Stationary electrical polarizing field and charge in plasma of the solar atmosphere
The dependence of the proton velocity and concentration, electric field, electric charge and electron density on a distance from the centre of the Sun is derived within the framework of hydrodynamical two-zoned model.
Gespeichert in:
| Veröffentlicht in: | Кинематика и физика небесных тел |
|---|---|
| Datum: | 2005 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Головна астрономічна обсерваторія НАН України
2005
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/79635 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Stationary electrical polarizing field and charge in plasma of the solar atmosphere / V.M. Efimenko, V.V. Tokiy, N.V. Tokiy // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 169-171. — Бібліогр.: 4 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859999052702154752 |
|---|---|
| author | Efimenko, V.M. Tokiy, V.V. Tokiy, N.V. |
| author_facet | Efimenko, V.M. Tokiy, V.V. Tokiy, N.V. |
| citation_txt | Stationary electrical polarizing field and charge in plasma of the solar atmosphere / V.M. Efimenko, V.V. Tokiy, N.V. Tokiy // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 169-171. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Кинематика и физика небесных тел |
| description | The dependence of the proton velocity and concentration, electric field, electric charge and electron density on a distance from the centre of the Sun is derived within the framework of hydrodynamical two-zoned model.
|
| first_indexed | 2025-12-07T16:35:37Z |
| format | Article |
| fulltext |
STATIONARY ELECTRICAL POLARIZING FIELD
AND CHARGE IN PLASMA OF THE SOLAR ATMOSPHERE
V. M. Efimenko1, V. V. Tokiy2, N. V. Tokiy2
1Astronomical Observatory, National Taras Shevchenko University of Kyiv
3 Observatorna Str., 04053 Kyiv, Ukraine
e-mail: efim@observ.univ.kiev.ua
2A. A. Galkin Donetsk Physical and Technical Institute, NAS of Ukraine
72 R. Luxemburg Str., 83114 Donetsk, Ukraine
The dependence of the proton velocity and concentration, electric field, electric charge and electron
density on a distance from the centre of the Sun is derived within the framework of hydrodynamical
two-zoned model.
INTRODUCTION
A system of four equations including the continuity, ion motion, local electron equilibrium equations and
equation of quasineutrality of stationary spherically symmetric plasma flow under the homogeneous temperature
of components is presented in [1]. The dependence of the proton velocity and concentration, electric field,
electric charge and electron density on a distance from the centre of the Sun is derived in [1–3 ] for isothermal
solar corona. The present work is based on these same simplifying assumptions, excepting the assumption
of isothermal solar corona. The purpose of the present work is the consideration of a stationary expansion of
plasma in vacuum within the framework of hydrodynamical two-temperature-zoned model (T is the temperature
of high-temperature zone and T ′ is the temperature of low-temperature zone).
BASIC EQUATIONS
We denote the proton density of high-temperature zone by n(r), and its radial velocity by V (r). We shall suppose
the conditions at boundary of high-temperature zone at r = a to be given n0. If as well as [1] the electron
mass me is neglected, the equation of motion for electrons for a stationary task turns to a condition of local
equilibrium:
0 = −k
n
d(Tn)
dr
− eE. (1)
The equation of motion for protons for a stationary task takes the form:
mV
dV
dr
= −k
n
d(Tn)
dr
+ eE − m
MSG
r2
, (2)
where G is the gravitational constant, MS denotes the mass of the Sun, E is radial component of an electric
field, V is radial component of ions velocity, m denotes the mass of a proton, −e is the charge of an electron.
The condition of charge neutrality of plasma is designated
ne = np = n. (3)
The continuity equation is:
1
r2
d
dr
(nV r2) = 0. (4)
The Eqs. (1), (2), (3), and (4) form a system of equations for stationary expansion of plasma with homoge-
neous distribution of electrons and protons temperatures allowing one to find spherical symmetric distributions
electrons ne(r), protons np(r), velocity of protons V (r), and electrical field E(r) under given boundary condi-
tions.
In low-temperature zone, in Eqs. (1)–(4) we substitute T , n, E, V , ne, np for T ′, n′, E′, V ′, n′
e, n′
p.
Density particles, n′
0, at r = a in low-temperature zone was defined from the condition of the continuity of
the flow at aspiration of width of a transitive zone between high and low temperatures to zero.
c© V. M. Efimenko, V. V. Tokiy, N. V. Tokiy, 2004
169
SOLUTION FOR HIGH-TEMPERATURE ZONE
Eqs. (1) – (4) are so simple that they may be integrated analytically to give V (r) implicitly from(
V
Vc
)2
− ln
(
V
Vc
)2
= 4 ln
r
rc
+
4rc
r
+ Const. (5)
Five types of solution are presented in [4], depending on the value of Const. The solar wind solution (type
IV) corresponds to the value Const =–3, obtained by putting V = Vc and r = rc in Eq. (5).
An approximate expression in a solar corona with locations near rc can be derived for V , n, E, and q.
At distances r < rc the dependence of the proton velocity on a distance from the centre of the Sun is:
V = Vc
[
1 −
√
2
√
ln
r
rc
+
rc
r
− 1
]
. (6)
The dependence of the proton concentration on a distance from the centre of the Sun is:
n =
n0a
2
r2
[
1 −√
2
√
ln a
rc
+ rc
a − 1
]
[
1 −√
2
√
ln r
rc
+ rc
r − 1
] . (7)
The dependence of the electric field on a distance from the centre of the Sun is:
E(r) =
2kT
er
⎡
⎢⎣1 +
rc
r − 1
2
√
2
√
ln r
rc
+ rc
r − 1
[
1 −√
2
√
ln r
rc
+ rc
r − 1
]
⎤
⎥⎦ . (8)
Using Maxwell’s equation for integral on the closed spherical surface S of radius r, we derive a charge of
high-temperature zone of solar corona near the Sun at distances r < rc
q(r) =
8πε0kTr
e
⎡
⎢⎣1 −
rc
r − 1
2
√
2
√
ln r
rc
+ rc
r − 1
[
1 −√
2
√
ln r
rc
+ rc
r − 1
]
⎤
⎥⎦ , (9)
where the designations are entered:
Vc =
√
2kT
m
, (10)
rc =
GMSm
4kT
. (11)
At distances r > rc the dependence of the proton velocity is:
V = Vc
[
1 +
√
2
√
ln
r
rc
+
rc
r
− 1
]
. (12)
The dependence of the proton concentration is:
n =
n0a
2
r2
[
1 +
√
2
√
ln a
rc
+ rc
a − 1
]
[
1 +
√
2
√
ln r
rc
+ rc
r − 1
] . (13)
The dependence of the electric field is:
E(r) =
2kT
er
⎡
⎢⎣1 −
rc
r − 1
2
√
2
√
ln r
rc
+ rc
r − 1
[
1 +
√
2
√
ln r
rc
+ rc
r − 1
]
⎤
⎥⎦ . (14)
Using (14), we derive a charge of high-temperature zone of solar corona near the Sun at distances r > rc:
q(r) =
8πε0kTr
e
⎡
⎢⎣1 +
rc
r − 1
2
√
2
√
ln r
rc
+ rc
r − 1
[
1 +
√
2
√
ln r
rc
+ rc
r − 1
]
⎤
⎥⎦ . (15)
170
SOLUTION FOR LOW-TEMPERATURE ZONE
Eqs. (1) – (4) may be integrated analytically as well.
By analogy for V ′, n′, E′, and q′ an approximate expression in low-temperature of a solar corona with
locations at distances r � r′c may be derived.
At distances r � r′c where V ′ � V ′
c we shall obtain an approximate expression for distribution of protons
velocity in stationary spherical symmetric flow in low-temperature zone of the solar corona
V ′(r) = V ′
c
(
r′c
r
)2
exp
(
3
2
− 2r′c
r
)
, (16)
where V ′
c and r′c we defined from (10) and (11) substitution T for T ′.
Density particles in low-temperature zone were defined from a condition of continuity of the flow at aspiration
of width of a transitive zone between high and low temperatures to zero.
n′(r) = n′
0 exp
(
2r′c
r
− 2r′c
a
)
, (17)
where
n′
0 = n0
Vc
V ′
c
(
a
r′c
)2 [
1 −√
2
√
ln
a
rc
+
rc
a
− 1
]
exp
(
2r′c
a
− 3
2
)
. (18)
We derive an approximate expression for an electrical field in low-temperature zone of solar corona near
the Sun:
E =
GMSm
2er2
. (19)
Using Maxwell’s equation for the integral on the closed spherical surface S of radius r, we derive a charge
of low-temperature zone of the solar corona near the Sun:
q′(r) =
2πε0GMSm
e
. (20)
CONCLUSION. ELECTRICAL AND GRAVITATIONAL FORCES NEAR THE SUN
Using (7) and (8) let us carry out a comparison of forces of the electron and proton gas pressure, electrical and
gravitational forces acting on protons and electrons near layer of the solar corona at r = rc. Electrical force
acting on electron is equal to the force of the electron gas pressure:
FEe = −FPe =
−12 (kT )2
GMSm
. (21)
The forces of the proton gas pressure, electrical and gravitational forces acting on protons near the solar
corona layer at r = rc are equal to:
FEp = −4
3
FPp =
−16 (kT )2
GMSm
. (22)
Estimations show that force of the proton gas pressure and electrostatic force acting on proton are the main
accelerating forces. The ratings of values of electrical fields and charge of the Sun show that they are very small.
However, near the surface of the Sun the electrical force acting on a proton is comparable with gravitational
one. The sum of proton gas pressure force and electrical force acting on a proton is 1.5 times stronger than
force of the gravitational attraction of a proton to the Sun. The electrical force acting on an electron surpasses
gravitational force many times over. All this can play a decisive role in finding a mechanism of solar activity.
[1] Efimenko V. M., Tokiy V. V., Tokiy N. V. The electric field and charge in the Solar corona // Kinematics and
Physics of Celestial Bodies.–2004.–20, N 1.–P. 27–34.
[2] Geiss J., Hirt P., Leutwyler H. On acceleration and motion of ions in corona and solar wind // Solar Phys.–1970.–
12.–P. 458–483.
[3] Parker E. N. Dynamics of the interplanetary gas and magnetic fields // Astrophys. J.–1958.–128.–P. 664–676.
[4] Priest E. R. Solar Magneto-hydrodynamics / Ed. B. M. McCormac.–Dordrecht: D. Reidel, 1982.–21.–470 p.
171
|
| id | nasplib_isofts_kiev_ua-123456789-79635 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0233-7665 |
| language | English |
| last_indexed | 2025-12-07T16:35:37Z |
| publishDate | 2005 |
| publisher | Головна астрономічна обсерваторія НАН України |
| record_format | dspace |
| spelling | Efimenko, V.M. Tokiy, V.V. Tokiy, N.V. 2015-04-03T16:46:35Z 2015-04-03T16:46:35Z 2005 Stationary electrical polarizing field and charge in plasma of the solar atmosphere / V.M. Efimenko, V.V. Tokiy, N.V. Tokiy // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 169-171. — Бібліогр.: 4 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79635 The dependence of the proton velocity and concentration, electric field, electric charge and electron density on a distance from the centre of the Sun is derived within the framework of hydrodynamical two-zoned model. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS2: Physics of Solar Atmosphere Stationary electrical polarizing field and charge in plasma of the solar atmosphere Article published earlier |
| spellingShingle | Stationary electrical polarizing field and charge in plasma of the solar atmosphere Efimenko, V.M. Tokiy, V.V. Tokiy, N.V. MS2: Physics of Solar Atmosphere |
| title | Stationary electrical polarizing field and charge in plasma of the solar atmosphere |
| title_full | Stationary electrical polarizing field and charge in plasma of the solar atmosphere |
| title_fullStr | Stationary electrical polarizing field and charge in plasma of the solar atmosphere |
| title_full_unstemmed | Stationary electrical polarizing field and charge in plasma of the solar atmosphere |
| title_short | Stationary electrical polarizing field and charge in plasma of the solar atmosphere |
| title_sort | stationary electrical polarizing field and charge in plasma of the solar atmosphere |
| topic | MS2: Physics of Solar Atmosphere |
| topic_facet | MS2: Physics of Solar Atmosphere |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79635 |
| work_keys_str_mv | AT efimenkovm stationaryelectricalpolarizingfieldandchargeinplasmaofthesolaratmosphere AT tokiyvv stationaryelectricalpolarizingfieldandchargeinplasmaofthesolaratmosphere AT tokiynv stationaryelectricalpolarizingfieldandchargeinplasmaofthesolaratmosphere |