Non-stationary model of the solar core
The main parameters of the standard model of the Sun are considered, according to which the Sun is considered as a spherically symmetric and quasistatic star, and thermonuclear reactions of the pp-cycle mainly occur inside it and the energy is uniformly released at a rate of 2·10⁻⁴J/(kg·s). Based on...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2020
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/194537 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Non-stationary model of the solar core / S.F. Skoromnaya, V.I. Tkachenko // Problems of atomic science and tecnology. — 2020. — № 3. — С. 101-104. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-194537 |
|---|---|
| record_format |
dspace |
| spelling |
Skoromnaya, S.F. Tkachenko, V.I. 2023-11-27T12:22:52Z 2023-11-27T12:22:52Z 2020 Non-stationary model of the solar core / S.F. Skoromnaya, V.I. Tkachenko // Problems of atomic science and tecnology. — 2020. — № 3. — С. 101-104. — Бібліогр.: 19 назв. — англ. 1562-6016 PACS: 52.35.-g, 52.35.Fp, 11.80.-m; 13.15.+g https://nasplib.isofts.kiev.ua/handle/123456789/194537 The main parameters of the standard model of the Sun are considered, according to which the Sun is considered as a spherically symmetric and quasistatic star, and thermonuclear reactions of the pp-cycle mainly occur inside it and the energy is uniformly released at a rate of 2·10⁻⁴J/(kg·s). Based on observational data it was concluded that the Sun is not a star with uniformly ongoing processes, it is characterized by oscillatory processes and flashes. It is proposed to consider the non-stationary model of the Sun, in which it is required to take into account the existence of electromagnetic waves in the plasma of the solar core and, as a result, the existence of wave collapses (WC). A three-dimensional axially symmetric WC is considered and an estimate of the velocity of removal of the plasma of the solar core during the development of a three-dimensional axially symmetric WC is given. For the considered WC the existence of three directions of flows of elementary plasma volumes relative to the observer is demonstrated: one direction is due to the moving the elementary plasma volume from the observer and the other - to him. The third direction of moving of the elementary plasma volumes is perpendicular to the direction of observation and their velocity relative to the observer is zero. It is concluded that the existence of such motions of elementary plasma volumes during the development of WC can leave a definite imprint on the parameters of the synthesis products in them. Розглянуто основні параметри стандартної моделі Сонця, згідно з якою Сонце розглядається як сферичносиметрична і квазістатична зірка, а всередині неї протікають переважно термоядерні реакції рр-циклу, і відбувається рівномірне виділення енергії зі швидкістю E = 2·10⁻⁴Дж/(кг·с). Виходячи iз спостережних даних, зроблено висновок про те, що Сонце не є зіркою з рівномірно поточними процесами, йому притаманні коливальні процеси і спалахи. Запропоновано розглядати нестаціонарну модель Сонця, в якій необхідно враховувати існування електромагнітних хвиль в плазмі ядра Сонця і, як наслідок, існування хвильових колапсів (ХК). Розглянуто тривимірний аксіально-симетричний ХК, і дана оцінка швидкості виносу плазми ядра Сонця при розвитку тривимірного аксіально-симетричного ХК. Для розглянутого ХК показано існування трьох напрямків потоків елементарних обсягів плазми відносно спостерігача: один напрямок обумовлено рухом елементарного обсягу плазми від спостерігача, інший - до нього. Третій напрям руху елементарних обсягів плазми здійснюється перпендикулярно напрямку спостереження, і швидкість їх рухів відносно спостерігача дорівнює нулю. Зроблено висновок про те, що існування таких рухів елементарних обсягів плазми при розвитку ХК може накладати певний відбиток на параметри продуктів синтезу в них. Рассмотрены основные параметры стандартной модели Солнца, согласно которой Солнце рассматривается как сферически-симметричная и квазистатическая звезда, а внутри нее в основном протекают термоядерные реакции рр-цикла, и происходит равномерное выделение энергии со скоростью E = 2·10⁻⁴Дж/(кг·с). Исходя из наблюдательных данных, сделан вывод о том, что Солнце не является звездой с равномерно текущими процессами, ему присущи колебательные процессы и вспышки. Предложено рассматривать нестационарную модель Солнца, в которой необходимо учитывать существование электромагнитных волн в плазме ядра Солнца и, как следствие, существование волновых коллапсов (ВК). Рассмотрен трехмерный аксиально-симметричный ВК, и дана оценка скорости выноса плазмы ядра Солнца при развитии трехмерного аксиально-симметричного ВК. Для рассмотренного ВК показано существование трех направлений потоков элементарных объемов плазмы относительно наблюдателя: одно направление обусловлено движением элементарного объема плазмы от наблюдателя, другое - к нему. Третье направление движения элементарных объемов плазмы осуществляется перпендикулярно направлению наблюдения, и скорость их движения относительно наблюдателя равна нулю. Сделан вывод о том, что существование таких движений элементарных объемов плазмы при развитии ВК может накладывать определенный отпечаток на параметры продуктов синтеза в них. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Beam dynamics Non-stationary model of the solar core Нестаціонарна модель ядра сонця Нестационарная модель ядра солнца Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Non-stationary model of the solar core |
| spellingShingle |
Non-stationary model of the solar core Skoromnaya, S.F. Tkachenko, V.I. Beam dynamics |
| title_short |
Non-stationary model of the solar core |
| title_full |
Non-stationary model of the solar core |
| title_fullStr |
Non-stationary model of the solar core |
| title_full_unstemmed |
Non-stationary model of the solar core |
| title_sort |
non-stationary model of the solar core |
| author |
Skoromnaya, S.F. Tkachenko, V.I. |
| author_facet |
Skoromnaya, S.F. Tkachenko, V.I. |
| topic |
Beam dynamics |
| topic_facet |
Beam dynamics |
| publishDate |
2020 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Нестаціонарна модель ядра сонця Нестационарная модель ядра солнца |
| description |
The main parameters of the standard model of the Sun are considered, according to which the Sun is considered as a spherically symmetric and quasistatic star, and thermonuclear reactions of the pp-cycle mainly occur inside it and the energy is uniformly released at a rate of 2·10⁻⁴J/(kg·s). Based on observational data it was concluded that the Sun is not a star with uniformly ongoing processes, it is characterized by oscillatory processes and flashes. It is proposed to consider the non-stationary model of the Sun, in which it is required to take into account the existence of electromagnetic waves in the plasma of the solar core and, as a result, the existence of wave collapses (WC). A three-dimensional axially symmetric WC is considered and an estimate of the velocity of removal of the plasma of the solar core during the development of a three-dimensional axially symmetric WC is given. For the considered WC the existence of three directions of flows of elementary plasma volumes relative to the observer is demonstrated: one direction is due to the moving the elementary plasma volume from the observer and the other - to him. The third direction of moving of the elementary plasma volumes is perpendicular to the direction of observation and their velocity relative to the observer is zero. It is concluded that the existence of such motions of elementary plasma volumes during the development of WC can leave a definite imprint on the parameters of the synthesis products in them.
Розглянуто основні параметри стандартної моделі Сонця, згідно з якою Сонце розглядається як сферичносиметрична і квазістатична зірка, а всередині неї протікають переважно термоядерні реакції рр-циклу, і відбувається рівномірне виділення енергії зі швидкістю E = 2·10⁻⁴Дж/(кг·с). Виходячи iз спостережних даних, зроблено висновок про те, що Сонце не є зіркою з рівномірно поточними процесами, йому притаманні коливальні процеси і спалахи. Запропоновано розглядати нестаціонарну модель Сонця, в якій необхідно враховувати існування електромагнітних хвиль в плазмі ядра Сонця і, як наслідок, існування хвильових колапсів (ХК). Розглянуто тривимірний аксіально-симетричний ХК, і дана оцінка швидкості виносу плазми ядра Сонця при розвитку тривимірного аксіально-симетричного ХК. Для розглянутого ХК показано існування трьох напрямків потоків елементарних обсягів плазми відносно спостерігача: один напрямок обумовлено рухом елементарного обсягу плазми від спостерігача, інший - до нього. Третій напрям руху елементарних обсягів плазми здійснюється перпендикулярно напрямку спостереження, і швидкість їх рухів відносно спостерігача дорівнює нулю. Зроблено висновок про те, що існування таких рухів елементарних обсягів плазми при розвитку ХК може накладати певний відбиток на параметри продуктів синтезу в них.
Рассмотрены основные параметры стандартной модели Солнца, согласно которой Солнце рассматривается как сферически-симметричная и квазистатическая звезда, а внутри нее в основном протекают термоядерные реакции рр-цикла, и происходит равномерное выделение энергии со скоростью E = 2·10⁻⁴Дж/(кг·с). Исходя из наблюдательных данных, сделан вывод о том, что Солнце не является звездой с равномерно текущими процессами, ему присущи колебательные процессы и вспышки. Предложено рассматривать нестационарную модель Солнца, в которой необходимо учитывать существование электромагнитных волн в плазме ядра Солнца и, как следствие, существование волновых коллапсов (ВК). Рассмотрен трехмерный аксиально-симметричный ВК, и дана оценка скорости выноса плазмы ядра Солнца при развитии трехмерного аксиально-симметричного ВК. Для рассмотренного ВК показано существование трех направлений потоков элементарных объемов плазмы относительно наблюдателя: одно направление обусловлено движением элементарного объема плазмы от наблюдателя, другое - к нему. Третье направление движения элементарных объемов плазмы осуществляется перпендикулярно направлению наблюдения, и скорость их движения относительно наблюдателя равна нулю. Сделан вывод о том, что существование таких движений элементарных объемов плазмы при развитии ВК может накладывать определенный отпечаток на параметры продуктов синтеза в них.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/194537 |
| citation_txt |
Non-stationary model of the solar core / S.F. Skoromnaya, V.I. Tkachenko // Problems of atomic science and tecnology. — 2020. — № 3. — С. 101-104. — Бібліогр.: 19 назв. — англ. |
| work_keys_str_mv |
AT skoromnayasf nonstationarymodelofthesolarcore AT tkachenkovi nonstationarymodelofthesolarcore AT skoromnayasf nestacíonarnamodelʹâdrasoncâ AT tkachenkovi nestacíonarnamodelʹâdrasoncâ AT skoromnayasf nestacionarnaâmodelʹâdrasolnca AT tkachenkovi nestacionarnaâmodelʹâdrasolnca |
| first_indexed |
2025-11-25T10:58:46Z |
| last_indexed |
2025-11-25T10:58:46Z |
| _version_ |
1850510644477952000 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2020. №3(127) 101
NON-STATIONARY MODEL OF THE SOLAR CORE
S.F. Skoromnaya1, V.I. Tkachenko1,2
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine;
2V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: tkachenko@kipt.kharkov.ua
The main parameters of the standard model of the Sun are considered, according to which the Sun is considered as
a spherically symmetric and quasistatic star, and thermonuclear reactions of the pp-cycle mainly occur inside it and the
energy is uniformly released at a rate of 42 10 J/(kg·s). Based on observational data it was concluded that the Sun is
not a star with uniformly ongoing processes, it is characterized by oscillatory processes and flashes. It is proposed to
consider the non-stationary model of the Sun, in which it is required to take into account the existence of electromag-
netic waves in the plasma of the solar core and, as a result, the existence of wave collapses (WC). A three-dimensional
axially symmetric WC is considered and an estimate of the velocity of removal of the plasma of the solar core during
the development of a three-dimensional axially symmetric WC is given. For the considered WC the existence of three
directions of flows of elementary plasma volumes relative to the observer is demonstrated: one direction is due to the
moving the elementary plasma volume from the observer and the other to him. The third direction of moving of the
elementary plasma volumes is perpendicular to the direction of observation and their velocity relative to the observer is
zero. It is concluded that the existence of such motions of elementary plasma volumes during the development of WC
can leave a definite imprint on the parameters of the synthesis products in them.
PACS: 52.35.-g, 52.35.Fp, 11.80.-m; 13.15.+g
STANDARD SOLAR MODEL
The Standard Solar Model (SSM) is the representa-
tion of the Sun in the form of a gas sphere with various
degrees of hydrogen ionization depending on the radius.
Hydrogen is in a fully ionized state, i.e. is a fully ion-
ized gas in the inner region of the Sun. This model de-
scribes a spherically symmetric and quasistatic star, the
internal structure of which is described by several dif-
ferential equations of hydrostatic equilibrium obtained
from the basic laws of physics. SSM is used to test the
theory of star evolution [1, 2].
SSM assumes that the Sun consists of 3 zones [2]:
1. The inner zone has a size of 6
1 7 10R R m,
which is a small part of the star, but just in this zone
thermonuclear reactions of the pp-cycle mainly proceed
and energy is released: 42 10E J/(kg·s). Its tempera-
ture 7~1.5 10T K, pressure and matter density
8~ 10P MPa and 5~ 1.5...1.6 10 kg/m3. Energy
from this zone as a result of weak convection is trans-
ferred to zone 2.
2. The static radiation zone is located in the interval
of 8
1 2 4.9 10R R R m. In this zone due to X-ray
radiation the temperature rapidly decreases from 107 K
to 106 K. The mean free-path length of X-ray radiation
1/l is small and diffusion from the center to the
surface takes 106…107 years, i.e. radiation is transmitted
very slowly to zone 3.
3. The external convective zone is in the interval
8
2 7 10R R m and contains about ~ 2% of the total
mass of the Sun. The temperature in this zone varies
from 6 310 6 10T K and the density is of the order
of 3~ 1.5 10 kg/m3. The outside part of this zone is the
photosphere. Above this zone is the chromosphere with
9~ 3 10хр kg/m3 and then comes the corona with a
density of 1210к
kg/m3.
SSM well describes the experimental results based
on data obtained from sensing the Sun. The strongest
evidence of its validity would be direct observation of
solar neutrinos. However, the disagreement in the re-
sults arising from the SSM of the estimated number of
neutrinos and experimental data led to the discovery of
the phenomenon of neutrino oscillations confirmed in a
number of experiments [3].
The above data are based on the Sun quasistaticity.
It means that the thermonuclear reactions of synthesis of
pp-cycle, 44 2 2 ep He e [4] as basic on the Sun
[2], uniformly release energy in the inner zone of the
Sun at a rate of 42 10 J/kg per second. As a result of
the reaction four protons are combined into a helium
nucleus with the emission of two positrons and two
electron neutrinos. Thus, hydrogen is "converted" into
helium in the Sun.
In fact, the uniformity of energy release is doubtful,
since quasistaticity in the inner zone of the Sun is dis-
turbed by the waves propagating in the plasma. The
existence of waves inside the Sun, for example, is indi-
cated by the fact of occurrence of the Sun radius fluc-
tuations [5]. Besides, a faster rotation of the solar core
relative to the outer layers has recently been observed.
This rotation generates g-modes inside the Sun which
are the oscillations caused by gravity [6].
The availability of the above-mentioned oscillations
can excite electromagnetic waves in the plasma, which
in turn will initiate electromagnetic wave collapses
(WC) [7 - 14] and, as a result, the appearance of accel-
erated flows of solar matter in the solar core. The accel-
erated flows of solar matter can occur as a result of ex-
plosive removal of particles from the cavity formed in
the plasma due to the effect of ponderomotive forces
and represent a density hole.
Recognition with fact of existence of accelerated
flows of solar matter in the solar core caused by wave
collapses can change the conclusions based on SSM and
give a new approach to the study of solar neutrinos.
In this paper we consider the conditions for originat-
ing the wave collapses in the inner zone of the Sun.
ISSN 1562-6016. ВАНТ. 2020. №3(127) 102
WAVE COLLAPCE
Wave collapse (WC) – explosive in time increase of
energy density in a given volume. WC is one of the fun-
damental processes in the theory of wave propagation in
dispersive media. In some cases WC is a result of solv-
ing the nonlinear Schrödinger equation (NSE).
This equation for a complex field has the form:
2 0,t (1)
where index t denotes a temporal partial derivative;
Laplacian.
NSE is an analogue of the dispersion nonlinear
equation in partial derivatives and one of the fundamen-
tal equations of nonlinear physics, which has attracted
the attention of researchers for more than half a century
[15-17].
There are many examples of WC implementation.
These include the collapse of Langmuir waves [6, 7],
self-focusing of the electromagnetic field in optical fibers
[9, 10] and weakly nonlinear hydrodynamic disturbances
on a static cosmic background [11], the behavior of deep-
water waves and killer waves in an ocean [12, 13].
However, the above examples do not provide a
complete list of WC implementations. The only thing
that unites these processes is that they are all described
by the nonlinear Schrödinger equation.
These studies have shown that in the two- and three-
dimensional NSE models the wave collapse, as a phe-
nomenon of the formation of a singularity over a finite
period of time, play the same fundamental role as the
solitons that are realized in the one-dimensional model
and are the wave formations of an equilibrium shape
conserving in space.
In the case of multidimensional WC (multidimen-
sional NSE model) the equilibrium is disturbed, the me-
dium becomes unsteady and nonlinear processes deter-
mine WC dynamics. Study of the conditions of occur-
rence of the temporal dynamics of “explosive” increas-
ing the amplitude of WC field is important because
knowledge of WC main features makes it possible to
evaluate the efficiency of a collapse as a non-linear
mechanism of transformation of wave energy into other
types of energy.
It should be noted that many studies have been de-
voted to WC development in various environments.
For example, strict NSE solutions, explosive solu-
tions and their asymptotic behavior near critical sizes
are discussed in detail in the review [17].
In [18, 19] the conditions of WC occurrence are dis-
cussed in detail and criteria for selecting the type of self-
similar solutions for the numerical study of the NSE are
given. As a rule, numerical calculations use various multi-
dimensional difference algorithms. In some cases they
violate conservatism and conservation laws; in others they
take much time for calculation and require a large RAM.
A method for selecting NSE self-similar variables to
describe the development of multidimensional WC was
proposed first in [14]. It is demonstrated that the re-
quired self-similar variables along with the law of con-
servation of the number of quanta and the Hamiltonian
ensure the conservation of the mean square radius of the
wave train. As a result of selection of such self-similar
variables transition to a non-inertial reference frame is
realized, where WC do not occur and the dynamics of
the wave train is determined by the equation for the ax-
ial coordinate.
The proposed self-similar variables in the two- and
three-dimensional cases (axially symmetric and spheri-
cally symmetric WC) allow us to write the mean square
of the radius of the wave train in a universal form: for
both the two-dimensional and three-dimensional
(spherically symmetric) cases, where the mean square of
the radius of the wave train is constant and is equally
expressed through the Hamiltonian of the system. It is
shown that in physical variables (radius, time) the rate
of development of a spherically symmetric WC is
higher than two-dimensional.
An explosive increase of the field amplitude for an
axially symmetric three-dimensional WC occurs along
the axis of the system. In this case, there are two possi-
ble ways of WC developing.
The first way is observed when the characteristic
size of the wave train along the axis z exceeds the radial
(a sphere stretched along the axis z). Then the dynamics
of the development of the axial WC will continue until
the axial half-width of the wave train coincides with its
radius. In this case the WC transfers into the stage of a
spherically symmetric WC and the rate of collapse de-
velopment increases from 2 2 1 2
0( )t t to 2 2 3 4
0( )t t .
The second way can be developed if the characteris-
tic size of the wave train along the axis z is less than the
radial (a sphere compressed along the axis z). In this
case the wave train with initially shape of a compressed
sphere will be transformed into a “presolar disk” [14].
We consider the conditions of occurrence and give
estimates of the characteristic parameters of the three-
dimensional axially symmetric WC in the plasma of the
Sun inner zone.
THREE-DIMENTIONAL AXIALLY
SYMMETRIC WC
First of all, during WC development we will be in-
terested in the parameters characterizing the processes
of plasma removal from the forming cavity. For an out-
side observer the elements of the plasma volume pushed
out by the ponderomotive forces from the cavity will be
in different reference frames. The first two reference
frames are such that one moves from the observer, the
other towards. The third reference frame is such that
the direction of motion of plasma volume elements is
transverse to the observer's gaze direction in it.
For such reference frames the consideration of a
three-dimensional axially symmetric WC is most pref-
erable, since it is occurs more frequently in space [14]
and, moreover, has different characteristic length scales
in the radial and axial directions.
It is known from [14] that Jacobi functions cn z,k ,
defined as zeros, of the boundary of the wave train
along the axis z 1,2 10z h , will move towards the
origin of coordinates according to the law
2 2 2
1,2 1 0 0z t h t t t , i.e. axial WC will develop,
where t is the time of the collapse development, 0t is the
time of its formation. Moreover, by virtue of choice of
ISSN 1562-6016. ВАНТ. 2020. №3(127) 103
self-similar substitution [14] the radial size of the WC
remains unchanged. Thus, the electric field will increase
in time at the origin of coordinates. As consequence,
non-uniformity of the field along the coordinate z will
lead to pushing out of the plasma by ponderomotive
forces and formation of a cavity.
To determine the order of magnitude of the velocity
of the elementary plasma volume movement we esti-
mate the characteristic plasma parameters of the inner
zone of the Sun.
They are as follows [1, 2]: plasma density 3210e in n m-3,
temperature 31.3·10eT eV, electron thermal velocity
53. ·105TiV m/s, ion thermal velocity 71. ·105TeV m/s,
ionic Langmuir frequency 152.1 10pi s-1, ion sound
velocity 54.6 10SС m/s, wavelength of the ion sound
91.4 10 m, Debye radius 112.67 10D
m.
Since the axial pushing out of the elementary plasma
volume is faster than the radial one [14] let us estimate
its moving velocity in this direction from the velocity of
the wave train boundary moving. At that, account must
be taken of the fact that the velocity of plasma removal
1,2V from the cavity is directed in the opposite direction
to the velocity of the wave train boundary movement,
i.e. 1,2 1,2V dz dt . Hence, we have:
1
2 21 2
1,2 0
0
.
h
V t t t
t
(2)
If we assume in (2) that 1h , 1
0 pit , then at
0t t the plasma moving velocity will increase explo-
sively and can reach large, but not limiting light values
1
2 2
6
1
0 0
2.9 10 1t tV
t t
m/s, ( 8
1 3 10V c m/s),
since when the velocity of the elementary plasma vol-
ume is close to the light, the conditions of applicability
of our consideration are violated.
The collapse stage will complete when the amplitude
of plasma oscillations reaches such a value that the elec-
tron motion paths begin to intersect [8]. At that, the
electron velocity will become higher than the thermal
one; they will leave the cavity and take away the energy
of Langmuir oscillations. After this, the cavity will “be
collapsed” by the shock wave at the velocity of sound,
the plasma will return to its original state and will again
be ready to form a wave collapse.
As you can see, there are flows of elementary
plasma volumes moving from the cavity in the solar
core, characterized by a sufficiently high velocity 1V ,
and the flows of elementary plasma volumes moving in
the opposite direction at a sound speed, caused by the
"collapse" of the cavity.
Let us evaluate the consequences of WC development
by the example of antineutrinos that are generated in the
plasma core of the Sun in reference frames moving with
velocity 1V in the direction of the axis x from the ob-
server on the Earth and in the opposite direction. Let us
represent neutrinos as wave functions with energies :
1,2 sinv kx t , (3)
where 1 ,kV pi , k frequency and
wave number of the ion-sound wave. The superposition
of waves (3) at a neutrino velocity of the order c gives
the path difference
1 1
1
1
2 ; .S
S
S S
C c V VxL kV t kC x
C c C cV
If, for example, consider 810 s-1, 1V 100 m/s,
then the path difference will be of the order of
386.7 10 m. This value corresponds in order of magni-
tude to the vacuum oscillation length 3110 10 m [4] in
the solar core.
Thus, the development of a three-dimensional axi-
ally symmetric WC is possible in the inner zone of the
Sun. Under such conditions the plasma is removed from
the forming WC cavity. At that, for the selected direc-
tion of observation the motion of elementary plasma
volumes will be oriented in such a way that one volume
moves from the observer and the other toward him. The
velocity of the elementary plasma volume moving is
zero for the direction of motion transverse to the direc-
tion of observation. The existence of such motions of
elementary plasma volumes can leave a definite imprint
on the parameters of the products of thermonuclear fu-
sion in them.
CONCLUSIONS
A non-stationary model of the solar core is discussed
in this paper. The main parameters of the standard model
of the Sun, according to which the Sun is considered as a
spherically symmetric and quasistatic star, are analyzed.
The thermonuclear reactions of the pp-cycle proceed in-
side the Sun and the energy is uniformly released at a rate
of 42 10E J/(kgs). Based on observational data it was
concluded that the Sun is not a star with uniformly pro-
ceeding processes. It is characterized by oscillational per-
turbations of the internal volume and flares on the sur-
face. Based on this, it was proposed to consider the non-
stationary model of the Sun in which it is required to take
into account the existence of electromagnetic waves in
the plasma of the solar core and, as a result, the existence
of WC. A three-dimensional axially symmetric WC is
analyzed in the paper and the velocity of the cavity
plasma removal during the development of the three-
dimensional axially symmetric WC is estimated. The
availability of three directions of flows removing the
elementary plasma volumes from the cavity relative to
the observer's gaze is demonstrated for the considered
type of WC. One direction of the flow is realized when
the elementary volume of the plasma moves away from
the observer and the other toward him. The third direc-
tion of the flow is transverse to the observer's gaze direc-
tion. At that, the velocity of the removal of elementary
plasma volumes is zero. It is concluded that the existence
of such motions of elementary plasma volumes can leave
a definite imprint on the parameters of the synthesis
products in them. By the example of antineutrinos gener-
ated as a result of the development of WC in the plasma
core of the Sun and located in reference frames moving in
opposite directions from the observer, it is demonstrated
that the path difference between them is of the order of
the oscillation length in the solar core.
ISSN 1562-6016. ВАНТ. 2020. №3(127) 104
REFERENCES
1. Fizicheskaya e`ncziklopediya: [t. 5] / Gl. red. A. M.
Prokhorov, redkol.: D.M. Alekseev i dr. M. T. 5:
Stroboskopicheskie pribory` Yarkost`. Bol`shaya
ros. e`nczikl. 1998, 760 s. (in Russian).
2. http://nuclphys.sinp.msu.ru/astro/astro12.htm
3. G.V. Klapdor-Klajngrotkhaus, K. Czyuber. As-
trofizika e l̀ementarny`kh chasticz. M.: «Uspekhi
fizicheskikh nauk», 2000, 496 s. (in Russian).
4. D.V. Naumov. Vvedenie v fiziku nejtrino // Pis`ma v
E`ChAYa. 2011, t. 8, № 7(170), s. 1192-1231.
5. Alexander Kosovichev and Jean-Pierre Rozelot.
Cyclic Changes of the Sun's Seismic Radius // The
Astrophysical Journal. 2018, v. 861, № 2, р. 1-5.
6. E. Fossat, P. Boumier, T. Corbard, et al. Asymptotic g
modes: Evidence for a rapid rotation of the solar core
// Astronomy and Astrophysics. 2017, v. 604, A40.
7. E. Zakharov. Collapse and Self-focusing of Lang-
muir Waves // Handbook of Plasma Physics / Eds.
M.N. Rosenbluth and R.Z. Sagdeev, v. 2 / Eds.
A.A. Galeev and R.N. Sudan. 1984, р. 81-121.
8. V.E. Zakharov. Collapse of Langmuir waves //
JETP. 1972, v. 35, p. 908-914.
9. A. Hasegawa. Solitons in Optical Communications //
Clarendon Press, Oxford, NY, 1995.
10. B.A. Malomed. Variational methods in nonlinear
fiber optics and related fields // Progress in Optics.
2002, v. 43, p. 69-191.
11. R.E. Kates, D.J. Kaup // Astronomy and Astrophys-
ics. 1988, v. 206, № 1, p. 9-17.
12. T.B. Benjamin and J.E. Feir. The disintegration of
wavetrains in deep water, Part 1 // J. Fluid Mech.
1967, v. 27, p. 417-430.
13. M. Onorato, A.R. Osborne, M. Serio, and S. Ber-
tone. Freak waves in random oceanic sea states //
Phys. Rev. Lett. 2001, v. 86, p. 5831-5834.
14. S.F. Skoromnaya, V.I. Tkachenko. Self-Similar So-
lutions of Multi-Dimensional Nonlinear Schrödinger
Equations // Problems of Atomic Science and Tech-
nology. Series “Plasma Electronics and New Meth-
ods of Acceleration”. 2008, № 4, p. 237-241.
15. J. Ablowitz and H. Segur. Solitons and the Inverse
Scattering Transform, SIAM (Philadelphia, 1981).
M.J. Ablowitz and P.A. Clarkson. Solitons, Nonlin-
ear Evolution Equations and Inverse Scattering //
Cambridge University Press (Cambridge, 1991).
MR0642018 (84a:35251), MR1149378 (93g:35108)
16. M.J. Ablowitz, B. Prinari and A.D. Trubatch. Dis-
crete and Continuous Nonlinear SchrЁodinger Sys-
tems // Cambridge University Press, Cambridge,
2004. MR2040621(2005c:37117).
17. C. Sulem, P.-L. Sulem. The Nonlinear Schrödinger
Equation. Self-Focusing and Wave Collapse.
Springer // Applied Mathematical Sciences. 1999,
v. 139, 322 р.
18. V.E. Zakharov, E.A. Kuzneczov. Kvaziklassiche-
skaya teoriya trekhmernogo volnovogo kollapsa //
ZhTE`F. 1986, t. 91, v. 4(10), p. 1310-1324 (in Russian).
19. E.A. Kuzneczov. Integral`ny`e kriterii volnovy`kh
kollapsov. Izv. Vuzov // Radiofizika. 2003, t. XLVI,
№ 5, 6, p. 342-359 (in Russian).
Article received 10.03.2020
НЕСТАЦИОНАРНАЯ МОДЕЛЬ ЯДРА СОЛНЦА
С.Ф. Скоромная, В.И. Ткаченко
Рассмотрены основные параметры стандартной модели Солнца, согласно которой Солнце рассматривается как сфе-
рически-симметричная и квазистатическая звезда, а внутри нее в основном протекают термоядерные реакции рр-цикла,
и происходит равномерное выделение энергии со скоростью 42 10E Дж/(кг·с). Исходя из наблюдательных данных,
сделан вывод о том, что Солнце не является звездой с равномерно текущими процессами, ему присущи колебательные
процессы и вспышки. Предложено рассматривать нестационарную модель Солнца, в которой необходимо учитывать
существование электромагнитных волн в плазме ядра Солнца и, как следствие, существование волновых коллапсов
(ВК). Рассмотрен трехмерный аксиально-симметричный ВК, и дана оценка скорости выноса плазмы ядра Солнца при
развитии трехмерного аксиально-симметричного ВК. Для рассмотренного ВК показано существование трех направле-
ний потоков элементарных объемов плазмы относительно наблюдателя: одно направление обусловлено движением эле-
ментарного объема плазмы от наблюдателя, другое к нему. Третье направление движения элементарных объемов
плазмы осуществляется перпендикулярно направлению наблюдения, и скорость их движения относительно наблюдате-
ля равна нулю. Сделан вывод о том, что существование таких движений элементарных объемов плазмы при развитии
ВК может накладывать определенный отпечаток на параметры продуктов синтеза в них.
НЕСТАЦІОНАРНА МОДЕЛЬ ЯДРА СОНЦЯ
С.Ф. Скоромна, В.І. Ткаченко
Розглянуто основні параметри стандартної моделі Сонця, згідно з якою Сонце розглядається як сферично-
симетрична і квазістатична зірка, а всередині неї протікають переважно термоядерні реакції рр-циклу, і відбувається
рівномірне виділення енергії зі швидкістю 42 10E Дж/(кг·с). Виходячи iз спостережних даних, зроблено висновок
про те, що Сонце не є зіркою з рівномірно поточними процесами, йому притаманні коливальні процеси і спалахи. За-
пропоновано розглядати нестаціонарну модель Сонця, в якій необхідно враховувати існування електромагнітних хвиль в
плазмі ядра Сонця і, як наслідок, існування хвильових колапсів (ХК). Розглянуто тривимірний аксіально-симетричний
ХК, і дана оцінка швидкості виносу плазми ядра Сонця при розвитку тривимірного аксіально-симетричного ХК. Для
розглянутого ХК показано існування трьох напрямків потоків елементарних обсягів плазми відносно спостерігача: один
напрямок обумовлено рухом елементарного обсягу плазми від спостерігача, інший до нього. Третій напрям руху еле-
ментарних обсягів плазми здійснюється перпендикулярно напрямку спостереження, і швидкість їх рухів відносно спо-
стерігача дорівнює нулю. Зроблено висновок про те, що існування таких рухів елементарних обсягів плазми при розвит-
ку ХК може накладати певний відбиток на параметри продуктів синтезу в них.
|