Simplified transportation model of thermal neutrons through the matter
The effective model providing simulation of thermal neutrons transportation through various matters was scrutinized. Calculation of neutron trajectory is carried out by Monte-Carlo method. The model was tested on the tasks with analytical solutions of diffusion equation. The developed model can be u...
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nasplib_isofts_kiev_ua-123456789-1111332025-02-09T18:04:39Z Simplified transportation model of thermal neutrons through the matter Спрощена модель проходження теплових нейтронiв крiзь речовину Упрощённая модель прохождения тепловых нейтронов через вещество Buki, A.Yu. Kalenik, S.A. Shapoval, I.M. Ядернo-физические методы и обработка данных The effective model providing simulation of thermal neutrons transportation through various matters was scrutinized. Calculation of neutron trajectory is carried out by Monte-Carlo method. The model was tested on the tasks with analytical solutions of diffusion equation. The developed model can be used for the practical important problems of activation analysis and neutron spectrometry etc. due to model simplicity and high speed of code calculations. Розглянута ефективна модель, що забезпечує симуляцію розповсюдження теплових нейтронів у різноманітних речовинах. Розрахунок траєкторії руху нейтрона здійснюється методом Монте-Карло. Модель протестована на задачах, які мають аналітичний розв'язок рівняння дифузії. Розроблена модель, з огляду на простоту та високу швидкість розрахунків її програмної реалізації, може бути корисною при розв'язанні практичних задач активаційного аналізу, спектрометрії нейтронів та ін. Раcсмотрена эффективная модель, обеспечивающая симуляцию распространения тепловых нейтронов в различных веществах. Расчет траектории движения нейтрона осуществляется методом Монте-Карло. Модель протестирована на задачах, которые имеют аналитическое решение уравнения диффузии. Разработанная модель ввиду простоты и высокой скорости счёта её программной реализации может быть полезной при решении практических задач активационного анализа, спектрометрии нейтронов и т.п. In summary authors consider as a pleasant duty express to A.V. Torgovkin gratitude for useful remarks and for the idea that the considered design procedure can be applied not only to thermal neutrons but also for neutrons with energy up to several MeV. 2011 Article Simplified transportation model of thermal neutrons through the matter / A.Yu. Buki, S.A. Kalenik, I.M. Shapoval // Вопросы атомной науки и техники. — 2011. — № 3. — С. 50-53. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 28.20.Gd, 07.05.Tp https://nasplib.isofts.kiev.ua/handle/123456789/111133 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Ядернo-физические методы и обработка данных Ядернo-физические методы и обработка данных |
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Ядернo-физические методы и обработка данных Ядернo-физические методы и обработка данных Buki, A.Yu. Kalenik, S.A. Shapoval, I.M. Simplified transportation model of thermal neutrons through the matter Вопросы атомной науки и техники |
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The effective model providing simulation of thermal neutrons transportation through various matters was scrutinized. Calculation of neutron trajectory is carried out by Monte-Carlo method. The model was tested on the tasks with analytical solutions of diffusion equation. The developed model can be used for the practical important problems of activation analysis and neutron spectrometry etc. due to model simplicity and high speed of code calculations. |
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Article |
| author |
Buki, A.Yu. Kalenik, S.A. Shapoval, I.M. |
| author_facet |
Buki, A.Yu. Kalenik, S.A. Shapoval, I.M. |
| author_sort |
Buki, A.Yu. |
| title |
Simplified transportation model of thermal neutrons through the matter |
| title_short |
Simplified transportation model of thermal neutrons through the matter |
| title_full |
Simplified transportation model of thermal neutrons through the matter |
| title_fullStr |
Simplified transportation model of thermal neutrons through the matter |
| title_full_unstemmed |
Simplified transportation model of thermal neutrons through the matter |
| title_sort |
simplified transportation model of thermal neutrons through the matter |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2011 |
| topic_facet |
Ядернo-физические методы и обработка данных |
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https://nasplib.isofts.kiev.ua/handle/123456789/111133 |
| citation_txt |
Simplified transportation model of thermal neutrons through the matter / A.Yu. Buki, S.A. Kalenik, I.M. Shapoval // Вопросы атомной науки и техники. — 2011. — № 3. — С. 50-53. — Бібліогр.: 5 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-11-29T06:58:15Z |
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| fulltext |
SIMPLIFIED TRANSPORTATION MODEL OF
THERMAL NEUTRONS THROUGH THE MATTER
A.Yu. Buki, S.A. Kalenik∗, I.M. Shapoval
National Scientific Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received April 27, 2011)
The effective model providing simulation of thermal neutrons transportation through various matters was scrutinized.
Calculation of neutron trajectory is carried out by Monte-Carlo method. The model was tested on the tasks with
analytical solutions of diffusion equation. The developed model can be used for the practical important problems of
activation analysis and neutron spectrometry etc. due to model simplicity and high speed of code calculations.
PACS: 28.20.Gd, 07.05.Tp
1. INTRODUCTION
The simulation of neutrons transportation through
matters configured in elements of installation is the
actual task for modern nuclear and radiation physics.
Calculation of neutrons field in various environments
and volumes is very interesting in designing experi-
mental and industrial installations in which neutrons
are used, for example, in installations for the neutron
activation analysis, radioisotopes production, neu-
tron spectrometry etc.
The distribution of neutrons, which have slowed
down in the non-uniform environments with given
geometrical configuration to velocity of thermal bal-
ance (thermal neutrons), presents the important as-
pect of the task. The neutron fields from the neu-
tron sources, which are surrounded by the moderator
or the field into studied object, which are also sur-
rounded by moderator, are often of interest. The
experimental research methods of such problems are
far away from being always fitted within accessible
scientific resources while dealing with them and are
limited by requirements of personnel safety. The an-
alytical methods use assumptions of uniformity, sim-
plicity and symmetry for interaction domain geome-
try.
For these reasons the research with the usage
of Monte-Carlo simulation methods for the basic
processes of neutrons interaction with the matter has
advantages. MCNP [1] and GEANT [2] packages are
commonly used tools to simulate the given class of
tasks.
Authors could not use both widely known sim-
ulation package MCNP (Fermi Lab, USA) since its
license isn’t free, and GEANT 3 one, which due to
its bottom energy thresholds limits is out of the ther-
mal neutrons simulation domain. Package GEANT 4,
version 4.9.3, already covers the given transportation
task of neutrons. However its validity in this energy
range is still in the stage of verification. Should be
also mentioned that there are non-negligible distinc-
tions between GEANT and MCNP simulation results
for the same problems.
The authors point of view is that advantages of
the above mentioned software products present signif-
icant difficulties in solving of specific tasks in which
is required to develop the effective and transparent
representation of object. Such advantages are: wide
scope of processes on types of interactions and mech-
anisms, participating particles, combinational oppor-
tunities of geometry and physical and chemical prop-
erties of materials, the interface of management and
processing of results, etc. The development of ther-
mal neutrons effective models is also covered by such
class of tasks.
2. DESCRIPTION OF THE MODEL
The simulation of the thermal neutrons interaction
with matter has shown that the distributions of neu-
tron velocities and thermal atoms movement are of
Maxwell’s type. However this task can be consid-
erably simplified. In the present work the following
approach to the thermal neutrons field calculation is
offered:
• all thermal neutrons move with constant of av-
erage for the given temperature velocity;
• the fluctuation of molecules are negligible;
• the elastic neutrons scattering with atoms
changes of their initial trajectory but the mod-
ule of velocity is saved.1
∗Corresponding author. E-mail address: kalesha@kipt.kharkov.ua
1Note, that such neutron transportation simplified model was given in [3]; however one doesn’t contain the verification of
simplification. Moreover work [3] doesn’t analyze the reduction of computer resources consumption by simplified model.
50 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2011, N3.
Series: Nuclear Physics Investigations (55), p.50-53.
Physical simplicity of the approach reduces probabil-
ity of mistakes into algorithms. The fact that our
model does not consider Maxwell’s distribution of
neutrons velocity reduces speed of the calculations es-
sentially. The last is very importance when the need
calculation time of a task exceeds reasonable limits.
Fig.1. Transportation of thermal neutrons through plates by various materials, N is the relative output
of neutrons, z is a thickness of a plate, L is a length of diffusion. Points are the simulation results, the
curves are the analytical calculations (formula (2)), µc is macroscopical cross-section of capture, µe is
macroscopical cross-section of elastic scattering
By the realization of this approach the method
of Monte-Carlo is used. The pseudo-random gen-
erators algorithm is applied to support of the basic
processes similarly applied in [2]. The spatial step l
between events of realization of these processes cal-
culates using formula:
l = − 1
µ
· ln(1− ξ), (1)
where ξ - the random uniformly distributed num-
ber in [0, 1], µ - the cross-section, corresponding the
mechanism of interaction. By means of formula (1)
the steps for each of processes taken into considera-
51
tion are generated. Then the process with the mini-
mal generated value of step length l is taken out. So
as the energy of thermal neutrons is small, the in-
teraction of neutrons with matter take place in two
channels only, which are capture and elastic scatter-
ing. The cross-sections of these processes are pre-
sented in [4] and designated as µc, µe, accordingly.
Thus by means of formula (1) the step for the chan-
nel of capture (lc) and for the channel of scattering
(le) are generated. The calculation of neutron trajec-
tory stops in the case if the least step length value
corresponds to the capture process. The interacting
particle has a new pulse direction and neutron con-
tinues the motion with velocity of the same absolute
value in the case of scattering process The choice of
direction of movement after elastic scattering is de-
fined from the solution of collision task for two bodies,
one from which is basic (atom - the scattering cen-
ter). The value of a impact parameter is generated to
obtain the new direction of movement. The neutron
finding into the given volume during transportation
is controlled permanently.
3. RESULTS OF MODELING
In view of assumptions are made in the considered
approach, the created model and its program real-
ization should be verified. We’ll use for this purpose
the analytical calculations describing distribution of
thermal neutrons for cases of tasks with simple geom-
etry. Such tasks are: the distribution of neutrons in
the plate from a parallel flat source and the distrib-
ution of neutrons in a sphere with a point source in
its center. The solutions of the diffusion equation for
these cases with condition of µc << µe are:
N = N0 · e−z/L for the plate, (2)
N = N0 · (1/r + 1/L) · e−r/L for the sphere,(3)
where N is output of neutrons from a plate/sphere,
N0 is number of neutrons gone out from source, z is
thickness of plate, r is sphere radius, L is length of
diffusion.
Fig.1 shows results of mathematical simulating
of neutron distribution in plates from various mate-
rials and calculation with formula (2). Simulation
and formula (3) distributions of thermal neutrons
in spherical volumes of water and heavy water are
shown in Fig.2. Each point corresponds to calcu-
lation with 107 neutrons emitted by source. Two
calculated curves are resulted in some graphics as
for the same matters value L in reference books [4]
and [5] are various. From the presented figures the
good accordance of simulation results and analytical
calculations is clear. The is an exception for the case
of iron, where requirement for analytical calculation
approximation µc << µe is not valid. We notice that
this requirement is not restriction of the developed
model and it is possible to investigate the neutrons
transportation through matter with any values µc
and µe. For example, in case of cadmium (for which
µc/µe = 350) the developed model can be used, how-
ever additional testing for similar cases is desirable.
4. THE CONCLUSIONS
The good accordance of simulation results and ana-
lytical calculations shows suitability of the developed
model for the solution of tasks with more general
geometry and non-uniform structure of matters. The
reason of this is that the geometry peculiarities and
structure heterogeneities of object cannot cancel the
correct character of simulating of thermal neutrons
interaction with matter.
Fig.2. An output of neutrons from spherical volume. r - radius of sphere, other designations as on Fig.1.
The program realization for practical application
proves that the important advantage of our approach
is the increasing of the calculation speed in com-
parison with standard packages. The most of neu-
tron sources (the gamma-neutron converter, division
of nucleus) have the average energy nearby 2 MeV.
Therefore our further work will be directed to expan-
sion of a range of simulating neutrons energy up to
10 MeV in order to solve of wider range of tasks in
the nuclear and radiation physics.
52
ACKNOWLEDGEMENTS
In summary authors consider as a pleasant duty ex-
press to A.V. Torgovkin gratitude for useful remarks
and for the idea that the considered design procedure
can be applied not only to thermal neutrons but also
for neutrons with energy up to several MeV. 2
References
1. MCNP - A General Monte-Carlo N-Particle
Transport Code. Version 4B, Transport Meth-
ods Group Los Alamos National Laboratory, 25
March 1997.
2. GEANT Detector Description and Simulation
Tool. CERN, Geneva, 1993.
3. I. Sobol. Monte-Carlo method. - M: ”Nauka”,
1968, p.64.
4. Tables of physical sizes/ Under ed. Acad.
I.K. Kikoina. M: ”Atomizdat”, 1976, p.1006.
5. B. Prays, K. Horton, K. Spinni. Protection from
nuclear radiations. M: ”Izd. I.L.”, 1959, p.490.
УПРОЩЁННАЯ МОДЕЛЬ ПРОХОЖДЕНИЯ ТЕПЛОВЫХ НЕЙТРОНОВ
ЧЕРЕЗ ВЕЩЕСТВО
А.Ю. Буки, С.А. Каленик, И.Н. Шаповал
Раcсмотрена эффективная модель, обеспечивающая симуляцию распространения тепловых нейтронов
в различных веществах. Расчет траектории движения нейтрона осуществляется методом Монте-Карло.
Модель протестирована на задачах, которые имеют аналитическое решение уравнения диффузии. Раз-
работанная модель, ввиду простоты и высокой скорости счёта её программной реализации, может быть
полезной при решении практических задач активационного анализа, спектрометрии нейтронов и т.п.
СПРОЩЕНА МОДЕЛЬ ПРОХОДЖЕННЯ ТЕПЛОВИХ НЕЙТРОНIВ
КРIЗЬ РЕЧОВИНУ
О.Ю. Буки, С.О. Каленик, I.М. Шаповал
Розглянута ефективна модель, що забезпечує симуляцiю розповсюдження теплових нейтронiв у рiзно-
манiтних речовинах. Розрахунок траєкторiї руху нейтрона здiйснюється методом Монте-Карло. Мо-
дель протестована на задачах, якi мають аналiтичний розв’язок рiвняння дифузiї. Розроблена модель,
з огляду на простоту та високу швидкiсть розрахункiв її програмної реалiзацiї, може бути корисною
при розв’язаннi практичних задач активацiйного аналiзу, спектрометрiї нейтронiв та iн.
2It is possible in case when by transportation through matter the neutron energy loss is not great. For example, such
case can be realized often in practice the calculation of neutrons transportation through a lead plate with thickness in some
centimeters.
53
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