Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system
This paper considers the formation process of the protosolar hydrogen-helium cloud in chronological order. From the list of hypotheses about the solar system formation, the electromagnetic hypothesis of Alfvén was selected since it is based on the plasma state of the protosolar hydrogen-helium cloud...
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Andrieieva, O.L. Tkachenko, V.I. Tkachenko, G.A. 2023-12-08T14:45:43Z 2023-12-08T14:45:43Z 2023 Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system / O.L. Andrieieva, V.I. Tkachenko, G.A. Tkachenko // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 25-31. — Бібліогр.: 31 назв. — англ. 1562-6016 PACS: 94.05.Pt, 96.60.Fs DOI: https://doi.org/10.46813/2023-143-025 https://nasplib.isofts.kiev.ua/handle/123456789/195962 This paper considers the formation process of the protosolar hydrogen-helium cloud in chronological order. From the list of hypotheses about the solar system formation, the electromagnetic hypothesis of Alfvén was selected since it is based on the plasma state of the protosolar hydrogen-helium cloud. It presumably describes a supernova explosion and its contribution to the solar system formation. The spatial-temporal dynamics of changes in the density and velocity of ions in a cylindrical two-component hydrogen-helium plasma is described. It is shown that the motion velocities of two-type particles represent Benard cells oscillating with different periods. The proposed electromagnetic wave model was used to calculate the distribution of hydrogen and helium ions in the solar system at the beginning of its formation and after a supernova explosion. У хронологічній послідовності розглянуто процес формування протосонячної воднево-гелієвої хмари. Електромагнітна гіпотеза Альфвена була обрана зі списку гіпотез про формування Сонячної системи, оскільки в її основі лежить плазмовий стан воднево-гелієвої хмари. Описаний, ймовірно, вибух наднової та оцінений його внесок у формування Сонячної системи. Описано просторово-часову динаміку зміни і густини та швидкості іонів у циліндричній двокомпонентній воднево-гелієвій плазмі. Показано, що швидкості руху частинок сорту α є осцилюючими з різними періодами осередку Бенара. На основі запропонованої електромагнітної хвильової моделі проведено розрахунок розподілу іонів водню та гелію в Сонячній системі на початку її формування та після вибуху наднової. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology Basic plasma physics Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system Електромагнітна хвильова модель опису розподілу водню і гелію при формуванні сонячної системи Article published earlier |
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| title |
Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system |
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Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system Andrieieva, O.L. Tkachenko, V.I. Tkachenko, G.A. Basic plasma physics |
| title_short |
Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system |
| title_full |
Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system |
| title_fullStr |
Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system |
| title_full_unstemmed |
Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system |
| title_sort |
electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system |
| author |
Andrieieva, O.L. Tkachenko, V.I. Tkachenko, G.A. |
| author_facet |
Andrieieva, O.L. Tkachenko, V.I. Tkachenko, G.A. |
| topic |
Basic plasma physics |
| topic_facet |
Basic plasma physics |
| publishDate |
2023 |
| language |
English |
| container_title |
Problems of Atomic Science and Technology |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Електромагнітна хвильова модель опису розподілу водню і гелію при формуванні сонячної системи |
| description |
This paper considers the formation process of the protosolar hydrogen-helium cloud in chronological order. From the list of hypotheses about the solar system formation, the electromagnetic hypothesis of Alfvén was selected since it is based on the plasma state of the protosolar hydrogen-helium cloud. It presumably describes a supernova explosion and its contribution to the solar system formation. The spatial-temporal dynamics of changes in the density and velocity of ions in a cylindrical two-component hydrogen-helium plasma is described. It is shown that the motion velocities of two-type particles represent Benard cells oscillating with different periods. The proposed electromagnetic wave model was used to calculate the distribution of hydrogen and helium ions in the solar system at the beginning of its formation and after a supernova explosion.
У хронологічній послідовності розглянуто процес формування протосонячної воднево-гелієвої хмари. Електромагнітна гіпотеза Альфвена була обрана зі списку гіпотез про формування Сонячної системи, оскільки в її основі лежить плазмовий стан воднево-гелієвої хмари. Описаний, ймовірно, вибух наднової та оцінений його внесок у формування Сонячної системи. Описано просторово-часову динаміку зміни і густини та швидкості іонів у циліндричній двокомпонентній воднево-гелієвій плазмі. Показано, що швидкості руху частинок сорту α є осцилюючими з різними періодами осередку Бенара. На основі запропонованої електромагнітної хвильової моделі проведено розрахунок розподілу іонів водню та гелію в Сонячній системі на початку її формування та після вибуху наднової.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195962 |
| citation_txt |
Electromagnetic wave model of hydrogen and helium distribution at the formation of the solar system / O.L. Andrieieva, V.I. Tkachenko, G.A. Tkachenko // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 25-31. — Бібліогр.: 31 назв. — англ. |
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2025-11-26T19:38:02Z |
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2025-11-26T19:38:02Z |
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| fulltext |
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143).
Series: Plasma Physics (29), p. 25-31. 25
https://doi.org/10.46813/2023-143-025
ELECTROMAGNETIC WAVE MODEL OF HYDROGEN AND HELIUM
DISTRIBUTION AT THE FORMATION OF THE SOLAR SYSTEM
O.L. Andrieieva1,2, V.I. Tkachenko1,2, G.A. Tkachenko1
1V.N. Karazin Kharkiv National University, Kharkiv, Ukraine;
2National Science Centre “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: tkachenko@kipt.kharkov.ua
This paper considers the formation process of the protosolar hydrogen-helium cloud in chronological order.
From the list of hypotheses about the solar system formation, the electromagnetic hypothesis of Alfvén was selected
since it is based on the plasma state of the protosolar hydrogen-helium cloud. It presumably describes a supernova
explosion and its contribution to the solar system formation. The spatial-temporal dynamics of changes in the
density and velocity of ions in a cylindrical two-component hydrogen-helium plasma is described. It is shown that
the motion velocities of two-type particles represent Benard cells oscillating with different periods. The proposed
electromagnetic wave model was used to calculate the distribution of hydrogen and helium ions in the solar system
at the beginning of its formation and after a supernova explosion.
PACS: 94.05.Pt, 96.60.Fs
INTRODUCTION
Many different models of the origin and
development of the solar system are known [1, 2]. But
none of them meets the characteristics of the generally
accepted theory due to insufficient correspondence with
observational data. It is a generally accepted fact that
the primary composition of stellar matter was formed
starting from the age of the Universe of 20 min, and
consisted of helium ‒ 4 (4Не), about 25...26 %,
deuterium about 1 %, traces of heavier elements to
boron, and the rest ‒ hydrogen about 74...75 % [3]. In
the further evolution of the Universe, its averaged
composition with respect to hydrogen and helium did
not change and corresponded to the ratio of 1 helium
atom to 11 hydrogen atoms [4]. The formation of
interstellar clouds began about 2.7 billion years ago [3].
As a result of gravitational compression one of these
clouds gave rise to the formation of the solar system,
which ended about 4.57 billion years ago [5] According
to [6] hereinafter we will call the cloud that gave rise to
the solar system the protosolar nebula. Before the
formation of the protosolar nebula, at the end of The
Epoch of Reionization (before the expiration of 2.7
billion years from the moment the Universe began [7]),
helium and hydrogen, apparently, were in the ionization
state. The hypothesis that the hydrogen-helium
protosolar nebula is in the ionization state, i. e. in the
form of plasma is known. One of the well-known
modern hypotheses of the origin of the solar system is
based on the plasma state of the hydrogen-helium cloud
of the solar system ‒ the electromagnetic hypothesis of
the Swedish astrophysicist H. Alfven (1908–1995) and
the English astrophysicist F. Hoyle (1915–2001).
According to this hypothesis, the original gas cloud,
from which both the Sun and the planets of the solar
system were formed consisted of ionized gas exposed to
the influence of electromagnetic fields [8]. At the same
time, the primary plasma was concentrated in certain
areas around the central body and recombined into small
solid granules. Then under the influence of the
gravitational force granules stuck together into so-called
embryos, and during further accretion, large cosmic
bodies were formed: planets, if the central body is the
Sun, and satellites, if they are planets [9]. In this paper
we will base on the electromagnetic hypothesis. All
estimates and reasoning will be since the protosolar
nebula was in the ionization state. Presumably, it is
known that at the initial stage of the solar system
formation, when it was an ionized hydrogen - helium
dust cloud, there was a supernova explosion, which the
researchers called Coatlicue [10]. The supernova had a
mass of about 30 solar masses and was located at a
distance of 5...10 pс [11, 12]. The fact of the existence
of a supernova and its characteristics were determined
from the presence of aluminum-26 in meteorites that
were ejected by a massive star [11]. Obviously, the
supernova underwent a thermonuclear explosion, since
after the explosion nothing remained in its place [1, 12].
The main factor of the supernova influence on nearby
objects in the solar system is, among other things,
thermonuclear gamma quanta with energies up to
24 MeV [13]. As a result of photodisintegration, such
gamma quanta can cause reactions of the nucleus decay
of a helium ion into a neutron and a 3-helium ion
4He(γ,n)3He or into a hydrogen ion and a tritium ion
4He(γ,p)3He [14, 15]. Summarizing all the above, we
can state with a certain degree of probability that the
protosolar hydrogen ‒ helium cloud (nebula) was in two
states separated in time. In the first of them, the
protosolar cloud was in the ionization state where
electromagnetic waves could exist [16], which could
lead to fluctuations of the mass fraction of hydrogen and
helium ions in space and time.
In the second state, thermonuclear gamma quanta
from a supernova explosion in a short time could violate
the conditions for the existence of electromagnetic
waves and increase the mass fraction of hydrogen due to
the decay of helium nuclei.
The purpose of this paper is to develop an
electromagnetic hypothesis of the solar system formation.
mailto:tkachenko@kipt.kharkov.ua
26 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
FAST AND SLOW ISWs IN A CYLINDRICAL
TWO-COMPONENT HYDROGEN-HELIUM
PLASMA
Let us consider low-frequency fluctuations of a
cylindrical plasma volume consisting of two ion types.
In cylindrical coordinates, we orient the cylinder axis
along the Oz axis. The height of the cylinder is h, and
the cylinder is in the range 0 z h. The radius of the
cylinder is R0. We will consider axially symmetric
fluctuations. Therefore, all solutions depend on the
variables r, z and do not depend on the azimuthal
angle. Under the conditions mentioned above, in a
two-component plasma there are independent
unattenuated small perturbations of the velocity and
density of plasma ions of each type, which are described
as fast and slow ISWs. In this case, similarly to what
was shown in [18] for a plasma consisting of two types
of particles, it is possible to separately describe the
motion of each of the plasma components in the quasi-
hydrodynamic approximation:
𝜕�⃗⃗� 𝛼
𝜕𝑡
=
𝑍𝛼𝑒
𝑚𝛼
�⃗� ,
𝜕𝑛𝛼
𝜕𝑡
+ 𝑑𝑖𝑣(𝑛𝛼𝜈 𝛼) = 0, (1)
where index = H, He refers to hydrogen H or helium
He, n n(𝑟 ,t) and 𝜈 𝛼 𝜈 𝛼(𝑟 ,t) ‒ are the hydrodynamic
density and velocity of 𝛼-type ions, �⃗� ‒ is the electric
field strength, e > 0 ‒ is the electron charge. Equations
(1) should be supplemented by the Poisson equation,
which establishes a relationship between the perturbed
values of the particle density and the electric field
strength:
𝑑𝑖𝑣(�⃗� ) = 4𝜋𝑒(∑ 𝑍𝛼𝛼 �̂�𝛼 − �̂�𝑒), (2)
where �̂�𝛼= n-n0, �̂�𝑒 = ne - n0eare the deviations of
particles density of -type ions and electrons from
equilibrium values. In (11), it is assumed that the
condition of plasma quasineutrality is satisfied:
Zn0 = n0e, wheren0e ‒ is the equilibrium plasma
electron density. Since electrons are characterized by
high thermal velocities, we will assume that at low-
frequency fluctuations they are in equilibrium and their
density is described by the Boltzmann formula:
𝑛𝑒(𝑟, 𝑡) = 𝑛0𝑒 𝑒𝑥𝑝 (−∑
𝑍𝛼𝑒𝜑𝛼(𝑟 ,𝑡)
𝛩𝛼
𝛼 ), (3)
where 𝜑𝛼(𝑟 , 𝑡) ‒ is the potential of the electric field of
𝛼-type particle, 𝐸⃗⃗ ⃗ = −𝛻 ∑ 𝜑𝛼 .𝛼
In (3) ZH = 1, ZHe = 2, and the temperature is
given in the form H=Te, He=TeZHeHe
2
n0e/((He
2+H
2)n0H) so that the equations (1)-(3)
describe the spectra of a fast ISW, in the absence of a
slow one, and vice versa.
We will assume that all fluctuations are small in
amplitude. According to (10) the relations are as
follows:
𝜈 𝛼 =
𝑍𝛼𝑒
𝑚𝛼
�⃗� ∑
1
𝜔
𝑓𝛼(𝑟, 𝑧) 𝑐𝑜𝑠(𝜔𝑡),𝛼 (4)
�̂�𝛼 = −𝑛0𝛼
𝑍𝛼𝑒
𝑚𝛼
�⃗� ∑
1
𝜔2 𝑓𝛼(𝑟, 𝑧) 𝑠𝑖𝑛(𝜔𝑡)𝛼 .
From (3) for small perturbations of the electron
density we have:
�̂�𝛼 = 𝑛0𝑒 ∑
𝑍𝛼𝑒𝜑𝛼(𝑟 ,𝑡)
𝛩𝛼
𝛼 . (5)
Using (4), (5), we obtain the Poisson equation (2),
written in terms of the perturbed potentials of the
electric field created by α-type ions:
∑
𝜕2
𝜕𝑡2 Δ𝜑𝛼 +𝛼 4𝜋𝑒(∑ 𝑍𝛼
𝑍𝛼𝑛0𝛼𝑒
𝑚𝛼
𝛼 ∑ Δ𝜑𝛼𝛼 −
𝑛0𝛼 ∑
𝑍𝛼𝑒
𝛩𝛼
𝛼
𝜕2
𝜕𝑡2 𝜑𝛼) = 0. (6)
We will consider the potential perturbations as an
axially symmetric function and define it in the form
(𝑟 ,t) =f(r,z)sin(t), where f(r,z) =CJ0(qrr)sin(qzz),
J0(x) ‒ the zero-order Bessel function of the first kind,
C − are constants, qr and qz ‒ are the radial and
vertical wavenumbers of waves propagating in 𝛼-type
particles. The choice of such a dependence of the
electric potential on the coordinates is like the
description of the spatial distribution of the velocity
potential of a viscous incompressible fluid in a
cylindrical Benard cell [19]. Assuming in (4) the factors
for sin(Ht) and sin(Het), equal to zero, we obtain the
spectra of fast H and slow He ISWs in the long-
wavelength limit:
𝜔𝐻 = 𝑞𝐻𝑟𝐷𝑒√𝛺𝐻
2 + 𝛺𝐻𝑒
2 , 𝜔𝐻𝑒 = 𝑞𝐻𝑒𝑟𝐷𝛺𝐻𝑒 , (7)
where 𝑞𝛼 = √𝑞𝑟𝛼
2 + 𝑞𝑧𝛼
2 ‒ are the wavenumbers of the
ISW of -type particles. From equations (4),
considering the continuity equation (1), the perturbed
densities �̑�𝛼 and the velocity potentials 𝜓𝛼of -type
ions, where 𝜈 𝛼 = −�⃗� 𝜓𝛼, can be represented as:
𝑛𝛼 = −𝐴𝛼𝐽0(𝑞𝑟𝛼𝑟) 𝑠𝑖𝑛( 𝑞𝑧𝛼𝑧) 𝑠𝑖𝑛(𝜔𝛼𝑡), (8)
𝜓𝛼 = −𝐵𝛼𝐽0(𝑞𝑟𝛼𝑟) 𝑠𝑖𝑛( 𝑞𝑧𝛼𝑧) 𝑐𝑜𝑠(𝜔𝛼𝑡),
where 𝐴𝛼𝜔𝛼 = 𝑛0𝛼𝑞𝛼
2𝐵𝛼 .
To preserve the number of particles in the volume of
a two-component plasma, we assume that the perturbed
radial velocities of ions are equal to zero on the lateral
and vertical boundaries of the cylinder:
𝜈𝑟𝛼(𝑟 , 𝑡)|𝑧=0,𝑧=ℎ,𝑟=𝑅0
= 0. (9)
The radial and vertical velocities are determined from
the velocity potential (17) and have the form:
𝜈𝑧𝛼(𝑟 , 𝑡) =
𝜕
𝜕𝑧
𝜓𝛼(𝑟 , 𝑡) = (10)
= −𝐵𝛼𝑞𝑧𝛼𝐽0(𝑞𝑟𝛼𝑟) 𝑐𝑜𝑠(𝑞𝑧𝛼𝑧) 𝑐𝑜𝑠(𝜔𝛼𝑡),
𝜈𝑟𝛼(𝑟 , 𝑡) =
𝜕
𝜕𝑟
𝜓𝛼(𝑟 , 𝑡) =
= 𝐵𝛼𝑞𝑧𝛼𝐽1(𝑞𝑟𝛼𝑟) 𝑠𝑖𝑛(𝑞𝑧𝛼𝑧) 𝑠𝑖𝑛(𝜔𝛼𝑡).
From (18) and (19) it follows that the radial and
vertical wavenumbers should have the values:
𝑞𝑟𝛼 =
𝜎1,𝑛𝛼
𝑅0
; 𝑞𝑧𝛼 =
𝑚𝛼𝑛
ℎ
, (11)
where 1,n− n-th zero of the Bessel function of the first
kind of the first order, J1 (1,n) = 0 [20, 21],
n = 1, 2, 3…; m = 1, 2, 3…, ‒ integers, which for
different 𝛼can either coincide or take on different
values. Thus, based on (9)-(11), fluctuations in the
density and velocity of plasma-type ions are
determined by the equations:
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 27
𝑛𝛼 = 𝑛0𝛼 − 𝐴𝛼𝐽0(𝑞𝑟𝛼𝑟) 𝑠𝑖𝑛(𝑞𝑧𝛼𝑧) 𝑠𝑖𝑛(𝜔𝛼𝑡), (12)
𝜈𝑟𝛼 = 𝐵𝛼𝑞𝑧𝛼𝐽1(𝑞𝑟𝛼𝑟) 𝑠𝑖𝑛(𝑞𝑧𝛼𝑧) 𝑐𝑜𝑠(𝜔𝛼𝑡), (13)
𝜈𝑧𝛼 = −𝐵𝛼𝑞𝑧𝛼𝐽0(𝑞𝑟𝛼𝑟) 𝑐𝑜𝑠(𝑞𝑧𝛼𝑧) 𝑐𝑜𝑠(𝜔𝛼𝑡).
SPATIAL-TEMPORAL DYNAMICS
OF CHANGES IN ION DENSITY
IN AN CYLINDRICAL TWO-COMPONENT
HYDROGEN-HELIUM PLASMA
Let us analyze the dependence of the ion density
distribution in space on time. As follows from (12),
fluctuations in the density of different types of ions
occur at different frequencies and with different
amplitudes of deviation from the equilibrium
background. For a description of fast and slow ISWs
close to real conditions in a two-component cylindrical
plasma of a cloud of the solar system protomatter, we
will proceed from the condition that the radius of the
cylinder significantly exceeds its height, i. e. R0>>h.
When comparing the obtained theoretical results with
experimental data on the distribution of the mass
fraction of hydrogen and helium in the solar system
[17], it can be seen that the radial modes n ‒ should be
bigger than 1, and the vertical modes m ‒ should be
equal to 1. The analysis of the dependences on the
coordinates and time of the projections of the velocities
of ions of different types (13) has its own specifics, and
it is difficult to display it on a graph. Therefore, to
simplify this analysis consider the graphs of the
dependence of the Stokes lines, on
= BJ0(qrr)sin(z/h) the spatial coordinates. In this
case, the projections of the vector outgoing from the
Stokes line and tangent to it on the r and z axes
determine the corresponding projections of the velocity,
considering the sign of the velocity potential. To
analyze the Stokes lines, we introduce the following
simplifications: we assume that the wave numbers qr,
qz are the same for-type ions. On this basis, in units
of 𝛼the distribution of Stokes lines for the velocity of -
type ions in the coordinate intervals 0 r R0, 0 z h
can be reduced to the same form = J0(qrr)sin(qzz). For
this case, the Stokes lines are shown in Fig. 1.
Fig. 1. Stokes lines = J0(qrr)sin(qzz) in relative units
for the case qr = 1,4/R0 13.3/R0; qz=/h
Fig. 1. shows that the ions in each of the vertical
stripes make closed movements along the Stokes lines.
In light colors, some move along closed trajectories in
one direction, in dark ones ‒ in the opposite direction.
The direction of movement of ions changes in time
proportionally to cos(t). In general, the motion
velocities of -type ions are Benard cells oscillating
with different periods of the time.
PROCESSES ACCOMPANYING THE
PHOTODISINTEGRATION OF HELIUM
IONS BY HIGH-ENERGY
THERMONUCLEAR GAMMA QUANTA
Let us briefly characterize the conditions and
process of photodisintegration of a helium ion by a
high-energy thermonuclear gamma quantum. This
process is accompanied by the decay of a helium
nucleus into a neutron and a helium-3 ion or into a
hydrogen ion and a tritium ion [13]. As follows from
[22], the reaction threshold E(,n) = 20.6 MeV is higher
than the E(,p) = 19.8 MeV threshold, but they are all less
than the gamma quantum energy E. In addition, the
ratio of the cross sections of reactions
= (,p)/(,n)=1.13 is bigger than unity, where
(,p) = 1.5 mb, (,n) =1.5 mb ‒ are the cross sections
for the reaction with the formation of a proton and a
neutron respectively.
For somewhat higher energies of gamma quanta of
(25±0.5) MeV the ratio of the reaction cross sections
also exceeds unity: =1.350.1 [23].
An important fact is the asymmetry of the cross
sections for the reactions 4He(,p)3H which consists in
the fact that in the center-of-mass system the maximum
of the reaction cross section is observed for nucleons
emitted almost perpendicular to the direction of gamma
quantum propagation. Such asymmetry has been
demonstrated experimentally for linearly polarized
gamma quanta with energy of 21...30 MeV with a
proton yield [24], and with energy of 27...30 MeV with
a neutron yield [25], as well as for linearly polarized
gamma quanta with energy of 40 MeV for protons and
neutrons [26, 27]. In papers [26, 27] it is shown that the
cross section of the reaction (,p) is maximum for polar
angles of the order of /2, measured from the
direction of gamma quanta propagation. However,
measurements were carried out for azimuthal angles
/2, measured from the polarization vector of
linearly polarized gamma quanta (Fig. 2), when the
reaction cross section for this angle is minimal [26, 27].
Fig. 2. Diagram of the direction of the proton emission
because of the reaction (,p)
28 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
In the experimental paper [24], the gamma quanta of
the collimated beam of bremsstrahlung of the
synchrotron were linearly polarized with the electric
field vector located in the plane of the axial section of
the Wilson chamber and perpendicular to the direction
of their propagation. The vectors of the emission
direction of fission reaction products (,p) and the
vector of the direction of gamma quanta propagation are
coplanar.
From the experimental results obtained in [24-27],
the following conclusions can be drawn:
‒ gamma quanta enter mainly into the reaction (,p);
‒ the maximum yield of reaction products (,p) is
observed for polar angles of the order of /2,
measured from the direction of propagation of gamma
quanta, and the minimum for azimuthal angles 0,
measured from the polarization vector of linearly
polarized gamma quanta;
‒ protons emit at a polar angle /2 relative to the
direction of propagation of gamma quanta, and at an
azimuthal angle /2, when the reaction cross section
is minimal. In this case, the traces of the expansion of
the reaction products in the polar angle for the proton
𝜃and the polar angle for tritium satisfy the conditions
= + 160and the transverse components of the
impulses are equal;
‒ for linearly polarized gamma quanta, the reaction
4He(,p)3H has a maximum cross section (maximum
number of decays) for polar proton emission angles
/2, and azimuthal angles 0 relative to the
polarization direction of the gamma quantum. Fig. 2
represents the implemented in [24] diagram of the
direction of the proton emission as a result of the
reaction (,p) showing the designation of certain angles.
In the figure 𝑝 𝑝, 𝑝 𝑦 ‒ are the impulses of the proton (red
arrow) and the gamma quantum, 𝐸⃗⃗ ⃗ ‒ is the vector of the
electric field of the linearly polarized gamma quantum
(blue arrow). As a result of the reaction (,p) a certain
amount of accelerated hydrogen ions and tritium ions
are additionally formed in the plasma volume due to the
decay of helium ions.
EVOLUTION OF PROTOSOLAR NEBULA
TAKING INTO ACCOUNT THE
SUPERNOVA EXPLOSION
Some of the accelerated hydrogen ions, due to the
path length comparable to the cylinder height h, will
remain in the plasma volume. The peripheral part of the
accelerated plasma ions and the accelerated tritium ions,
due to their large mean free path, will leave the plasma
volume. How exactly this separation of accelerated ions
can take place will be considered in the next section.
Thus, after a supernova explosion, the number of
hydrogen ions in the plasma will increase, while the
number of helium ions will decrease. In this state, the
hydrogen-helium ionized cloud will continue its
evolution, which consists in the expansion of the
Universe and, therefore, the general cooling of the
plasma. At temperatures below 4000 K, electrons and
atomic nuclei will recombine, and the plasma will turn
into a neutral gas [28]. In the future, gravitational
attraction will come into force, as a result of which
protoplanetary rings will be formed, and then the
planets of the solar system will appear [6]. However,
this stage of the formation of the solar system is not
considered in the paper. In further calculations, we will
proceed from the fact that the content of hydrogen and
helium in the Sun and the planets of the solar system
should correspond to the moment of the supernova
explosion, which caused the ISW attenuation and
coincided with the onset of plasma recombination. To
confirm the proposed theoretical model of the influence
of fast and slow ISWs on the solar system formation, we
will use the data on the abundance of hydrogen and
helium in the solar system at the present time [17, 29].
These data are comparable with the conclusions of the
electromagnetic wave model of the solar system
formation proposed in this paper. Let us start the
comparison with the fact that the mole fractions of
hydrogen and helium, calculated from the number of
their atoms in the Universe, are the values of the order
of 92 and 8 %, respectively [4, 29]. Hence, it follows
that the mass fraction of hydrogen and helium is
determined by values of the order of 74 and 26 % [4]. In
the calculations, it is necessary to consider that the mass
fractions of α-type ions are proportional to their
densities (20). As a result, to describe the spatial-
temporal dynamics of the mass fraction of 𝛼-type ions
in the solar system, we obtain the equations:
𝐶𝛼 = 𝐶0,𝛼 − 𝐷𝛼𝐽0 (
𝜎1,𝑛𝛼
𝑅0
𝑟) 𝑠𝑖𝑛 (
𝑛
ℎ
𝑧) 𝑠𝑖𝑛(𝜔𝛼𝑡), (14)
where CO,H 74, CO,He 26 − initial abundance of 𝛼-
type ions by mass in the solar system (%), D −
constants.
We use (14) to describe experimental data on the
mass content of hydrogen and helium in the planets of
the solar system. In Fig. 3. markers show the mass
fraction of hydrogen and helium atoms in the planets of
the solar system at the present time. The dashed lines
show the mass fractions of hydrogen and helium ions
obtained using (14) in the two-component hydrogen-
helium plasma of the solar system protomatter cloud at
the moment before the supernova explosion.
Fig. 3. Distribution of hydrogen and helium atoms in
the solar system. Markers ‒ experimental data [16, 17],
dashed lines are described by formulas (14)
Comparison of the content of hydrogen and helium
atoms at present with the data of formula (14) shows
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 29
that after the supernova explosion the mass fraction of
hydrogen ions jumped by 15 %, and the mass fraction of
helium ions decreased by 15 %.
SCENARIO OF CONFINEMENT
OF ACCELERATED HYDROGEN IONS
IN PLASMA
To substantiate the above process of redistribution of
the mass fraction of plasma ions, let us briefly discuss
the conditions under which the photodecomposition of
4He(,p)3H by thermonuclear gamma quanta with an
energy of 24 MeV can occur. From experimental studies
it follows that in the photodecomposition of 4He(,p)3H
by gamma quanta the cross section of the fission
reaction is anisotropic for emitted nucleons and is
maximum at a polar angle ϑ/290 with respect to the
direction of gamma quanta propagation [26, 27, 30].
The change in the mass fraction of helium ions by ‒
15 % and hydrogen by 15 % noted in the previous
section is possible provided that instead of four helium
ions, one hydrogen ion appears in the plasma volume,
the remaining 3 accelerated hydrogen ions and 4
accelerated tritium ions must leave its limits. It should
be noted that such a clear correspondence of the
transformation of helium ions into hydrogen ions is
possible under conditions when gamma quanta are
linearly polarized. And that's why. From [27] it follows
that the traces of hydrogen and tritium ions are coplanar
with the beam of gamma quanta, their emission angle
satisfies the condition, = + 160 and the
transverse components of the pulses are equal. From the
solution of equations (2)-(4) it follows that in the
laboratory system a proton emits at an angle close to
= /2 and a tritium ion at an angle =0.41 73.9,
which corresponds to the condition 160.This
direction of the proton trajectory corresponds to the
maximum value of the cross section for the reaction
4He(,p)3H [26, 27, 30] along the polar angle. According
to the azimuthal angle 02, measured from the
direction of the polarization vector of the gamma quanta
beam, the distribution of the reaction cross-section is
proportional to (1+cos(2)), where ‒ is a constant
determined by the degree of polarization of gamma
quanta, and the registered N scattering events in the
range of polar angles and [27]. From this it
follows that in the azimuthal angle the reaction cross
section is maximum at 0. Thus, it can be concluded
that with linear polarization of gamma quanta directed
along the cylinder axis, the decay reaction cross section
is maximum. In this case, the protons move parallelly to
the axis of the plasma cylinder, which ensures a 15 %
increase in the mass fraction of hydrogen uniform along
the radius of the cylinder. To calculate the possibility of
such ions separation, let us determine the velocities of
fission products. From the law of momentum
conservation, it follows that the velocities of ion
emission are approximately correlated as Vp3VT,
where Vp, VT ‒ are the velocities of hydrogen (proton)
and tritium ions respectively. It follows from the law of
energy conservation that the velocity of a proton is of
the order of Vp 3∙10-2 s, where c is the light speed, and
it propagates perpendicular to the direction of gamma
quantum propagation. Tritium ions move in the
direction opposite to the proton with a polar angle
= 0.41 73.9 relative to the direction of the gamma
quantum propagation.
With the above parameters the mean free path of a
hydrogen ion is lHVHH,H
-10.5∙1010 cm, where
H,H ‒ is the frequency of collisions of accelerated
hydrogen ions with hydrogen ions of plasma. It can be a
little less than h. In this case, some part of the
accelerated hydrogen ions will be retained in the plasma
volume. Tritium ions have a path length
lTVTT,H
-1 3∙1012 cm, where T,H ‒ is the frequency of
collisions of accelerated tritium ions with hydrogen ions
of plasma, and therefore, they will fly out of the plasma
cylinder without encountering obstacles. To implement
the above scenario of ion separation as result of
photodisintegration of helium, it is necessary that the
supernova be in a plane passing perpendicular to the
axis of the cylinder and dividing the cylinder in half. In
this case, the supernova should generate linearly
polarized gamma radiation, the polarization vector of
which is collinear with the cylinder axis. Such polarized
radiation can be generated by distributed cosmic matter
around a supernova [31]. The polarization of gamma
quanta provides the predominant production of
accelerated hydrogen ions, which move parallelly to the
axis of the plasma cylinder. In this case, the change in
the mass fractions of hydrogen and helium along the
radius of the plasma cylinder will be the same.
CONCLUSIONS
The paper briefly, in chronological order, considers
the process of the protosolar hydrogen-helium cloud
formation. From a large list of hypotheses of the solar
system formation, the electromagnetic hypothesis of the
solar system formation of Alfvén was selected, since it
is based on the plasma state of the protosolar hydrogen-
helium cloud. A supernova explosion is presumably
described and its contribution to the solar system
formation is estimated. This contribution consists in the
fact that before the supernova explosion, the protosolar
hydrogen-helium cloud was in the ionization state, and
electromagnetic waves propagated in it leading to
fluctuations in the mass fraction of hydrogen and
helium. Due to the supernova explosion, the
electromagnetic waves were attenuated, the
redistribution of the mass fraction of hydrogen and
helium occurred in the protosolar hydrogen-helium
cloud, which did not change after the action of
gravitational forces and corresponds to that at the
present time. Based on the assumptions made, an
electromagnetic wave model is proposed for describing
the density distribution of hydrogen and helium ions
during the solar system formation. To substantiate the
existence of electromagnetic waves in such plasma, an
estimate of its parameters was carried out. It is proposed
to consider fast and slow ion-sound waves in a
cylindrical two-component hydrogen-helium plasma as
electromagnetic waves. The spatial-temporal dynamics
of changes in the density and velocity of ions in a
cylindrical two-component hydrogen-helium
30 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
plasma is described. It is shown that the motion
velocities of 𝛼-type particles are Benard cells oscillating
with different periods. The proposed wave model is
used to calculate the distribution of hydrogen and
helium ions in the solar system at the beginning of its
formation and after a supernova explosion. It has been
suggested that the redistribution of the mass fractions of
hydrogen and helium was due to the photodisintegration
of helium ions by high-energy 24 MeV thermonuclear
gamma quanta from a supernova in reactions (,p). The
parameters and conditions of such reactions are
described. It is noted that for 15 % of the redistribution
of the mass fractions of hydrogen and helium, the
gamma quanta of the supernova should be linearly
polarized, with an electric field strength vector collinear
to the axis of the solar system. With such an
arrangement of the supernova and the solar system, a
part of the accelerated protons will remain in the plasma
volume due to their path length comparable to the
transverse size of the solar system, and the accelerated
tritium ions will leave the plasma region due to their
large path length. Comparison of the electromagnetic
wave model describing the distribution of hydrogen and
helium during the solar system formation with
observational data has a high quantitative agreement.
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Article received 15.12.2022
https://en.wikipedia.org/wiki/Chronology_of_the_universe
https://en.wikipedia.org/wiki/Chronology_of_the_universe
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 31
ЕЛЕКТРОМАГНІТНА ХВИЛЬОВА МОДЕЛЬ ОПИСУ РОЗПОДІЛУ ВОДНЮ І ГЕЛІЮ
ПРИ ФОРМУВАННІ СОНЯЧНОЇ СИСТЕМИ
О.Л. Андрєєва, В.І. Ткаченко, Г.А. Ткаченко
У хронологічній послідовності розглянуто процес формування протосонячної воднево-гелієвої хмари.
Електромагнітна гіпотеза Альфвена була обрана зі списку гіпотез про формування Сонячної системи,
оскільки в її основі лежить плазмовий стан воднево-гелієвої хмари. Описаний, ймовірно, вибух наднової та
оцінений його внесок у формування Сонячної системи. Описано просторово-часову динаміку зміни і
густини та швидкості іонів у циліндричній двокомпонентній воднево-гелієвій плазмі. Показано, що
швидкості руху частинок сорту 𝛼 є осцилюючими з різними періодами осередку Бенара. На основі
запропонованої електромагнітної хвильової моделі проведено розрахунок розподілу іонів водню та гелію в
Сонячній системі на початку її формування та після вибуху наднової.
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