~500 times along the assembly thickness. There
fore the single imitating experiment opens up the possibility to study the radiation and corrosion stability of Hastelloy irradiated
in the molten fluorides medium in a wide range of doses of electron beam energy deposition and radiation damage of alloy.
INTRODUCTION
The accelerated electrons irradiation test bench ba
sed on the 10 MeV LUE-10 linac has been recently cre
ated in NSC KIPT and the imitating experiments are
carried out on this bench in order to study the effects of
irradiation on the corrosion stability and mechanical
properties of the Hastelloy Nickel-Molybdenum-Chro
mium alloy in aggressive medium of molten fluorides.
These investigations are of great importance for the de
velopment [1] and the choice of optimal structural mate
rials for the new-generation accelerator driven transmu
tation reactors with molten-salt blanket.
In imitating experiments the efficient utilization of
the electron beam energy stimulates the application of
thick heterogeneous targets (assemblies) with total
thickness comparable with the range of primary elec
trons (controlled by the rate of their energy losses). Re
lativistic electrons intensively lose their energy in sub
stance due to inelastic collisions and radiative processes
of interaction. In turn the secondary bremsstrahlung
photons emitted by electrons produce secondary elec
trons of rather high energies as well as the electron-
positron pairs. All these processes give rise to complex
radiation fields of charged particles and gamma quanta
in matter that become strongly non-uniform at penetra
tion distances comparable with the range of electron
beam. For heterogeneous targets additional complexity
of the radiation fields takes place due to certain fine
scattering effects near the interfaces of materials.
The radiation stimulated chemical reactions are de
termined by the rate and the density of the radiation en
ergy deposition in the area of the contact of the material
with the melt. The locally deposited energy of some
electronvolts is enough to activate a chemical reaction
or diffusional replacements of atoms.
The surface and bulk radiation damage effects are
mainly due to the energy transferred by electrons in ela
stic collisions with atoms. To induce a displacement of
atom the locally transferred energy has to be larger then
the Frenkel pair production threshold, Ed ≈ 25…30 eV.
Due to the beam slowing down processes the energy
locally deposited by radiation essentially depends on the
beam penetration depth. Therefore the energy deposited
in surface layers of specimens in molten fluorides is
dramatically depending on the specimen location and
thickness. For this reason the target assembly design can
be chosen in such a way that provides irradiation of
many specimens with different irradiation rates and dos
es. If the assembly thickness is comparable with the pri
mary electrons slowing down range, and the assembly
contains N specimens, then we have 2×N surfaces of
contact of alloy with the molten salt. Consequently we
obtain the possibility to investigate the irradiation im
pact on the corrosion in wide range of the deposited en
ergy values. On the other hand, the specimen thickness
has to be large enough to get representative information
on the irradiation impact on mechanical properties.
To elaborate such an optimal experimental setup and
to facilitate the adequate interpretation of experimental
data the very detailed calculations of the electron beam
deposited energy distributions in irradiated assemblies
are required. Due to the complexity of the radiation
fields in thick heterogeneous targets the interrelated
problems of quantitative prediction of the electron beam
energy deposition and the optimization of target design
are non-trivial and stimulate the application of advanced
methods of mathematical modeling for adequate de
scription of secondary effects of primary electrons
transport in matter.
In the present work the 8…10 MeV electron beams
radiation fields and the associated deposited energy pro
files in the various designs of containers (ampoules) that
hold the irradiated alloy samples embedded into the
melt of fluorides are calculated by means of the Monte
________________________________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2005. № 4.
Серия: Физика радиационных повреждений и радиационное материаловедение (87), с. 24-31.
24
mailto:sdul@kipt.kharkov.ua
Carlo computer modeling method. The main objective
of these calculations consists in the substantiation of the
choice of the ampoule design optimal form the point of
view of investigation of the dependence of irradiation
effects on the surface and in the bulk of samples on the
electron beam energy deposition rate.
1. MODELING SETUP AND METHODS
1.1. EXPERIMENTAL GEOMETRY
The overall design and dimensions of ampoules to
be used in experiments on the irradiation of the Hastel
loy samples in liquid medium of molten fluorides are il
lustrated by the sketch depicted in fig. 1. The ampoule
thickness is chosen to be comparable with the slowing
down length (the range) of the primary electrons.
30 mm
40 mm
40
m
m
10
m
m
Fig. 1. The general view of target ampoule for irradia
tion of Hastelloy in the medium of molten salts
The leakproof container is a rectangular paral
lelepiped with the centered cylindrical cavity. In experi
ment the cavity holds the assembly of thin Hastelloy
plates periodically arranged orthogonally to the electron
beam axis and is filled by the melt of fluoride salts. The
flat single-layered set of 16 such containers in the irradi
ation chamber is irradiated by the scanning beam of
electrons. The accelerator scanning system forms the
quasi-parallel broad electron beam and provides uni
form conditions of irradiation of all target containers.
Because of the flat geometry of the target assembly the
beam attenuation and energy deposition is essentially
depending on the beam penetration depth only.
1.2. MATERIALS
The target ampoule is made from the Carbon-Carbon
(C-C) composite material with density ρ = 1.5 g/cm3.
The molten fluorides liquid mix used in experiments
contains (by molar fractions) 50% of ZrF4 and 50% of
NaF salts and has the density 3.3 g/cm3.
Different versions of the Hastelloy brand Ni/Mo/Cr
alloys are slightly varying by elemental composition
and density. In the present work, as well as in the imitat
ing experiments under consideration, the manufactured
in NSC KIPT [1] Hastelloy Type A alloy with density
8.9 g/cm3 was investigated (see Table 1).
One should note that the variation of chemical com
position of different sorts of Hastelloy-type alloys have
only weak effect on the slowing down of energetic elec
trons because major contribution to the stopping power
is determined by Ni and Mo components that do not
vary significantly from one sort to another.
Table 1
The elemental composition of the Hastelloy A alloy
used in experiments and modeling
ELEMENT Z FRACTION
at% wgt%
Al 13 0.83 1.85
Si 14 0.15 0.32
Ti 22 0.47 0.59
Cr 24 6.70 7.74
Mn 25 0.50 0.55
Fe 26 1.50 1.61
Ni 28 78.15 80.01
Mo 42 11.70 7.32
The total ranges of electrons in the target materials
of interest calculated using the continuous slowing
down approximation (CSDA) by means of the U.S.
NIST supplied reference computer code ESTAR [2] are
depicted in fig. 2 as functions of electron energy.
0 2 4 6 8 10 12 14 16 18 20
10-3
10-2
10-1
100
101
C
SD
A
ra
ng
e,
c
m
Electron energy, MeV
C-C
Fluoride
Hastelloy
Fig. 2. Energy dependencies of the continuous slowing
down approximation ranges of electrons in the target
materials used in experiments and modeling
It is clear from this figure that for energies up to
10 MeV the ranges do not exceed 1…2 cm in fluorides
and 5…8 mm in Hastelloy. It means that for such ener
gies the total range of electrons in the target assembly is
comparable with the size of containers, and the com
plete absorption of primary electrons should occur.
Due to the rapid decrease of ranges with the decrea
se of electron energy the ranges of scattered and sec
ondary electrons that spread in lateral directions of the
target assembly are typically much smaller then the
ranges of primary electrons. Therefore taking into ac
count the actual shape and dimensions of the target am
poule the influence of fringe effects determined by the
transversal heterogeneity of the target assembly can be
neglected in the first approximation. In this approxima
tion the problem of the energy deposition calculation
can be considered in the one-dimensional geometry that
is described only by the strong heterogeneity along the
beam penetration depth.
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25
The results of the ESTAR-based calculations of the
stopping power of electrons in the materials under con
sideration are shown in fig. 3.
These calculations testify that for the energy region
peculiar for imitating experiments the slowing down of
electrons becomes to be influenced by the radiative en
ergy losses. Consequently the irradiation of ampoules
would be accompanied with the noticeable rate of pro
duction of secondary bremsstrahlung photons having
high penetration capability.
Thus the radiative energy losses, along with ioniza
tion ones, have to be taken into account in the energy
deposition calculations.
10-2 10-1 100 101 102 10310-2
10-1
100
101
102
collisional
radiative
total
St
op
pi
ng
p
ow
er
, M
eV
·c
m
2 /g
Electron energy, MeV
Molten Fluorides
10-2 10-1 100 101 102 10310-2
10-1
100
101
102
collisional
radiative
total
St
op
pi
ng
p
ow
er
, M
eV
·c
m
2 /g
Electron energy, MeV
Hastelloy
Fig. 3 Ionization (collisional), radiative and total stop
ping power (ρ–1·dE/dx) of electrons in the melt of fluo
ride salts (a) and in the Hastelloy alloy (b)
1.3. METHODS OF CALCULATIONS
For one-dimensional geometry the energy Edep de
posited per one atom of a medium at depth z during the
time t of electron irradiation can be estimated using the
following expression:
∫
0
E 0
ϕ e E , z ⋅∣ dE
dx
E , z ion
∣ dE
E γ ¿ϕ γ E γ , z ¿ μen E γ , z dE γ ¿
Edep z , t = t
n z
⋅¿ {¿}¿{}
, (1)
where n is the atomic concentration of the material at
depth z, ϕe and ϕγ are the energy spectra of the electron
and photons flux density at this depth, (dE/dx)ion is the
ionization stopping power of electrons with energy E for
the material at depth z, µen is the linear energy absorp
tion coefficient of the photons with energy Eγ in this
material, E0 is the energy of primary electrons.
To estimate the point defects (Frenkel pairs) produc
tion in elastic collisions of electrons with atoms the fol
lowing method can be used. The number of displace
ments per atom (dpa) including the secondary displace
ments produced by primary knocked atom (PKA) is ex
pressed by the following formula:
C z , t = t⋅∫
Ed z
E0
ν T , z dT ∫
Ed z
E0
ϕ e E , z dσ T ; E , z
dT
dE
, (2)
where dσ/dT is the differential cross-section of the
transfer of energy T in elastic collision of electron with
atom, ν is the radiation damage function describing the
secondary atoms displacements in the collision cascade
produced by a PKA with energy T, Ed is the displace
ment threshold energy. The dependencies of these quan
tities on depth z emphasize the layered structure of the
heterogeneous target.
The differential cross-section dσ/dT is derived from
the relativistic Mott cross-section of elastic scattering
(see, e.g., Ref. 3):
dσ T , E
dT
=4π Za0 E R
mc2
2
⋅1 −β 2
β4 ⋅
T m
T 2 ׿
¿×[1 −β 2T
T m
πα
β ⋅T
T m
−
T
T m ]
,
(3)
where Z is the target atomic number, a0 and ER are the
Bohr atomic radius and the Rydberg energy, m is the
electron mass, β = v/c is the ratio of electron velocity v
and the speed of light c, α is the fine structure constant,
and Tm is the maximal energy of a recoil atom of mass
M in elastic collision with an electron of energy E:
T m E =
2 E⋅E2 mc2
Mc2 . (4)
The radiation damage function for rather low PKA
energies peculiar for electron irradiation can be estimat
ed using the Kinchin-Pease model [3]:
ν T ={ 0,
1,
T /2 E d ,
T Ed
Ed≤T2 ⋅Ed
T 2 ⋅Ed
. (5)
For multicomponent targets, such as Hastelloy, the
calculations according to Eqs. 3 to 5 have take into ac
count different probabilities of electron impact with
each sort of atom (determined by its atomic fraction) as
well as the perturbation of the radiation damage func
tion due to the multicomponent nature of the atomic col
lision cascade.
The calculations according to Eqs. 1 and 2 require
the knowledge of the depth dependencies of the elec
trons and photons flux densities energy spectra. These
functions can be calculated analytically only in certain
degenerated cases (e.g. for thin target with the thickness
much less then the range of primary electrons). Howev
er such simplifications are not adequate for our case of
26
(a)
(b)
thick heterogeneous targets and the problem requires the
application of numerical methods of calculations, or the
computer modeling methods.
For calculations we have used the Monte Carlo met
hod implemented in the specially developed computer
code based on the Geant4 toolkit [4] that provides the
modeling of radiation transport in heterogeneous multi
component media with complex geometries.
The modeling code takes into account all major phy
sical processes of electromagnetic interactions. For
charged particles (electrons and positrons) they include
ionization energy losses, multiple scattering, elastic
(Möller or Bhabba) scattering and δ-electrons produc
tion, the annihilation of positrons and the bremsstrah
lung photons emission. For secondary photons the pho
toabsorption, incoherent (Compton) scattering and gam
ma conversion (e± pairs production) are taken into ac
count. Hadronic processes such as nuclear reactions ini
tiated by electron and photons were neglected in our
calculations because their contribution into the energy
deposition is marginal for the beam energies of interest.
The code simulated the electron-photon cascades
initiated by primary electrons and calculated the parti
cles’ and energy fluxes, the particles’ energy and angu
lar distributions as well as the deposited energies by
means of the statistical averaging of the physical quanti
ties of interest over a large (~107) number of cascades.
The histories of primary and secondary particles
transport were followed down to the energies at which
the ranges of electrons and positrons as well as the mean
free-path lengths of photons fall down to 10 µm. At
these cut-off energies (that are different for each materi
al and a sort of particle) the particles trajectories were
interrupted and their energy was locally deposited in the
material correspondent to the particle’s path endpoint.
The heterogeneous layered media were modeled that
simulate different versions of the target designs and
consist of alternate layers of fluorides melt and Hastel
loy enclosed by the outer layers of C-C material repre
senting the container walls.
The modeling was carried out for broad parallel
beam of electrons. In different calculations the beam en
ergy varied from 8 to 10 MeV. Angular and energy
spreads of primary beam were neglected. However the
filtration and scattering of electrons by 0.3 mm thick
steel foil at beam entrance was taken into account.
The spatial resolution of the modeling results in
Hastelloy and molten fluorides was 0.05 mm. The statis
tical errors of Monte Carlo averaging procedures was
typically better then 0.5%.
2. MODELING RESULTS AND DISCUSSION
In our calculations the parameters of optimization of
the target design were the number, the values of thick
ness and the positions of Hastelloy plates in the melt as
well as the thickness of surrounding C-C walls.
2.1. PRELIMINARY TARGET DESIGN
The preliminary estimations have been made for the
target design depicted in fig. 4 at primary electrons en
ergy 8 MeV.
According to this preliminary design 1.5 mm thick
Hastelloy plates are embedded into the melt so that the
width of each layer of fluorides equals to 7.5 mm. For
this case the depth dependencies of electrons and pho
tons energy fluences (calculated per one primary elec
tron fallen on the unit of target surface area) and the
profile of deposited energy are shown in fig. 5.
As it is clear from fig. 5,a, the front C-C wall of the
target ampoule attenuates the energy flux of electrons
very weakly. It is due to the low atomic number and
density of Carbon.
In contrast, due to the high stopping the layers of the
melt, and especially of the Hastelloy alloy, strongly af
fect the flux. In the design considered primary electrons
are practically completely absorbed in the first layer of
Hastelloy that is characterized by strong gradients of
both energy fluence and deposited energy.
carbon, 5 mm
fluoride, 7.5 mm
Hastelloy, 1.5 mm
Fig. 4. The transversal section of the preliminary target
design with thick layers of Hastelloy and fluorides melt
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
10-3
10-2
10-1
100
101
8 MeV
En
er
gy
fl
ue
nc
e,
M
eV
/c
m
2 p
er
e
- /c
m
2
Depth, cm
e-, total
e-, primary
photons
carbon, 5.0 mm
fluoride, 7.5 mm
Hastelloy, 1.5 mm
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
10-3
10-2
10-1
100
101
8 MeV
D
ep
os
ite
d
en
er
gy
,
M
eV
/c
m
3 p
er
e
- /c
m
2
Depth, cm
carbon, 5.0 mm
fluoride, 7.5 mm
Hastelloy, 1.5 mm
Fig. 5. Penetration depth dependencies of the energy
fluences (a) of electrons and photons (incl. the energy
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2005. № 4.
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27
(a)
(b)
fluence of primary electrons) and the deposited energy
profile (b) for 8 MeV irradiation of the target of prelim
inary design (see fig. 4). The quantities are normalized
per unit of primary electrons fluence
Inside the carbon wall and especially in the first la
yer of the molten fluorides the considerable production
of bremsstrahlung gamma quanta by high-energy prima
ry electrons takes place. Then the gamma radiation is
rather slowly attenuated in the subsequent layers of the
target. As a result the energy deposited in the second
plate of Hastelloy is completely due to secondary elec
trons produced mainly by the bremsstrahlung photons
incoherent scattering process and weakly depends on
the penetration depth within the plate and the melt layer.
Thus the preliminary design of fig. 4 is far from op
timality: in fact it allows to study the dependence of sur
face irradiation effects on the deposited energy only for
two “melt-Hastelloy” interfaces of four available.
2.2. TARGET DESIGN OPTIMIZATION
The evident way for target optimization consists in
the increase of beam energy, the decrease of thickness
of the molten fluorides layers and the increase of the
Hastelloy plate number in the target assembly.
Basing on the preliminary data of fig. 5 one can con
clude that the total thickness of the irradiated system
“melt-Hastelloy” should not exceed 1 cm. It is fairly
consistent with the ranges estimations shown in fig. 2.
Within the scope of the overall geometry of the target
ampoule (see fig. 1) it can be provided by means of the
insertion of the C-C half-liners (shaped as cylindrical
segments) into the container’s cavity.
This method accompanied by the decreasing of
Hastelloy plates thickness down to 0.6 mm and the in
creasing of their number to 5 is implemented in the tar
get design depicted in fig. 6.
carbon, 5 - 15 mm
fluoride, 1.0 mm
Hastelloy, 0.6 mm
Fig. 6. The section of the target design with Carbon-
Carbon insertions and 5 equidistant plates of Hastelloy
The depth profiles of energy fluences and deposited
energy for 10 MeV irradiation of this target at different
thicknesses of beam entrance/exit carbon layers are
shown in figs. 7 and 8.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
10-3
10-2
10-1
100
101
Carbon:
5.0 mm
10.0 mm
15.0 mm
En
er
gy
fl
ue
nc
e,
M
eV
/c
m
2 p
er
e
- /c
m
2
Depth, cm
10 MeV
fluoride, 1.0 mm
Hastelloy, 0.6 mm
Electrons
a
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0
0.5
1.0
1.5
2.0
Carbon:
5.0 mm
10.0 mm
15.0 mmEn
er
gy
fl
ue
nc
e,
M
eV
/c
m
2 p
er
e
- /c
m
2
Depth, cm
10 MeV
fluoride, 1.0 mm
Hastelloy, 0.6 mm
Gamma quanta
b
Fig. 7. Depth dependencies of normalized energy flu
ences of electrons (a) (open markers — the contribution
of primary electrons) and gamma quanta (b) for differ
ent thicknesses of C-C layers at entrance and exit of
10 MeV electron beam. The target design of fig. 6
It is clear from fig. 7 that the variation of the thick
ness of the entrance carbon wall allows to control effi
ciently the evolution of radiation energy fluxes over the
penetration depth.
The analysis of data depicted in fig. 8 shows that in
side the assembly containing five Hastelloy plates the
overall range of the depth dependency of deposited en
ergy is practically the same for all thicknesses of carbon
layers under consideration. The significant gradient of
the energy deposition is obtained for three (of five)
Hastelloy plates while the opposite surfaces of two other
plates are in the same conditions of energy deposition. It
means that it is sufficient to irradiate three layers of
Hastelloy to obtain optimal information on the inter
faces irradiation effects.
The increase of the C-C layer thickness increases the
gradient of fluxes in the region of the front Hastelloy
layers that are described by the high level of energy de
position. At the same time the production rate of gamma
quanta (that leads to the smoothing of depth dependen
cies) is decreased because of stronger decrease of pri
mary electron energy in thicker layers of carbon.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
10-1
100
101
Carbon:
5.0 mm
10.0 mm
15.0 mm
D
ep
os
ite
d
en
er
gy
, M
eV
/c
m
3 p
er
e
- /c
m
2
Depth, cm
10 MeV
fluoride, 1.0 mm
Hastelloy, 0.6 mm
28
Fig. 8. Depth dependencies of deposited energies for
different thicknesses of C-C layers. The target design of
fig. 6, beam energy 10 MeV
Maximal gradients inside the Hastelloy layers take
place for 15 mm thick C-C layer. It is due to the overall
softening of electron energy spectrum in course of the
beam slowing down in carbon.
2.3. OPTIMIZED EXPERIMENTAL DESIGN
In accordance with the obtained computer modeling
data for actual experiments the target design depicted in
fig. 9 has been chosen. This design and the correspon
dent results of computer modeling of radiation transport
and beam energy deposition are discussed below.
ca
rb
on
, 1
5.
1
m
m
ca
rb
on
, 1
5.
1
m
m
f l u o r i d e , 2 .0 m m
H a s te l l o y , 0 .6 m m
Fig. 9. The optimized design of target for the experi
ment: sectional and top views
Within the scope of this target design appropriate C-
C insertion segments provide the thickness of front and
back carbon walls of target container equal to 15.1 mm.
Three pairs of the 0.3 mm thick Hastelloy plates are
tightly put together (in pairs) forming three 0.6 mm
thick Hastelloy layers embedded into the molten salt.
The inside surfaces of the Hastelloy specimens are
closely contacting but evidently certain small amount of
salt can penetrate between them. In our simulation this
minor amount is ignored. The chosen thickness and size
of the Hastelloy samples is considered to be enough to
conduct mechanical tests after irradiation.
Three layers of Hastelloy are separated with 2 mm
thick layers of melt. Such a thickness also allows to pre
vent the exhaustion of the molten salt chemical activity
during the rather long-term irradiation experiment.
For the target design under consideration the depth
dependencies of normalized energy fluences and de
posited energies depicted in fig. 10 show that all layers
of Hastelloy are characterized by strong gradients of
both flux density and deposited energy.
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
10-3
10-2
10-1
100
101
e-, total
e-, primary
gamma
En
er
gy
fl
ue
nc
e,
M
eV
/c
m
2 p
er
e
- /c
m
2
Depth, cm
10 MeV
carbon, 15.1 mm
fluoride, 2.0 mm
Hastelloy, 0.6 mm
15 16 17 18 19 20 21 22 23 24 25
10-2
10-1
100
101
D
ep
os
ite
d
en
er
gy
, M
eV
/c
m
3 p
er
e
- /c
m
2
Depth, mm
total
primary
fluoride, 2.0 mm
Hastelloy, 0.6 mm
10 MeV
Fig. 10. Depth dependencies of the particles normalized
fluences (a, incl. primary electrons and produced gam
mas) and the deposited energy profile (b) for optimized
target design of fig. 9. Primary electron energy 10 MeV
The overall range of provided deposited energies in
the near-surface regions of Hastelloy is about two orders
of magnitude. Thus all samples of alloy can be efficient
ly used for the analysis of the dependency of corrosion
and mechanical properties of Hastelloy on the value of
deposited energy.
In the first two layers of Hastelloy the major contri
bution into the energy deposition is formed by the pri
mary electrons. In the last layer (and especially in the
last Hastelloy plate) the main yield to the energy deposi
tion is due to the secondary electrons produced by the
Compton scattering of bremsstrahlung photons.
The data shown in fig. 11,a testify that the energy
spectrum of electrons (that includes both primary and
secondary charged particles) considerably changes with
the beam penetration depth. Typical energies of elec
trons are 4…6 MeV inside the first layer of Hastelloy
and 3…4 MeV in the second one. In the third layer the
electron energies fall down to 2 MeV and lower.
The photons energy spectra are typical for incoher
ent bremsstrahlung (see fig. 11,b) and only weakly de
pend on penetration depth. In the low energy region the
weak annihilation photons peak (Eγ = 511 keV) has been
found at modeling that testifies the existence of certain
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2005. № 4.
Серия: Физика радиационных повреждений и радиационное материаловедение (87), с. 24-31.
29
(a)
(b)
contribution of the e± pairs production processes into the
energy deposition in the target.
16
18
20
22
24
10
-3
10
-2
10
-1
10
0
10
1
10
2
0 1 2 3 4 5 6 7 8 9 10
E
ne
rg
y
fl
ue
nc
e
sp
ec
tr
um
, c
m
-2
p
er
e
- /c
m
2
E lectron energy , M eVD
ep
th
, m
m
a
17
18
19
20
21
22
23
0 1 2 3
4
5
6
7
8
9
10
10-2
10-1
100
101
D ep th, m m
E
ne
rg
y
fl
ue
nc
e
di
st
ri
bu
t i
o n
, c
m
-2
p
er
e
- / c
m
2
Pho ton energy , M eV
b
Fig. 11. Energy spectra of energy fluences of electrons
(a) and photons (b) inside the Hastelloy layers
10-5
10-4
10-3
10-2
10-1
100
0°
30°
60°
90°
120°
150°
180°10-5
10-4
10-3
10-2
10-1
100
0 20 40 60 80 100 120 140 160 180
0.0
0.1
0.2
0.3
E
le
ct
ro
n
an
gu
la
r
di
st
ri
bu
tio
n,
r
el
.u
n.
layer #1
layer #2
layer #3
Polar angle, deg.
Fig. 12. Angular distributions of electrons inside three sequential layers of Hastelloy. Zero polar angle corresponds
to the primary beam direction
1.50 1.75 2.00 2.25 2.50
101
102
103
104
D
ep
os
ite
d
en
er
gy
E de
p, e
V
/a
to
m
Depth, cm
10 MeV
2·1019 e-/cm2
Hastelloy, 0.6 mm
fluoride, 2.0 mm
1.50 1.75 2.00 2.25 2.50
10-6
10-5
10-4
10-3
D
is
pl
ac
em
en
ts
p
er
a
to
m
Depth, cm
10 MeV
2·1019 e-/cm2
Hastelloy, 0.6 mm
fluoride, 2.0 mm
Fig. 13. The penetration depth dependency of the deposited energy (a) and the total number of atomic displace
ments (b) in Hastelloy at experimental conditions for optimized target design
The modeling of angular distributions of electrons in
the Hastelloy layers (see fig. 12) has shown that elec
trons experience considerable scattering in the target. As
a result the deposited energy depth dependency is for
med by complex broad angular distribution of fast char
ged particles that incorporates the significant fraction of
scattered and secondary electrons that propagate in the
direction opposite to the primary beam direction.
2.4. DISCUSSION
The final data of the Monte Carlo computer model
ing of the deposited energy depth profile in the “melt-
Hastelloy” system at 700 hours long target irradiation
by the electron beam with energy 10 MeV and current
density 1.25 µA/cm2 are depicted in fig. 13a. The data
have been obtained by means of appropriate scaling of
normalized data of fig. 10b. The correspondent Hastel
loy radiation damage profile calculated at the displace
ment threshold energy Ed = 25 eV for all sorts of atoms
in the alloy is presented in fig. 13,b.
For interface regions of all Hastelloy plates the de
posited energies and the atomic concentrations of point
defects are summarized in Table 2 both in absolute (per
atom) and relative units.
Table 2
Deposited energies in the interface (near-surface) regions of the Hastelloy plates and the melt
SAMPLE SAMPLE
SURFACE MATERIAL
DEPTH DEPOSITED ENERGY POINT DEFECTS
cm eV/atom percentage dpa percentage
30
(a)
(b)
fluoride 1.7075 2221.52
1
1-1
1-2
2
2-1
2-2
Hastelloy
1.7125 5066.72 100.0 100.0 2.12×10–3 100.0 100.0
1.7375 4906.46 96.84 96.84 2.01×10–3 94.44 94.44
1.7425 4815.29 95.04 95.04 1.95×10–3 91.94 91.94
1.7675 4208.23 83.06 83.06 1.62×10–3 76.20 76.20
fluoride
1.7725 1794.76
1.9675 1010.82
3
3-1
3-2
4
4-1
4-2
Hastelloy
1.9725 2347.23 46.33 100.0 7.00×10–4 32.96 100.0
1.9975 1698.40 33.52 72.36 4.80×10–4 22.59 68.54
2.0025 1563.33 30.85 66.60 4.33×10–4 20.37 61.80
2.0275 969.88 19.14 41.32 2.44×10–4 11.48 34.83
fluoride
2.0325 375.17
2.2275 90.93
5
5-1
5-2
6
6-1
6-2
Hastelloy
2.2325 214.55 4.23 100.0 2.75×10–5 1.30 100.0
2.2575 107.01 2.11 49.88 1.06×10–5 0.50 38.64
2.2625 95.04 1.88 44.30 8.83×10–6 0.42 32.07
2.2875 63.82 1.26 29.74 4.42×10–6 0.21 16.07
fluoride 2.2925 24.39
The accelerator irradiation up to high electron fluen
ces leads to the significant values of specific deposited
energies that in average amounts to 2 keV per atom. At
such levels of deposited energy one can expect the con
siderable effects of irradiation on the corrosion process
es at the contact of Hastelloy with molten fluoride salts
and on the degradation of mechanical properties of alloy
under irradiation in aggressive environment.
At the same time one should mention that the level
of the Hastelloy radiation damage (see fig. 13b) for
electron irradiation is considerably lower then that for
neutron irradiation in reactor. However its depth depen
dence is even more strong then that of deposited energy:
it decreases by 500 times from the front surface of the
first specimen to the back surface of the last Hastelloy
plate.
Thus the chosen optimal design of target provides
the capability to clarify the dose dependencies of irradi
ation effects of interest using the results of single imitat
ing experiment because the surface layers of irradiated
samples are described by the considerably different
rates of energy deposition and radiation damage.
CONCLUSIONS
The detailed Monte Carlo modeling performed in the
present work has allowed to select from the variety of
possible versions the optimal design of the target for im
itating experiments on the investigation of corrosion and
mechanical properties of Hastelloy contacting with
molten fluorides under electron irradiation. Within the
scope of the experimental geometry proposed basing on
the modeling results the maximal variability of energy
deposition on different interfaces of Hastelloy and fluo
rides is obtained that provides the information on the
dose dependencies of the corrosion stability and the me
chanical properties degradation.
The modeling of such complex multicomponent het
erogeneous system that is presented by the irradiated as
semblies taking into account all valuable physical pro
cesses that determine the relativistic electrons energy
deposition in substance has been provided both the ob
tainment of important information on the kinetics of de
velopment of electron-photon processes in this system
and the quantitative calculation data on depth profiles of
energy deposition necessary for adequate analysis of the
results of imitating experiments.
The work is partially supported by the STCU Project
#294.
REFERENCES
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V’yugov et al. The development of alloy for fuel con
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619, Issue 1 (23), p. 87–94.
2.M.J. Berger. ESTAR, PSTAR, ASTAR — a PC pack
age for calculating stopping powers and ranges of elec
trons, protons and helium ions. NIST Report NISTIR-
4999, 1993. (IAEA-NDS-144, 1993).
3.M.W. Thompson. Defects and Radiation Damage in
Metals. Cambrige at the University Press. 1969.
4.S. Agostinelli, J. Allison, K. Amako, J. Apostolakis et
al. Geant 4 — a simulation toolkit //Nuclear Instruments
and Methods in Physics Research. Section A: Accelera
tors, Spectrometers, Detectors and Associated Equip
ment. 2003. v. 22, #3, p. 250–303.
ТРАНСПОРТ И ПОГЛОЩЕНИЕ ЭНЕРГИИ ЭЛЕКТРОННЫХ ПУЧКОВ
В ГЕТЕРОГЕННЫХ СБОРКАХ ОБРАЗЦОВ ХАСТЕЛЛОЯ, ПОГРУЖЕННЫХ В СМЕСЬ РАСПЛАВЛЕННЫХ
ФТОРИДОВ
А.С. Бакай, М.И. Братченко, С.В. Дюльдя
Путем математического моделирования методом Монте-Карло рассчитаны профили энерговыделения и концентраций образуемых
точечных дефектов в гетерогенных сборках тонких пластинок сплава хастеллой, погруженных в расплав фторидных солей, под облуче
нием пучками электронов с энергиями 8…10 МэВ. Детально исследована эволюция энергетических спектров, угловых распределений и
плотностей потока энергии электронов и вторичных гамма-квантов по глубине проникновения пучка в сборки различных конструкций.
________________________________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2005. № 4.
Серия: Физика радиационных повреждений и радиационное материаловедение (87), с. 24-31.
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На этой основе выполнена оптимизация конструкции сборки-мишени для имитационного эксперимента на электронном ускорителе
ЛУЭ-10. Показано, что для оптимизированной конструкции ампулы мишени в условиях эксперимента (700-часовое облучение электро
нами с энергией 10 МэВ) на различных поверхностях пластинок хастеллоя, контактирующих с расплавом, достигаются существенно
различные значения удельного энерговыделения (от ~5 кэВ/атом до ~60 эВ/атом), связанного с неупругими ионизационными потерями
энергии первичных и вторичных заряженных частиц. Концентрации точечных дефектов, образуемых в упругих столкновениях заря
женных частиц с атомами, на толщине сборки спадают приблизительно в 500 раз. Таким образом, единственный имитационный экспе
римент открывает возможность исследовать радиационную и коррозионную стойкость хастеллоя, облученного в среде расплавленных
фторидов, в широком интервале доз энерговыделения электронного пучка и радиационного повреждения сплава.
ТРАНСПОРТ ТА ПОГЛИНАННЯ ЕНЕРГІЇ ЕЛЕКТРОННИХ ПУЧКІВ
В ГЕТЕРОГЕННИХ ЗБІРКАХ ЗРАЗКІВ ХАСТЕЛОЯ, ЗАНУРЕНИХ У СУМІШ РОЗПЛАВЛЕНИХ ФТОРИДІВ
О.С. Бакай, М.І. Братченко, С.В. Дюльдя
Шляхом математичного моделювання методом Монте-Карло розраховані профілі енерговиділення та концентрацій точкових дефе
ктів, що утворюються в гетерогенних збірках тонких платівок сплаву хастелой, занурених у розплав фторидних солей, під опромінен
ням пучками електронів с енергіями 8…10 МеВ. Детально досліджена еволюція енергетичних спектрів, кутових розподілів та густин
потоку енергії електронів та вторинних гамма-квантів з глибиною проникнення пучка у збірки різних конструкцій. На цій основі ви
конана оптимізація конструкції збірки-мішені для імітаційного експерименту на електроннім прискорювачі ЛПЕ-10. Показано, що для
оптимізованої конструкції ампули мішені за умов експерименту (700-годинне опромінювання електронами з енергією 10 МеВ) на рі
зних поверхнях платівок хастелою, що контактують з розплавом, досягаються суттєво різні значення питомого енерговиділення (від
~5 кеВ/атом до ~60 еВ/атом), пов’язаного з непружними іонізаційними втратами енергії первинних та вторинних заряджених частинок.
Концентрації точкових дефектів, що утворюються у пружних зіткненнях заряджених частинок з атомами, на товщині збірки спадають
приблизно у 500 разів. Таким чином, єдиний імітаційний експеримент відкриває можливість дослідити радіаційну та корозійну
стійкість хастелою, опроміненого у середовищі розплавлених фторидів, в широкому інтервалі доз енерговиділення електронного пучка
та радіаційного пошкодження сплаву.
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