Technique for fissile materials detection using electron linac
The possibilities of technique for fissile materials detection using the pulse γ-quantum fluxes generated by electron linac are studied. The technique is based on detection of neutrons escaping from fissile materials after gamma irradiation (technique of delayed neutrons). The diffusion approach...
Gespeichert in:
| Datum: | 2005 |
|---|---|
| Hauptverfasser: | , , , , , , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/81233 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Technique for fissile materials detection using electron linac / A. Barrata, A.N. Dovbnja, L.V. Eran, S.P. Karasev, N.M. Kiryukhin, Yu.P. Mel’nik, Yu.N. Ranyuk, S.V. Trubnikov, I.N. Shljakhov // Вопросы атомной науки и техники. — 2005. — № 6. — С. 75-80. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-81233 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-812332015-05-14T03:02:41Z Technique for fissile materials detection using electron linac Barrata, A. Dovbnja, A.N. Eran, L.V. Karasev, S.P. Kiryukhin, N.M. Mel’nik, Yu.P. Ranyuk, Yu.N. Trubnikov, S.V. Shljakhov, I.N. Экспериментальные методы и обработка даных The possibilities of technique for fissile materials detection using the pulse γ-quantum fluxes generated by electron linac are studied. The technique is based on detection of neutrons escaping from fissile materials after gamma irradiation (technique of delayed neutrons). The diffusion approach is developed for description of spacetime evolution of neutron fluxes inside the prototype system, which is irradiated by external γ-source. The simulation of electromagnetic interaction with matter is performed using the program package GEANT. The feasibility of this technique is proved for the case of plane one-dimensional model for a three-zone homogeneous subcritical assembly consisting of ²³⁵U and ⁵⁶Fe. Досліджуються можливості методу виявлення матеріалів, які поділяються, з використанням імпульсних потоків γ-квантів, що генерує лінійний прискорювач електронів. Метод засновано на реєстрації нейтронів, випромінюваних матеріалом, що поділяється, після γ-опромінення (метод запізнілих нейтронів). Розвинуто дифузійний підхід для опису просторово-часової еволюції потоку нейтронів у досліджуваному об'єкті, що опромінюється зовнішнім джерелом γ-квантів. Моделювання процесів електромагнітної взаємодії з речовиною проводиться за допомогою пакету програм GEANT. Можливість запровадження цього методу підтверджено результатами розрахунків, проведених у випадку плоскої одновимірної моделі для гомогенної трьохзонної підкритичної збірки, у якій шар з ²³⁵U оточений двома шарами з ⁵⁶Fe. Исследуются возможности метода обнаружения делящихся материалов с использованием импульсных потоков γ-квантов, генерируемых линейным ускорителем электронов. Метод основан на регистрации нейтронов, испускаемых делящимся материалом поcле γ-облучения (метод запаздывающих нейтронов). Развит диффузионный подход для описания пространственно-временной эволюции потока нейтронов в исследуемом объекте, который облучается внешним источником γ-квантов. Моделирование процессов электромагнитного взаимодействия с веществом проводится с помощью пакета программ GEANT. Осуществимость этого метода подтверждена результатами расчетов, проведенных в случае плоской одномерной модели для гомогенной трехзонной подкритической сборки, в которой слой ²³⁵U окружен двумя слоями ⁵⁶Fe. 2005 Article Technique for fissile materials detection using electron linac / A. Barrata, A.N. Dovbnja, L.V. Eran, S.P. Karasev, N.M. Kiryukhin, Yu.P. Mel’nik, Yu.N. Ranyuk, S.V. Trubnikov, I.N. Shljakhov // Вопросы атомной науки и техники. — 2005. — № 6. — С. 75-80. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 61.20.ja http://dspace.nbuv.gov.ua/handle/123456789/81233 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Экспериментальные методы и обработка даных Экспериментальные методы и обработка даных |
| spellingShingle |
Экспериментальные методы и обработка даных Экспериментальные методы и обработка даных Barrata, A. Dovbnja, A.N. Eran, L.V. Karasev, S.P. Kiryukhin, N.M. Mel’nik, Yu.P. Ranyuk, Yu.N. Trubnikov, S.V. Shljakhov, I.N. Technique for fissile materials detection using electron linac Вопросы атомной науки и техники |
| description |
The possibilities of technique for fissile materials detection using the pulse γ-quantum fluxes generated by
electron linac are studied. The technique is based on detection of neutrons escaping from fissile materials after
gamma irradiation (technique of delayed neutrons). The diffusion approach is developed for description of spacetime
evolution of neutron fluxes inside the prototype system, which is irradiated by external γ-source. The simulation
of electromagnetic interaction with matter is performed using the program package GEANT. The feasibility of this
technique is proved for the case of plane one-dimensional model for a three-zone homogeneous subcritical assembly
consisting of
²³⁵U and ⁵⁶Fe. |
| format |
Article |
| author |
Barrata, A. Dovbnja, A.N. Eran, L.V. Karasev, S.P. Kiryukhin, N.M. Mel’nik, Yu.P. Ranyuk, Yu.N. Trubnikov, S.V. Shljakhov, I.N. |
| author_facet |
Barrata, A. Dovbnja, A.N. Eran, L.V. Karasev, S.P. Kiryukhin, N.M. Mel’nik, Yu.P. Ranyuk, Yu.N. Trubnikov, S.V. Shljakhov, I.N. |
| author_sort |
Barrata, A. |
| title |
Technique for fissile materials detection using electron linac |
| title_short |
Technique for fissile materials detection using electron linac |
| title_full |
Technique for fissile materials detection using electron linac |
| title_fullStr |
Technique for fissile materials detection using electron linac |
| title_full_unstemmed |
Technique for fissile materials detection using electron linac |
| title_sort |
technique for fissile materials detection using electron linac |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2005 |
| topic_facet |
Экспериментальные методы и обработка даных |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/81233 |
| citation_txt |
Technique for fissile materials detection using electron linac / A. Barrata, A.N. Dovbnja, L.V. Eran, S.P. Karasev, N.M. Kiryukhin, Yu.P. Mel’nik, Yu.N. Ranyuk, S.V. Trubnikov, I.N. Shljakhov // Вопросы атомной науки и техники. — 2005. — № 6. — С. 75-80. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT barrataa techniqueforfissilematerialsdetectionusingelectronlinac AT dovbnjaan techniqueforfissilematerialsdetectionusingelectronlinac AT eranlv techniqueforfissilematerialsdetectionusingelectronlinac AT karasevsp techniqueforfissilematerialsdetectionusingelectronlinac AT kiryukhinnm techniqueforfissilematerialsdetectionusingelectronlinac AT melnikyup techniqueforfissilematerialsdetectionusingelectronlinac AT ranyukyun techniqueforfissilematerialsdetectionusingelectronlinac AT trubnikovsv techniqueforfissilematerialsdetectionusingelectronlinac AT shljakhovin techniqueforfissilematerialsdetectionusingelectronlinac |
| first_indexed |
2025-07-06T05:42:24Z |
| last_indexed |
2025-07-06T05:42:24Z |
| _version_ |
1836875042021965824 |
| fulltext |
TECHNIQUE FOR FISSILE MATERIALS DETECTION USING
ELECTRON LINAC
A. Barrata1, A.N. Dovbnja2, L.V. Eran2, S.P. Karasev2, N.M. Kiryukhin3, Yu.P. Mel’nik2,
Yu.N. Ranyuk2, S.V. Trubnikov4, I.N. Shljakhov2
1Penn State University, Pennsylvania, USA
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: karasev@kipt.kharkov.ua
3Academy of Technology Sciences, Kharkov, Ukraine
4Kharkov National University, Kharkov, Ukraine
The possibilities of technique for fissile materials detection using the pulse γ-quantum fluxes generated by
electron linac are studied. The technique is based on detection of neutrons escaping from fissile materials after
gamma irradiation (technique of delayed neutrons). The diffusion approach is developed for description of space-
time evolution of neutron fluxes inside the prototype system, which is irradiated by external γ-source. The simulation
of electromagnetic interaction with matter is performed using the program package GEANT. The feasibility of this
technique is proved for the case of plane one-dimensional model for a three-zone homogeneous subcritical assembly
consisting of 235U and 56Fe.
PACS: 61.20.ja
1. INTRODUCTION
The problem of detecting fissile materials (FM) is
recently question of the hour in the context of the risk of
nuclear proliferation and the danger of executing acts of
terrorism. The perspective methods of FM detection are
the so-called active ones. Neutrons often use in these
methods, since they have a capacity for traversing the
materials without an essential attenuation of the initial
flux (see, e.g., [1]). The active techniques of FM diag-
nostics can be based on detection of neutrons escaping
from FM that undergo fisssion, which can be initiated by
neutron bombardment or gamma irradiation (technique
of delayed neutrons). So, the beam of gammas is offered
to use in [2] for detection of transuranium scraps.
The neutron or gamma fluxes of required intensity
can be produced using linear accelerators. It should be
stated that the neutrons, which are produced by the
corresponding (e,n) converter, have an angular
distribution close to spherically symmetric. Therefore,
the considerable part of neutron flux will be spent
ineffectively, and it is necessary to increase an electron
current for producing a required neutron flux. It will
gain in an irradiative loading examined sample. In
contrast to neutrons a γ-quantum flux produced by the
(e,γ) converter (at energy of an initial electron beam
more than 20 MeV) is mainly propagated in the
direction of initial electron beam with a small angular
divergence. It essentially facilitates a problem of
localizing a γ-quantum flux on an examined region.
FM, that are prepared for illegal transport, can be
disposed in special assemblies. These assemblies can
have multi-layer structure, in which the FM layers
alternate with the layers from other materials. It is
reasonable to assume also, that the assemblies should be
subcritical ones, in order to eliminate a possibility of
initiating an uncontrolled chain nuclear reaction.
The simplest model of subcritical assembly is the
one-dimensional model of plane infinite layers. This
model corresponds to the situation when neutron
leakage from assembly is absent in the transverse
direction. We shall also assume, that a material
composition of assembly does not include the hydric
materials. It allows considering only fast neutron-
induced nuclear processes, which occur in the assembly.
The purpose of the present work is to investigate a
feasibility of detecting FM with the help of the
technique of delayed neutrons, which is based on using
the bremsstrahlung flux produced by electron linac.
The diffusion approach, which has been developed
in [3], is used for describing the space-time evolution of
neutron fluxes inside the subcritical assembly irradiated
by external γ- source. The simulation of electromagnetic
interaction with the corresponding materials is
performed using the programme package GEANT. The
calculations are carried out for the case of a three-zone
homogeneous subcritical assembly, in which two 56Fe
layers surround 235U layer.
2. THE CALCULATION FORMALISM
In the one-group approximation the non-stationary
one-dimensional diffusion equation for the scalar
neutron flux Φ can be written in the form
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2005, № 6.
Series: Nuclear Physics Investigations (45), p. 75-80. 75
1 ( ) (1 )( )a f fD
v t x x
β ν∂ Φ ∂ ∂ Φ− Φ − − Σ Φ
∂ ∂ ∂
+ Σ
i i
l ll i
C Qλ= +∑ ∑ , (1)
( ) /l f f l f fl
β β ν ν= Σ Σ∑ , (2)
where Φ(x,t) is the scalar neutron flux, Σα(x)=Σjσα
jNj(x)
is the macroscopic cross section of the neutron reaction
of the α-type, (the index α corresponds to the reactions
of neutron absorption (a) and fission (f)), Nj(x) is the
concentration of j’th nuclide at the point x; σα
j is the
corresponding effective one-group microscopic cross
section of the j’th nuclide; νfΣf=Σjνf
jσf
jNj(x), νf
j is the
mean number of neutrons produced at the single nuclear
fission event for the j’th fissile nuclide; β is the
effective fraction of delayed neutrons, βj=Σiβj
i, here βj
i,
Cj
i and λj
i are the portion of delayed neutrons, the
concentration and decay constant of the precursor nuclei
in the i’th group of the j’th fissile nuclide,
correspondingly; D(x)=1/(3Σtr(x)) is the diffusion
coefficient, Σtr(x)) is the macroscopic transport cross-
section, v is the one-group neutron velocity.
To create a neutron flux in the system under
consideration we assume that the left boundary of the
system is subjected to an external photon flux Φγ
coming from a γ-source. The corresponding rate of
neutron generation in each space point of the assembly
due to the (γ,n) and (γ,f) reactions with nuclei involved
in the assembly composition is defined by the relation
max max
( , ) ( , )
( , ) ( , ) ( , )( )
th th
n f
E E
n f f
E E
Q x dE dE
γ γ
γ γ
γ γ γ γ γ γ γν= Σ Φ + Σ Φ∫ ∫ , (3)
( , ) ( , )( , ) ( ) ( )j j
n nj
x E E N xγ γ γ γσΣ = ∑
( , ) ( , )( ) ( , )Σf fE x Eγ γ γ γν
( , ) ( , )( ) ( ) ( ),= ∑ j j j
f fj
E E N xγ γ γ γν σ
where Σ(γ,n)(x,Eγ) (Σ(γ,f)(x,Eγ)) is the macroscopic cross
section for the (γ,n) (photo fission (γ,f)) reaction, σj
(γ,n)(E
γ) (σj
(γ,f)(Eγ)) is the total microscopic cross section for the
(γ,n) ((γ,f)) reaction with the j’th nuclide, νj
(γ,f)(Eγ) is the
mean number of neutrons which are produced at the
single photo fission event for the j’th fissile nuclide; Φγ
(Eγ) is the photon flux with energy Eγ, E th
(γ,n) (E th
(γ,f)) is
threshold energy for the corresponding (γ,n) ((γ,f))
reaction, Eγ
max is the upper limit of the gamma-radiation
energy.
We consider a finite one-dimensional space region 0
≤x≤ L with a certain distribution of FM and other
materials, which simulates the subcritical assembly. The
boundary conditions of the third kind for the flux Φ(x,t),
which correspond to the free assembly boundaries, are
used
0
( , )(0, ) 2 (0, ) 0
x
x tt D t
x =
∂ ΦΦ − =
∂ , (4)
( , )( , ) 2 ( , ) 0
=
∂ ΦΦ + =
∂ x L
x tL t D L t
x . (5)
Since the assembly under consideration is a multi-
layer one the continuity conditions for the neutron scalar
flux and neutron current must be satisfied at the bounda-
ry of media with the different physical properties:
/ //( , ) ( , )x t x tΦ = Φ , (6)
// /
/ //( , ) ( , )( , ) ( , )x t x tD x t D x t
x x
∂ Φ ∂ Φ=
∂ ∂
, (7)
where the primes mark the quantities belonging to diffe-
rent media.
These conditions are valid for any moment of time
within the time interval 0 ≤ t ≤ T considered. The initial
condition for the neutron flux Φ(x,t) at the moment t = 0
for all values x from the space interval 0 ≤ x≤ L is
chosen as
( , 0) 0x tΦ = = . (8)
The burn-up of FM will be neglected, since we con-
fine ourselves to consideration of the assembly opera-
tion during small time
The equations of nuclear kinetics for 6 groups of the
precursor nuclei of delayed neutrons take the form
( )∂ = − + Σ Φ
∂
i
i i il
l l l f f l
C C
t
λ β ν (9)
with the initial conditions
0( , 0) ( )= =i i
l lC x t C x . (10)
In the case under consideration the flux Φ weakly
varies during the characteristic decay time of the precur-
sor nuclei that emit delayed neutrons. Therefore, number
of the kinetic equations (9) can be reduced, using the
approach of one equivalent group of the precursor nuclei
( )∂ = − + Σ Φ
∂
l
l l l f f l
C C
t
λ β ν , (11)
0( , 0) ( )= =l lC x t C x , (12)
where / /= ∑ i i
l l l li
λ β β λ .
The complete statement of the problem considered
includes the set of partial differential equations (1), (11)
and corresponding initial and boundary conditions to
them as well. For solving this nonstationary problem we
have used the finite-difference method. To apply the
finite-difference technique a rectangular mesh with steps
h and τ (uniform for x and variable for t) in the range of
variables x and t is introduced. We shall find the
solutions of the set of the algebraic equations obtained
from Eq. (1) in this way using the implicit Crank-
Nickolson difference scheme [4] (for details, see [3]).
The solutions of Eq. (11) can be simplified by assuming
that the neutron flux Φ is constant during the time
intervals τ. This assumption can easily be satisfied by
choosing sufficiently small time intervals τ, on which
the flux value should be taken as Φ=(Φn+Φn+1)/2 (where
Φn is the neutron flux value for the n-th time layer).
Then the expressions for the concentrations of
precursor nuclei for the new (n+1)-th layer at every
node of the space mesh can be obtained using the
analytical approach described in Ref. [3]
( )1 ( ) 1l ln n l
l l f f l
l
C Ce eλ τ λ τβ ν
λ
−+
= + Σ Φ −
. (13)
The initial condition is chosen as Cl
0 = 0.
76
Thus, the set of partial differential equations (1) and
(11) is reduced using the Crank-Nickolson difference
scheme to the set of algebraic equations, in which
dependence of the concentrations of precursor nuclei on
the sought-for neutron flux Φ is defined by Eqs. (13).
The numerical solutions of this set of equations have
been calculated using the method like in [3].
For calculations of the effective one-group
microscopic cross sections we used the group neutron
fluxes Φg (g is the number of neutron energy group) for
the initial assembly calculated from solving the
stationary multigroup problem. Calculations were
performed in the 26-group approximation using the
library of group neutron constants from Ref. [5]. The
procedure for calculating the one-group effective cross
sections is defined by the relations (see [3])
26
1
( )
( )
gl g
l
g S
K
K
α
α
σ
σ
=
Φ
=
Φ∑ , (14)
26
1
( ) ( )g
S
g
K K
=
Φ = Φ∑ ,
where ΦS(K) is the neutron flux summed over 26 groups,
the index α corresponds to the reactions of neutron
capture, fission and scattering, the index K numerates
the node of the space calculation mesh.
The one-group neutron velocity is given by
26
1
1 1 ( )
( )
g
g
gS
K
v K v=
Φ=
Φ ∑ , (15)
where vg is the neutron velocity for the group g.
The transport cross section σtr is averaged according
to the following expression
26 26
1 1
( ) / ( )l gl g g g g
tr tr
g g
D K D Kσ σ
= =
= Φ Φ∑ ∑ , (16)
where Dg is the diffusion coefficient for the group g.
3. RESULTS OF CALCULATIONS
To solve the main problem of the present work it is
necessary to simulate intense neutron field inside the
subcritical assembly by the external γ-source. The
description of corresponding evolutionary problem is
based on the diffusion approach described above.
We consider a three-zone (layer) homogeneous
subcritical assembly that consists of the high-enriched
(100%) metal 235U fuel of porosity p = 0.8 and the
constructional material 56Fe (see Fig. 1).
X, cm 0 XL L XR
Zone 1 Zone 2 Zone 3
Φ γ
56Fe 56Fe
235U
100 %
Fig. 1. The subcritical assembly
The calculations start from distributing 235U and 56Fe
nuclei on the corresponding zones. The first (third) zone
(near the left (right) edge of the assembly) with the
width 25 cm of every one is filled only with 56Fe. The
second zone represents the thin layer of 235U. The
subcritical assembly width, 0 x LЈ Ј , is divided into
M = 200 intervals of the spatial calculation mesh. We
impose the boundary conditions (4)-(7) on the scalar
neutron flux Φ(x,t). To create the intense neutron flux in
the system we assume that the left boundary of the
assembly is subjected to an external photon flux Φγ(Eγ)
coming from a γ-source. The photon flux simulates
inside the assembly the neutron flux that is defined by
the density of neutron generation rate Q(x) (3).
0 40 80
1E-5
1E-4
1E-3
1E-2
1E-1
N/N0
Egam. (MeV)
Fig. 2. Relative dependence of γ - quantum in
energy Eγ calculated for the electron energies 25 MeV
(dashed curve) and 100 MeV (solid curve)
The parameters of the subcritical assembly under
consideration were determined by the numerical solution
of the multigroup criticality problem. So, the value of
effective multiplication factor of neutrons in this system
keff = 0.93 when the width of 235U layer was chosen to be
equal to 13 mm.
The simulation of electromagnetic interaction with
the corresponding materials was carried out for an
electron linac with the following parameters: the average
current 1 ma, the maximal energy of electron beam
100 MeV and the frequency 300 Hz. The tantalum target
was used as the (e,γ)-converter. The thickness of the
target is 6 mm.
Fig. 2 presents the energy distributions of γ - quanta,
which are calculated for two values of the electron
energy using the software package GEANT. These
spectra define the number of γ - quanta N of certain
energy that escape from the converter in a case, when
the initial electron beam contains N0 = 10 6 particles.
Fig. 3 shows the spatial distribution of the integral
γ - quantum flux, which is defined by the following
relation
max
0
0 5
1/ ( )
E
MeV
N N N E dE
N
γ
γ γ= ∫ , (17)
where N(Eγ) is the number of γ - quanta of energy Eγ.
77
As can be seen from Fig. 3, the γ - quantum flux
appreciably decreases depending on the distance of
penetrating into the assembly materials. This depen-
dence has the exponential character. The jump that the
curve undergoes in the second zone is explained by
more strong flux attenuation in 235U layer in contrast
with 56Fe layers. This is stipulated by value of the mass
attenuation factor for 235U, which is greater than that for
56Fe in the γ - quantum energy region of interest.
Fig. 3. Relative space distribution of the integral
γ - quantum flux inside the subcritical assembly for the
electron energy 100 MeV
Fig. 4 presents the spatial distribution of density of
neutron generation rate Q(x) (3) inside the subcritical
assembly that is calculated for the electron beam energy
100 MeV.
Fig. 4. Spatial distribution of Q(x) [×1016 cm-3s-1]
inside the subcritical assembly
In the first and third zones the curve of Q(x)
exponential decreases that corresponds to the photon
flux damping when the γ-radiation traverses the iron. In
the second zone the noticeable enhancement of Q(x)
value is observed. This burst of the neutron generation
rate is mainly conditional on the contribution of the (γ,f)
reaction on 235U to the formation of Q(x). The
photofission cross section takes on values that are
greater as compared with the (γ,n) cross sections for 235U
and 56Fe. It should be also noted that mean number of
neutrons produced at the single fission event of 235U is
greater than two and has the tendency to increase with
increasing photon energy. Besides the (γ,n) cross section
for 235U is greater than that for 56Fe in the giant dipole
resonance region.
Results of solving the nonstationary problem to
define the neutron flux inside the subcritical assembly
are presented at different time moments of turning the
external photon flux off toff in the succeeding figures.
Fig. 5. Spatial distribution of the neutron flux Φ(x)
[×1016 cm-2s-1] at time moments t1 = 3.544⋅10-7, t2 = 1
and t3 = 2 seconds. The photon flux is turned off at
toff = 1 second
Fig. 5 shows the space distribution of the neutron
flux for different moments of time. At the initial stage
for very small irradiation time (see the time moment t1)
the distribution shape to a considerable extent differs
from the distribution shape of the neutron flux for
greater intervals of irradiation time. The neutron flux
attains its maximum in the second layer (see Fig. 5) at
the time moment t2 when the photon flux is turned off.
The calculations show that the maximum value of the
neutron flux Φmax at this time moment constitutes only
about 80 % of Φmax value calculated for the
corresponding stationary problem. After turning the
photon flux off the space distribution of neutron flux at
the time moment t3 has the same shape as for the time
moment t2. However at the time moment t3 the Φmax
value becomes by about two orders of magnitude
smaller than that at the time moment t2.
Time dependence of Φmax for two values of toff = 1
and toff = 0.01 second is presented in Fig. 6. In both
cases at the time moment toff, when the photon flux is
turned off, Φmax reaches practically the same magnitude.
However during time after turning the photon flux off
the magnitudes of Φmax differ to a considerable degree in
going from one case to another. The distinction in the
corresponding magnitudes of Φmax is about two orders.
Note that the precursor nuclei of delayed neutrons
plays role of the neutron source inside the subcritical
assembly after turning the external photon flux off (see
Eq.(1)). The concentration CU of precursor nuclei, that
are product of fission of 235U, is proportional to the so-
called neutron fluence F = Φ t. Since the flunce in the
former case is greater than that in the latter one
approximately by a factor of 10 2, the same ratio is
observed between the CU values for these two time
78
moments toff. Apparently the distinction in the
corresponding magnitudes of Φmax mentioned above is
associated with this ratio between the CU values for the
time moments following after toff = 1 and toff = 0.01
second, correspondingly. One can see that the ratio
between the corresponding magnitudes of Φmax
conserves during one second after turning the photon
flux off in both cases. As a matter of fact this ratio takes
place a longer time period.
0.0 0.4 0.8 1.2 1.6
1E-5
1E-4
1E-3
1E-2
jL
t (s)
Fig. 6. Dependences of Φmax [×10 16 cm -2s -1] (top)
and jL [×10 16 cm -2s -1] (bottom) versus time. Curves are
calculated for the photon flux turned off at toff = 1
second (solid) and toff = 0.01 second (dashed)
The similar picture is observed in the time
dependences of the neutron leakage current jL = D∂Φ/∂x
from the right boundary of the assembly. The maximum
value, which jL reaches at the time moment of turning
the photon flux off toff = 1 second, is 3⋅1014 cm-2s-1 (see
Fig. 6 (bottom)). After turning the external γ - source off
at toff = 1 second the jL value rapidly falls off at first.
Then jL changes very slowly during one second and
takes on the magnitude of 3.4⋅1012 cm-2s-1 at the time
moment t = 2 seconds. Under the condition toff = 0.01
second jL takes on the value of 5.4⋅1010 cm-2s-1 at the
time moment t = 1.01 second.
Note that the energy production density reaches the
maximum value of about 17 kW t cm -3 in 235U layer at
both time moments of turning the external photon flux
off toff = 1 and toff = 0.01 second. After turning the
photon flux off the energy production density decreases
rapidly and takes on the values of 0.2 kW t cm - 3 and
0.32⋅10-2 kW t cm - 3 at the time moments t = 2 and
t = 1.01 seconds, correspondingly.
4. CONCLUSIONS
The feasibility of FM detection by the technique of
delayed neutrons has been proved in the special case of
the three-zone homogeneous subcritical assembly
consisting of 235U and 56Fe. The main features of the
technique have been studied for the case of the electron
linac with beam energy 100 MeV and the tantalum (e,γ)-
converter.
The neutron leakage current, which characterizes the
neutron flux emerging from the right boundary of the
assembly, is initiated and driven by the γ - quantum flux,
which generates neutrons with the rate Q(x) in each
space point of the assembly. The maximum value of this
neutron flux is equal to 3.5⋅10 14 cm-2s-1 for the stationary
problem that has been calculated with the time-constant
external photon flux. After turning the external γ-source
off the neutron flux is completely maintained inside the
assembly by precursor nuclei of delayed neutrons. These
nuclei, which are concentrated in the second zone after
fission of 235U, play the role of inner source that
generates neutrons with the rate λUCU. Thus, the neutron
flux substantially changes after turning the external γ-
source off. The flux decreases at first very rapidly by
two orders of magnitude. After that the neutron flux
changes very slowly during rather long time. The jL
value takes on 3.4⋅10 12 cm-2s-1 at the time moment t = 2
second for time of turning the external γ-source off
toff = 1 second. For the case toff = 0.01 second the
neutron flux takes on the value of 5.4⋅10 10 cm-2s-1 at the
time moment t = 1.01 second.
Hence, one can change the neutron flux emerging
from the assembly by choosing the gamma irradiation
time toff or the corresponding value of neutron fluence. In
the present analysis it is shown that these neutron fluxes
can take on the values, which are available for detection
by the existing neutron detectors. The corresponding
measurements can be carried out during rather long
period (several seconds) since the neutron flux does not
appreciably change over this period.
To embody the technique of delayed neutrons under
consideration the corresponding technology for
producing photon fluxes of high intensity is developed
using 100 MeV variable linac.
It should be noted, that the results obtained in the
present work, have a somewhat qualitative character,
since the plane one-dimensional model of the subcritical
assembly is not entirely corresponding to real cases. For
this reason, the results are better of theoretical interest
and serve to ascertain the main features of initiation and
evolution neutron flux that is generated inside the
subcritical assembly by the external γ-source. However,
all the above-made approximations allowed us to
describe the observed qualitative picture of the
processes well enough. It should also be stated that
results obtained with taking into account the neutron
leakage from the assembly in the transverse direction,
79
that is an attribute of the real assembly model, can
somewhat quantitatively alter the results presented
above. Of course, results obtained in the framework of
approach developed substantially depend on the material
composition of the subcritical assembly. The special
consideration is necessary in the case when the hydric
materials are in the composition of the assembly. The
main reason is associated with peculiarity of the neutron
interaction with the hydrogen nuclei, which is
characterized by strong anisotropy of scattering in
laboratory coordinate system and heavy loss of energy
in single collision as well. Thus, the use of diffusion
approximation in the case leads to appreciable distortion
of the neutron penetrability.
A further work is necessary to study the technique
under consideration using more complete mathematical
models.
ACKNOWLEDGEMENT
The work is supported by the CRDF project «Facili-
ty for detection of hidden nuclear devices in marine con-
tainers-feasibility study», grant № UK-E2-5023-KH-04.
REFERENCES
1. J. Romeyer–Dherby, L.M. Deider, Y. Beroud.
Development of active neutron interrogation devices
for alpha waste measurement. Proc of the ENC`90
(Lyon, France, 23-27 September 1990).
2. A. Lyossi, J. Romeyer-Dherby, F. Jallu, et al.
Transuranic waste by photon interrogation and on-
line delayed neutron counting // Nuclear Instruments
and Methods in Physics Research. 2000, v. B160,
p. 280-289.
3. S.P. Fomin, Yu.P. Mel’nik, V.V. Pilipenko,
N.F. Shul’ga. Investigation of Self-Organization of
the Non-Linear Nuclear Burning Regime in Fast
Neutron Reactors // Annals of Nuclear Energy. 2005
(in press).
4. J. Crank, P. Nicolson. A practical method for
numerical evaluation of solutions of partial
differential equations of the heat-conduction type //
Proc Camb. Phil. Soc. 1947, v. 43, p. 50-67.
5. L.P. Abagyan, et al.. Group Constants for
Calculations of Reactor and Shielding. Moscow: ″
Energoizdat″, 1981, 231 p. (in Russian).
МЕТОД ОБНАРУЖЕНИЯ ДЕЛЯЩИХСЯ МАТЕРИАЛОВ С ИСПОЛЬЗОВАНИЕМ
ЛИНЕЙНОГО УСКОРИТЕЛЯ ЭЛЕКТРОНОВ
А. Баратта, А.Н. Довбня, Л.В. Еран, С.П. Карасев, Н.М. Кирюхин, Ю.П. Мельник,
Ю.Н. Ранюк, С.В. Трубников, И.Н. Шляхов
Исследуются возможности метода обнаружения делящихся материалов с использованием импульсных
потоков γ-квантов, генерируемых линейным ускорителем электронов. Метод основан на регистрации
нейтронов, испускаемых делящимся материалом поcле γ-облучения (метод запаздывающих нейтронов).
Развит диффузионный подход для описания пространственно-временной эволюции потока нейтронов в
исследуемом объекте, который облучается внешним источником γ-квантов. Моделирование процессов
электромагнитного взаимодействия с веществом проводится с помощью пакета программ GEANT.
Осуществимость этого метода подтверждена результатами расчетов, проведенных в случае плоской
одномерной модели для гомогенной трехзонной подкритической сборки, в которой слой 235U окружен двумя
слоями 56Fe.
МЕТОД ВИЯВЛЕННЯ МАТЕРІАЛІВ, ЩО ПОДІЛЯЮТЬСЯ, З ВИКОРИСТАННЯМ
ЛІНІЙНОГО ПРИСКОРЮВАЧА ЕЛЕКТРОНІВ
А. Баратта, А.M. Довбня, Л.В. Єран, С.П. Карасьов, M.М. Кірюхін, Ю.П. Мельник,
Ю.M. Ранюк, С.В. Трубніков, І.M. Шляхов
Досліджуються можливості методу виявлення матеріалів, які поділяються, з використанням імпульсних
потоків γ-квантів, що генерує лінійний прискорювач електронів. Метод засновано на реєстрації нейтронів,
випромінюваних матеріалом, що поділяється, після γ-опромінення (метод запізнілих нейтронів). Розвинуто
дифузійний підхід для опису просторово-часової еволюції потоку нейтронів у досліджуваному об'єкті, що
опромінюється зовнішнім джерелом γ-квантів. Моделювання процесів електромагнітної взаємодії з
речовиною проводиться за допомогою пакету програм GEANT. Можливість запровадження цього методу
підтверджено результатами розрахунків, проведених у випадку плоскої одновимірної моделі для гомогенної
трьохзонної підкритичної збірки, у якій шар з 235U оточений двома шарами з 56Fe.
80
1Penn State University, Pennsylvania, USA
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The possibilities of technique for fissile materials detection using the pulse -quantum fluxes generated by electron linac are studied. The technique is based on detection of neutrons escaping from fissile materials after gamma irradiation (technique of delayed neutrons). The diffusion approach is developed for description of space-time evolution of neutron fluxes inside the prototype system, which is irradiated by external -source. The simulation of electromagnetic interaction with matter is performed using the program package GEANT. The feasibility of this technique is proved for the case of plane one-dimensional model for a three-zone homogeneous subcritical assembly consisting of 235U and 56Fe.
PACS: 61.20.ja
3. RESULTS OF CALCULATIONS
ACKNOWLEDGEMENT
|