The thermal neutron waves excitation in muldiplied media bounded by absorber
An excitation of neutron waves by an external wave source in the active zone of the neutron field is investigated. It is found that the forced neutron waves are transformed into proper (eigen) neutron waves on the borders of the active area. The practical applications of results in noise diagnostics...
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| Zitieren: | The thermal neutron waves excitation in muldiplied media bounded by absorber / A.A. Vodyanitskii, Yu.V. Slyusarenko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 348-352. — Бібліогр.: 11 назв. — англ. |
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| author | Vodyanitskii, A.A. Slyusarenko, Yu.V. |
| author_facet | Vodyanitskii, A.A. Slyusarenko, Yu.V. |
| citation_txt | The thermal neutron waves excitation in muldiplied media bounded by absorber / A.A. Vodyanitskii, Yu.V. Slyusarenko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 348-352. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | An excitation of neutron waves by an external wave source in the active zone of the neutron field is investigated. It is found that the forced neutron waves are transformed into proper (eigen) neutron waves on the borders of the active area. The practical applications of results in noise diagnostics of active area of nuclear reactor are discussed.
Зовнішнє хвильове джерело збуджує примусові нейтронні хвилі в активній зоні нейтронного поля. Ці хвилі перетворюються у власні нейтронні хвилі на межі активної зони. Результати мають практичні застосування в шумовій діагностиці активної зони реактора.
Внешний волновой источник возбуждает вынужденные нейтронные волны в активной зоне нейтронного поля. Эти волны преобразовываются в собственные нейтронные волны на границе активной зоны. Результаты имеют практические приложения в шумовой диагностике активной зоны реактора.
|
| first_indexed | 2025-12-07T13:25:09Z |
| format | Article |
| fulltext |
THE THERMAL NEUTRON WAVES EXCITATION IN MULTIPLIED
MEDIA BOUNDED BY ABSORBER
A.A. Vodyanitskii and Yu.V. Slyusarenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
e-mail: vodyanitskii@kipt.kharkov.ua
An excitation of neutron waves by an external wave source in the active zone of the neutron field is investigated.
It is found that the forced neutron waves are transformed into proper (eigen) neutron waves on the borders of the
active area. The practical applications of results in noise diagnostics of active area of nuclear reactor are discussed.
PACS: 28.20. −v
1. INTRODUCTION
The safety of nuclear energy is one of the most ac-
tual problems of the day. Diagnostics of the reactor ac-
tive zone is of importance here, and, in particular, noise
diagnostics of neutron flux oscillations, which reflect
acoustic and thermal vibrations in the equipment of the
active zone and first loop as well as properly of the
coolant and moderator.
The neutron-acoustic and neutron-thermal models of
diagnostics of nuclear reactors active zone are being
intensively developed [1-4] (other references see in pa-
per [5] in this issue). Different in practical orientation,
these works represent engineering developments which
remain to some degree formal without analytical de-
scription based on the equations of physical kinetics [6].
Pioneer researches of Fermi [7] and studies of other
authors [8−10] were conducted, however, on the basis
of general physics [6] principles.
It is of interest, therefore, to study the noise diagnos-
tics at the level of physical description and strictness.
Because neutron detectors reveal noises in the neutron
flux (and neutron density) variations, as well as the
thermocouples do in the reactor thermal field, a ques-
tion arises about the nature of such modulation of the
neutron and thermal fluxes.
An acoustic wave or other external source wave can
modulate the neutron field in the reactor active zone.
Here we confine ourselves to the problem of modula-
tion of neutron field by the external source wave in the
first coolant loop in the one-dimensional model of pla-
nar geometry. Early works on this subject (see [11] and
ref. therein) employed a different approach and led to
the results which were applied to the measurement of
various absorbers characteristics.
The obtained solution of the problem of neutron
field modulation by a running wave from the external
source can be easily complemented by the solution for
an external wave running in the opposite direction. The
sum of these solutions, as is generally known, is a
standing wave. And, naturally, a solution for a neutron
field modulation by waves of complex spectral compo-
sition can be obtained within the linear approach by
means of superposition of external waves with their
proper weights.
2. INITIAL EQUATIONS
AND FORMULATION OF THE PROBLEM
The density of thermal neutrons in the processes of
their reproduction, slowing down, diffusion and capture
in the multiplying medium of a nuclear reactor satisfies
an integro-differential equation. This equation is trans-
formed in the differential equation of a diffusive type
[8]
),(1),() 1(
trN
T
trN
T
KND
t
N
cc
−∆τ++∆=
∂
∂ . (1)
Here 3vtrlD = is the coefficient of the diffusion of
thermal neutrons, is the transporting free path, is
the average velocity of thermal neutrons; the inverse
time of the capture of neutrons is equal
trl v
∑ σ= a
a
cac NT v1
θνϕ= K
, where is the cross section of the
capture of neutrons by the nuclei of sort and is
their density. The coefficient of neutrons reproduction
equals to the product of new neutrons ap-
pearing on one act of fission and the probability
aσ
a a
ν
N
ϕ for
the fast neutron to be slowed down, times the coeffi-
cient of the use of thermal neutrons, or, in other
words, the probability of that the thermal neutron will
cause a fission,
θ
( )∑ σρ+σρσρ=θ a aaffff (2)
( is the fission cross section, fσ af ,ρ see in Eq. (16)
below). The neutron age is proportional to the aver-
age square of neutron free path and equals
τ
( ) ( EEl 0
2 ln 32≈ )E)(τ , where l is the average neu-
tron free path, =l ∑a
0E
1 , is the scat-
tering cross section of the nuclei of sort , is their
density, is the energy of fast neutrons, and is the
energy of thermal neutrons.
(σa
s E) a
sσaN ( )E
a aN
E
The system of equations for the density of neutrons
in active zone and out of it, , can be written as iN eN
( ) ),,( 1),( trN
T
KtrNTKDtN i
c
ici
−
+∆+=∂∂ τ (3)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2007, N3 (2), p. 348-352. 348
. ),(),( ceee TtrNtrNDtN −∆=∂∂ (4)
The problem that is described by this system of equa-
tions consists in the following. An active area lies be-
tween two parallel planes with co-ordinates
and . The absorber fills the whole space from
to , including the active zone. An external
wave excites the neutron field. When this wave, for
example, a sound wave, propagates in positive direction
from to , it runs through the active zone. For
each of the region in directi n, we find the solu ion
as the sum of two terms
and ) with boundary con-
ditions at
0>= hz
t
,(1 trN+
hz −=
+∞
−∞
),( trNe
z =
−∞
+∞
= N
h±
z
r
o
=),( trNi
) ,(2 trN
)(rNoi
(oe +
)
Here )( 00 ρ= kk , )( 00 ρ= qq and 0 ρ−ρ=ρ∆ . The
system of equations for perturbations of the density of
neutrons in the active zone and out of it containing the
external source of oscillations of the medium mass den-
sity 0),( ρ−ρ≡ρ∆ tr looks like (the index «0» is omit-
ted at the unperturbed quantities):
),(),( thNthN ei ±=± , (5)
hzehzi zNdzN ±=±= ∂∂=∂∂ ) () ( , (6)
where ie DDd = is the ratio of diffusion coefficients
for each region, which in what follows we consider
equal to unity.
The stationary state solutions of Eqs. (3), (4) is well
known for more general geometrical shapes of the ac-
tive zone, for example, for the «prism, isolated in
bases» [8, p. 132]. For further references we
will write down the solution for the basic state that is an
extreme case solution for the zone of finite transversal
dimension [8], when this dimension tends to infinity
(formally). The neutron density is searched in the form
hz ±=
kzANi cos0 = , hz ≤ ; qz
e BN −= e0 , hz ≥ . (7)
Boundary conditions (5) and (6) together with the con-
dition of having the non-zero values of constants and
yield the relation
A
B
dqkhk tg = (8)
and the relation between these constants
khAB hq cose = , (9) aa
where
eff
2 1
DT
Kk
c
−
= ,
cDT
q 12 = , eff .cD D K Tτ= + (10)
The relation between parameters (8) serves, for exam-
ple, for finding the neutron reproduction coefficient .
For small values , neglecting
K
1 <<kh ( ) 1<<ciTDKτ ,
one has
( )qhdhLdK e ≡=−1 . (11)
3. SOLUTION OF THE PROBLEM
OF NEUTRON WAVE EXCITATION
It is convenient to study the neutron density waves
writing down the system of equations (3) and (4) in the
following form
),(),( 21
eff trNktrNtND iii +∆=∂∂− , (12)
).,(),( 21 trNqtrNtND eee −∆=∂∂− (13)
Here the notations are the same as in Eq. (10). The
wave numbers and can be decomposed: k q
0
2
022
ρ∂
∂
ρ∆+=
kkk o ,
0
2
022
q
ρ∂
∂
ρ∆+= oqq .
),(),( 1211
1
eff trNktrNtND +∆=∂∂−
) cos(cos 2
1 ztkzkA ξ−ω+ , (14)
),(),( 22221 trNqtrNtND −∆=∂∂−
) cos( e cos )(2
1 ztqhqA zhq ξω −− − . (15)
Boundary conditions at are obtained now mak-
ing the substitutions and in Eqs.
(5) and (6).
hz ±=
1Ni →N 2NNe →
The equations (14) and (15) for variations of the
coolant and slowing medium densities in dependence of
spatial and temporal variables are given in the explicit
form. In Eqs. (14) and (15) the solution (7) and the rela-
tion (9) between the constants and were used. The
variations of the medium density are set in the form
A B
) cos(),( 1 zttz ξ−ωρ=ρ∆ , where sω=ξ is the wave
number and is the phase velocity of the external
source wave. The inverse capture time depends linear
on the average mass density
s
ρ if the nuclei relative
concentrations in absorber and fissile mediums are
constant
ar
vv1 ∑∑ σρ=σ=
a
a
aaac m
rNT ,
ρ
ρ
= a
ar . (16)
Here notations are the same as in Eq. (1). Perturbing
factors and , entering equations (14) and (15),
have the form:
2
1k 2
1q
ρ∂∂ρ= 2
1
2
1 kk , ρ∂∂ρ= 2
1
2
1 q q . (17)
The reproduction coefficient does not depend on
variation of the average density
K
ρ
The vibrating absorber present in the active zone can
vary density of neutrons. The «construction» of the ex-
ternal source, which influences the neutron field, takes
into account such situation, and it is reflected in equa-
tions (14), (15) (see (17) also).
Spatial-temporal dependences of the external source
in equation (14) were used for finding the partial solu-
tion of the equation in active zone, which is equal to
+
∆
= −
)(
ee
4
2
1
part
1 k
kAN
ikz
tiiz ωξ c.c.
)(
e
+
−∆
−
k
ikz
, (18)
349
Here complex conjugate terms are marked c.c., and for
compactness parameters are used, )( k±∆
=±∆ )( k eff
2 2 Dik ω−ξ±ξ ,
=±∆ )( iqe Diqi ω−ξ±ξ 22 , (19) C
=σ±δ )( iki +ξ+σ± , =ξ±ζ )( ξ±−σ iq .
The parameters and given above will
be used below.
)( iqe ±∆ )( σ±δ
The general solution of the equation (14) contains
two complex constants C and and a complex wave
number of proper oscillations of the neutron density, in
the active zone, µ , µ and . Its square
equals
1
κ+ i
2C
0>λ= 0>κ
effD2 iω+2 k=µ (see other parameters in
(10)). The general solution in the active zone is equal
.ee),(
2
1
gen
1
zitiziti CCtzN µ−ω−µ+ω− += (20)
The solution of equation (15) outside the active zone
contains a characteristic number which is equal to
( ) "' )( 2122 σ+σ=δ−=ωσ=σ iiq , , where 0'>σ
=σ' ( ) 21422 )4(1 qDq ω+ , . (21) 1 <<ω cT
Here ( )cDTq 12 = and ω=δ D .
Let us write down the particular solution (for outer
regions), which satisfy zero boundary condition at
(without c.c. terms): ±∞→z
)(q 2
1
part
2 e
)(
cos
2
),( zhtizi
e iq
khqAtzN ∓+ω−ξ
± ±∆
−= , (22)
where parameters are defined in Eq. (19). In
these formulas the upper sign applies for the values
and lower sign for .
)( iqe ±∆
z ≤hz ≥ h−
The general solution of the equation (15) looks like
the solution in the active zone hz ≥
c.c.e),( gen
2 += σω−
±±
ztiDtzN ∓ , (23)
Here the rule of upper and lower signs works as in the
expression (24) and the boundary conditions are taken
into account at ∞→z .
The boundary condition of the neutrons density con-
tinuity at together with the similar conditions of
the neutrons diffusive fluxes continuity, which follows
from equations (6), brings to four complex equations
needed to obtain the constants , , , and .
Excluding constants from these equations we get
two equations for constants C and C
hz ±=
1C 2C
2
+D −D
±D
1
hihih ACiCi 2 1 e
4
e )(e )( ξµµ σµσµ ±±± −=−± ∓
2 ikh ikh 2
1 1
e
( ) ( ) ( )k e e q cos
(k) ( k) ( iq)
± δ ±σ δ σ ζ ±ξ
× + ± ∆ ∆ − ∆ ±
∓∓ kh
. (24)
Each of these equations with signs and must be
read two times, the first time for the upper sign, second
time for lower sign.
± ∓
Constant , limited to the main terms in the ex-
pansion after the small parameter,
2C
) 1<<
=µ ) exp( Re hi
( Im exp µ− h , can be found with the upper sign in
Eq. (24) and can be found with the lower sign in
Eq. (24), each time omitting terms with one constant
and keeping with the other.
1
Next a supposition will be adopted, which is impor-
tant for practical applications of sound diagnostics in
the active zone of reactor, namely that ξ . Thus,
after neglecting quadratic in terms the expressions
k<<
ξ
=∆ )(k eff 2 Dik ω−ξ and become
complex conjugated (with the change of sign of
), and the formula for the density greatly simpli-
fies.
=)k−∆( )(* k∆−
)( k−∆
As a general solution, the expression for the internal
densityof the neutrons can be obtained as
+
∆
σδ
σ−µ
= ξ−µ
ω−µ
c.c.
)(
)(ee
4
),( *
2
1
gen
1 k
k
i
AtzN ihiz
tihi
c.c.c.c.
)(
)(ecos2 2
1 +
−
−∆
ξζ
+ ξ−µ
iq
khq
e
ihiz (25)
In the limit factors 0→ξ =∆ξζ )()( iqe
=−∆ξ−ζ )()( iqe ( ) )( ωσ i− Dq equal to each other.
Expression in the last round brackets in Eq. (25) have
been simplified, as well as in the similar expression
)()( * k∆σδ = ( ) ( )eff2 Dik ω+iki ξ+ξ+σ the quad-
ratic terms in the relative parameter ξ have been also
neglected.
4. PHYSICAL RESULTS AND DISCUSSION
The excitation of the neutron field in the active zone
under the action of internal and external to zone sources
with the frequency and the wave number ξ is de-
scribed by the sum of particular and general solutions.
The particular solution (18) after some transformations
takes the form
ω
∑ = ψ= 2
1
2
1
part
1 ),(cos
2
),( j jj tzNkAtzN , (26)
where is the maximum background neutron density
and the variable phases are equal to
A
=ψ ),(2 ,1 tz
±θ+±ξ−ω ) kzt ( . The phase changes θ can be de-
termined from the equations
±
( ) ( )k±∆=1iN exp2,1 θ± ,
and the squares of modules are equal to 2,1N
( )22
2,1 kN ±∆= 1 .
An appearance of two terms in (26) is due to the ori-
gin of the neutron field basic state in the active zone.
An external source, in particular a sound wave with the
wave number 0>ω=ξ s
ω
ξ ξ−k
, modulates the neutron den-
sity with the frequency and two combinational wave
numbers and . As a result two forced neu-
tron waves are exited which propagate without attenua-
tion with effective wave numbers. At the second
+k
ξ>k
350
term in the formula (26) describes the wave reflected
from the boundary with the velocity hz =
( ) 0vph <−ξω= k
0vph >
e),(gen
1
−= ANtzN
. At it will be the wave with
, which propagates in the same direction as the
modulating wave.
ξ<k
[ 2
1 Mkkz−
]khcosLq sin2
1 + +Ψ+
[ cos( +kh
)
cos e 2
1+ Mkkz
( ]} kh
( )
cossin2
1 Lq − ϕ+Ψ−
=Ψ≡Ψ ±± ),( tz ± h ∓
κ
κi µ
ω t z
+
)N tg θ
e M i ω±ξ
φ±tg ) effeff '22' DD ω±ξσωσ ∓ 2 kk ξ
(2 =N
2M
±ϕ
±
iL
ϕ=ϕ+
2L
The obtained solution (26) is true only for the active
zone region and describes the effective waves or
oscillations of the neutron density (only part of the
spatial period of the wave is located in the active zone).
However, phase correlations are just the same, as in the
obtained particular and general solutions.
Another feature in the physical interpretation of the
obtained solution can be seen from Eq. (20), presented
below in the real form:
{ )cos(cose ++ +Ψ φkhkh
( )+ϕ
)−−Ψ φ
− . (27)
This expression describes the waves of neutron den-
sity excited at the boundary of the active zone by the
non-proper neutron waves represented by the solution
Eq. (26). The following notations are used in Eq. (27):
θ−ξλ± h
λ
λ= =2
are the variable
phases of two waves, and are the real and imagi-
nary parts of wave numbers of proper neutron wave in
the active zone, µ , eff
2 Diω+k
(
(see
other notations in Eqs. (10)). Changes of the phases in
the relation to the phase of the external source, that en-
sure the formation of proper neutron waves in the reac-
tor active zone, can be found from the following rela-
tions σ−µe ,=θ ii 1 i. e. ( ) ( )'"" σ+' µσ−µ= , and
( ) ( )eff2' Dkik+σ=±φ ,
= ( ([ , )]
where the squares of the modules are equal to:
( ) )[ ]22 '""'1 σ+µ+σ−µ ,
( )( ) ( )2
eff
22222 4 Dkk ω+ξξ++σ= , and
= ( ) ( )Diiqiq ω−ξξξσ+σ−± 2)"(' 2 ∓∓ .
The parameter is arbitrary. Ignoring it to its small-
ness yields
ξ
≡±L =2L ( )[ ] 2222 '" ω−σ+σ qD ,
, π+ϕ=ϕ− .
At small values real and imaginary parts of
the wave number and σ are defined in the text af-
ter the Eq. (20) and in Eq. (21); in this case the quanti-
ties и take the form
1 <<ω cT
'σ "
φ tg
=2L ( )( )41 41 222
cTq ω+ , =ϕ tg cT 2ω− .
The expression for the density of neutrons (27) in
the region hz ≤
)h+
+Ψcos
takes into account the damping of the
proper neutron waves. Terms with exponent
and with harmonic functions of phase
, i.e. and sin , describe the evolution of
the density of the neutron wave that propagates in the
direction of propagation of the source wave which
modulates the neutron field. In this sense the proper
neutron wave is generated at the entry of the external
source wave in the active zone at its boundary .
[ (exp zκ−
+Ψ
]
+Ψ
hz −=
Similar considerations can be expressed with respect
to the terms with the exponential function
, . These terms describe the
evolution of the density of the neutron wave, generated
in the vicinity of the boundary of the active zone
which propagates and slowly attenuates in the opposite
(negative) direction. However, Eq. (27) has not symme-
try (or asymmetry) properties relative to replacement
. In the system there is a selected direction of
propagation of a running wave from the external source.
[ ])(exp hz +κ
zz −→
hzh ≤≤−
hz =
The proper neutron wave propagating in the positive
direction is localized at the place of its excitation, that
is, at the entry of the external source wave into the ac-
tive zone. The neutron wave propagating in the opposite
direction is localized in the region, where the wave of
external source goes out from the active zone. Similar
statements can be made concerning the excitation of the
proper neutron waves inside the active zone by the ex-
ternal source (terms with in Eq. (27)). 2
1q
We will remind that the resulted solution takes into
account the diffusion of thermal neutrons and their cap-
ture in the limited medium of active zone and outside of
it.
From the obtained general solution inside the active
zone, Eq. (27), and the equations for constants together
with exponents it is possible to make the
judgment about properties of the neutron field outside
of the active zone
) exp( hD σ± ∓
hz ≥ . The density oscillations out-
side the zone decrease according to the exponential law
( )[ hz −σ− Reexp ], ( , see Eq. (21) and the text
after Eq. (20)) at that time as the background neutron
density decreases according to the law:
'σ=Reσ
( )( )hzq −−exp ,
( )DTq c12 = .
5. CONCLUSION
The numerous researches (both theoretical and ex-
perimental) have allowed to develop the noise methods
of controlling the processes inside reactors. These
methods, due to the registration of neutron noises and
the fluctuations of temperature, allow to determine the
velocity of coolant, the state of the reactor criticality
and a number of other parameters (see the engineering
aspects of the problem in article [5] in this issue). At the
same time, the obtained information sometimes leads to
ambiguous interpretation of the observed processes.
That is why it is very important to have an idea about
the wave processes, which take place both in the active
351
zone and in the whole system of the reactor first coolant
loop.
The external (both inside and outside the active
zone) sources that are periodic in time and in space ex-
cite in the active zone the forced neutron waves at the
sources frequency with the properties described above.
The forced neutron wave is transformed at the vicinity
of active zone boundary in the proper neutron wave.
The conclusion about transformation of the forced
waves in the proper neutron waves can be of practical
importance in the noise diagnostics of the reactor active
zone. This effect must be taken into consideration in the
analysis of phase shift of the neutron wave recorded by
the neutron detectors positioned in the reactor different
measuring channels. Such analysis is used to make a
conclusion about the nature of the detected neutron flux
perturbations, and, in engineering interpretation, about
the origin of the excitation sources, to which, e.g., neu-
tron-thermal excitations can be attributed [3,4]. As can
be seen from the present paper, it is necessary to take
into account also the proper neutron waves which are
excited by the external wave sources, e.g., by the exter-
nal acoustic waves.
The authors are thankful to V.A. Rudakov for dis-
cussions on the problems of the vibration diagnostics of
WWER-1000, and L.N. Davydov and A.G. Sotnikov
for help in editing the English translation of the article.
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ВОЗБУЖДЕНИЕ ВОЛН ТЕПЛОВЫХ НЕЙТРОНОВ В РАЗМНОЖАЮЩЕЙ СРЕДЕ,
ОГРАНИЧЕННОЙ ПОГЛОТИТЕЛЕМ
А.А. Водяницкий, Ю.В. Слюсаренко
Внешний волновой источник возбуждает вынужденные нейтронные волны в активной зоне нейтронного
поля. Эти волны преобразовываются в собственные нейтронные волны на границе активной зоны. Результа-
ты имеют практические приложения в шумовой диагностике активной зоны реактора.
ЗБУДЖЕННЯ ХВИЛЬ ТЕПЛОВИХ НЕЙТРОНІВ В РОЗМНОЖУЮЧОМУ СЕРЕДОВИЩІ,
ОБМЕЖЕНОМУ ПОГЛИНАЧЕМ
О.А. Водяницький, Ю.В. Слюсаренко
Зовнішнє хвильове джерело збуджує примусові нейтронні хвилі в активній зоні нейтронного поля. Ці
хвилі перетворюються у власні нейтронні хвилі на межі активної зони. Результати мають практичні застосу-
вання в шумовій діагностиці активної зони реактора.
352
|
| id | nasplib_isofts_kiev_ua-123456789-111049 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:25:09Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Vodyanitskii, A.A. Slyusarenko, Yu.V. 2017-01-07T19:08:56Z 2017-01-07T19:08:56Z 2007 The thermal neutron waves excitation in muldiplied media bounded by absorber / A.A. Vodyanitskii, Yu.V. Slyusarenko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 348-352. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 28.20. −v https://nasplib.isofts.kiev.ua/handle/123456789/111049 An excitation of neutron waves by an external wave source in the active zone of the neutron field is investigated. It is found that the forced neutron waves are transformed into proper (eigen) neutron waves on the borders of the active area. The practical applications of results in noise diagnostics of active area of nuclear reactor are discussed. Зовнішнє хвильове джерело збуджує примусові нейтронні хвилі в активній зоні нейтронного поля. Ці хвилі перетворюються у власні нейтронні хвилі на межі активної зони. Результати мають практичні застосування в шумовій діагностиці активної зони реактора. Внешний волновой источник возбуждает вынужденные нейтронные волны в активной зоне нейтронного поля. Эти волны преобразовываются в собственные нейтронные волны на границе активной зоны. Результаты имеют практические приложения в шумовой диагностике активной зоны реактора. The authors are thankful to V.A. Rudakov for discussions on the problems of the vibration diagnostics of WWER-1000, and L.N. Davydov and A.G. Sotnikov for help in editing the English translation of the article. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Kinetic theory The thermal neutron waves excitation in muldiplied media bounded by absorber Збудження хвиль теплових нейтронів в розмножуючому середовищі, обмеженому поглиначем Возбуждение волн тепловых нейтронов в размножающей среде, ограниченной поглотителем Article published earlier |
| spellingShingle | The thermal neutron waves excitation in muldiplied media bounded by absorber Vodyanitskii, A.A. Slyusarenko, Yu.V. Kinetic theory |
| title | The thermal neutron waves excitation in muldiplied media bounded by absorber |
| title_alt | Збудження хвиль теплових нейтронів в розмножуючому середовищі, обмеженому поглиначем Возбуждение волн тепловых нейтронов в размножающей среде, ограниченной поглотителем |
| title_full | The thermal neutron waves excitation in muldiplied media bounded by absorber |
| title_fullStr | The thermal neutron waves excitation in muldiplied media bounded by absorber |
| title_full_unstemmed | The thermal neutron waves excitation in muldiplied media bounded by absorber |
| title_short | The thermal neutron waves excitation in muldiplied media bounded by absorber |
| title_sort | thermal neutron waves excitation in muldiplied media bounded by absorber |
| topic | Kinetic theory |
| topic_facet | Kinetic theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111049 |
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