Dynamics of nonquasineutral current filaments on different space - time scales
The earlier obtained results on the equilibrium and dynamics of the nonquasineutral current filaments for the size scale on the order of 1 µm and the time on the order of 1 ps are being applied to the objects in the atmosphere, the ionosphere and in the interstellar space. The main feature of the eq...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | Dynamics of nonquasineutral current filaments on different space - time scales / A.V. Gordeev, T.V. Losseva // Вопросы атомной науки и техники. — 2005. — № 1. — С. 75-77. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860056919594500096 |
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| author | Gordeev, A.V. Losseva, T.V. |
| author_facet | Gordeev, A.V. Losseva, T.V. |
| citation_txt | Dynamics of nonquasineutral current filaments on different space - time scales / A.V. Gordeev, T.V. Losseva // Вопросы атомной науки и техники. — 2005. — № 1. — С. 75-77. — Бібліогр.: 6 назв. — англ. |
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| description | The earlier obtained results on the equilibrium and dynamics of the nonquasineutral current filaments for the size scale on the order of 1 µm and the time on the order of 1 ps are being applied to the objects in the atmosphere, the ionosphere and in the interstellar space. The main feature of the equilibrium for the electron current filament consists in the presence of the strong electric field that appears as a result of the charge separation at the magnetic Debye radius rB. The numerical calculations of the ion dynamics due to the electric field of the filament are performed. It was obtained that the same equations can describe the equilibria and dynamics of the filaments from the micron size scale to the length of about millions km. Some arguments are presented in order to introduce a new approach for the lightning phenomena, where the magnetic field of the current in the lightning channel may play a decisive role.
Отримані раніше результати по рівновазі і динаміці неквазінейтральних токових філаментів для просторового масштабу порядку одного мікрона і тимчасового масштабу порядку однієї пікосекунди застосовуються до об'єктів в атмосфері, іоносфері й у міжзоряному просторі. Основною рисою нової рівноваги для електронного токового філамента є присутність електричного поля, що з'являється як результат поділу зарядів на магнітному дебаєвському радіусі r. Зроблено чисельні розрахунки іонної динаміки, зв'язаної з електричним полем філамента. Отримано, що ті ж самі рівняння можуть описувати рівновагу і динаміку філаментів від мікронного масштабу до довжини порядку мільйона км. Представлено аргументи, що вводять новий підхід для феномена блискавки, де магнітне поле в каналі блискавки може відігравати вирішальну роль.
Полученные ранее результаты по равновесию и динамике неквазинейтральных токовых филаментов для пространственного масштаба порядка одного микрона и временного масштаба порядка одной пикосекунды применяются к объектам в атмосфере, ионосфере и в межзвёздном пространстве. Основной чертой нового равновесия для электронного токового филамента является присутствие электрического поля, которое появляется как результат разделения зарядов на магнитном дебаевском радиусе rB. Произведены численные расчёты ионной динамики, связанной с электрическим полем филамента. Получено, что одни и те же уравнения могут описывать равновесие и динамику филаментов от микронного масштаба до длины порядка миллиона км. Представлены аргументы, которые вводят новый подход для феномена молнии, где магнитное поле в канале молнии может играть решающую роль.
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SPACE PLASMA
DYNAMICS OF NONQUASINEUTRAL CURRENT FILAMENTS ON
DIFFERENT SPACE – TIME SCALES
Alexander V. Gordeev,a Tatiana V. Losseva b
aRussian Research Center “Kurchatov Institute”, 1 Kurchatov Sq. , 123182, Moscow, Russia;
bInstitute of Geospheres Dynamics RAS, 38 Leninsky prospect, bldg.1, 119334, Moscow, Russia
The earlier obtained results on the equilibrium and dynamics of the nonquasineutral current filaments for the size
scale on the order of 1 µm and the time on the order of 1 ps are being applied to the objects in the atmosphere, the
ionosphere and in the interstellar space. The main feature of the equilibrium for the electron current filament consists
in the presence of the strong electric field that appears as a result of the charge separation at the magnetic Debye radius
rB. The numerical calculations of the ion dynamics due to the electric field of the filament are performed. It was
obtained that the same equations can describe the equilibria and dynamics of the filaments from the micron size scale
to the length of about millions km. Some arguments are presented in order to introduce a new approach for the lightning
phenomena, where the magnetic field of the current in the lightning channel may play a decisive role.
PACS: 52.58.Lq, 52.59.Px, 52.65.Kj, 52.80.Mg
INTRODUCTION
By the investigations of the laser pulses and the large
currents in high density plasmas the appearance of the
current filaments is a commonplace [1,2]. Therefore the
analysis of the structures of the current filaments and their
dynamics in high density plasmas is a very important
direction of the contemporary investigations [3,4]. In this
case the generation of the current filaments in the
magnetic field range 4πne me c2 << B2 << 4π ni mi c2
results in the charge separation at the magnetic Debye
scale rB ∼ | B |/(4πene) and the appearance of a very high
radial electric field that leads to the ion acceleration in the
radial direction. Such phenomena, which are connected
with the appearance of the current filament in the laser
and the Z-pinch plasmas displayed at a very small size
scale on the order of 1µm and a time scale on the order of
1 ps. However, it is obvious that these phenomena can
occur also in some another space-time scales, where there
exist the diverse plasma densities and the magnetic field’s
magnitudes. The appearance of the current filaments on
different space-time scales is connected with the
presence of the magnetic field everywhere in our
planetary system and in the cosmic space. One can show
that in definite ranges of the magnetic field and the
plasma density, the same equations can describe
equilibria and dynamics of the filaments with the size
scales from 10-4 cm to 106 km. As a very interesting
object for the possible application of the nonquasineutral
current filament presents the lightning phenomenon in the
Earth atmosphere, where already at the dart leader phase
the current magnitude of about 11 kA is registered in the
last measurements [5]. The simultaneous appearance of
the x-ray emission in the 30-250 keV range and also the
gamma-ray burst with the energies extending up to more
than 10 MeV in the dart leader stage of the lightning may
be explained within the framework of the present
approach. In addition, the return stroke phase of the
lightning may be interpreted as a reflected magnetic self-
insulation wave [6].
PHYSICAL MODEL AND MAIN EQUATIONS
By the describing of the nonquasineutral current filament
structure in the limit of the relativistic electron equations
the plasma dynamics can be considered in the following
range of the magnetic field
4πnemec2 << B2 << 4πnimic2 (1)
The l.h.s. of this inequality corresponds to the
nonquasineutrality of the electron filament at the Debye
magnetic radius rB∼ ∣B∣ /4πene and the r.h.s. of the
inequality (1) results in the appearance of the quasistatic
approximation for electrons as the small parameter ε = ω
pi rB/c << 1. Taking into account the quasistatic
approximation for electrons and introducing the
dimensionless quantities
Bθ , z=b1,2 4πme c2 ne ∞ , vez ,θ=v1,2c , ne=νne∞ ,
n i=n
ne∞
Z , I 1=4π ei1 , I 2=i24πm e c2
ne∞
,
one can obtain the system of the equations, which
describes the quasistatic electron filament structure in
accordance with the earlier constructed theory [3,4]
γ
∂v1
∂ ρ
=1 −v1
2 ρν i1−b1 v1 v 2νi2−g2 ,
−νv1=
1
ρ
∂
∂ ρ
ρb1
γ
∂v 2
∂ ρ
=−1 −v2
2 νi2−g 2 −v1v 2 ρν i1−b1 ,
νv 2=
∂ b2
∂ ρ
, g 2=b2−
γv2
ρ
,
ν=
γn2v1 v 2 b1 g 2γ2 v2
2 / ρ21 −v1
2 b1
21 −v2
2 g2
2
1/γ ρi1[ v1 v2 g21 −v1
2 b1 ]i2 [ v1 v2 b1−γv2 / ρ1 −v2
2 g 2 ]
,
v1 v2 >0.
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 75-77 75
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In such a setting of the problem the filament dynamics is
determined only by a relatively slow ion motion in the
electric field of the filament. In this case, block of the
nonstationary dimensionless equations, that describes the
dynamics of the current structure by the account of the
ion motion and the slow filament dynamics, takes the
form
∂n
∂ t
1
ρ
∂
∂ ρ
ρ nu =0,
∂u
∂ τ
u ∂ u
∂ ρ
=er−
1
n
∂ p
∂ ρ
−αu , (5)
∂ i1,2
∂ τ
n
ν
u1
ν
∂ er
∂ τ ∂ i1,2
∂ ρ
=0 ,
er=v1 b1−v 2 g2 , (6)
where the dimensionless radial electric field er is
introduced according to E r=er 4πne∞me c2 , and
α=ν in/ω pi takes into account the possible ion-atom
collisions with the ion-neutral frequency νin .
Here the dimensionless length ρ, time τ, and ion radial
velocity u and the dimensionless pressure p with the
isentropic exponent equal 2 are introduced
r= ρ me c2
4πe2 ne∞
,t=τ mi
4πe2 Zne∞
, v ir=uc Zme
mi
, pi=pne∞me c2 , p=λ n2
2
.
In addition, the initial conditions n(τ=0) =1 and u(τ
=0)=0, and the boundary conditions n(ρ=∞)=1 and u(ρ
=0)=u(ρ=∞)=0 will be used.
One should stress that because of the absence of the ion
trajectory’s bending the introduced values ne∞ and ni∞
correspond to the radius r∞ ∼ c/ωpi , which is in
accordance with r.h.s. of the inequality (1).
ESTIMATES FOR FILAMENTS WITH
DIFFERENT SPACE –TIME SCALES
Earlier on, the filament equilibrium was obtained, where
one bears in mind the typical parameters of the plasma
with electron density ne ∼ 1020 cm-3. And though all the
equations were presented in the dimensionless form, it
follows from the main inequality (1) that the magnetic
field is on the order of ∣B∣ ∼ 107- 3⋅107 G. However,
some another ranges of the parameters can also exist by
the fulfillment of the inequality (1). Of course, the
existence of such parameter “windows” does not prove
the real appearance of the equilibrium, however, this
gives a possibility to search such equilibria. The simplest
way to obtain the physical equivalent of the earlier
obtained nonquasineutral current filaments for other space
and time scales is the introduction of the three scale
factors in order to connect the previous values [3,4] with
subscript “0”and the values for new filaments with
subscript “1”. After some transformation according to
formulae
B0= λ1 B1 , n0=λ2 n1 , E0=λ3 E1 (7)
and by the account of the approximate relation λ1
2≈ λ2
according to (1) one can obtain that for the ionosphere
with B1≈ 1G and n1≈ 105 cm-3 the characteristic space and
time scales are r1≈ 102 m and t1≈ 3⋅ 10-5 s. The analogous
calculations for the interstellar space results in r1 ≈ 106 km
and t1≈ 1s.
It is obvious that the current filaments may be considered
also in a media with the only partial degree of the
ionization. As an example of the application of the
considered approach one can try to investigate the
lightning phenomena in the Earth atmosphere by the
initiation of the electric discharge between the charged
clouds and the Earth surface. According to the recent
concept of the lightning propagation in the Earth
atmosphere, this phenomenon is based on the streamer
breakdown at the very front of the lightning dart leader. In
such an approach the value of the electric field is a critical
point of the existing theory. In the present approach the
main effect that allows to resolve this problem consists in
the taking into account the magnetic field which arises
because of the current flow in the lightning channel.
According to the above presented theory by c/ωpe<< rB a
very strong radial electric field appear as a result of the
charge separation at the magnetic Debye radius rB. In
addition, when one assumes that the channel radius is
equal to r0 ≈ c/ωpe and one considers the l.h.s. of the
inequality (1) on the verge of the applicability
B2≈4πne me c2 , so from B = 2J/(r0c) one can obtain
that the current is equal to Jcr≈ JAe = 8.5 kA, which is
independent of the plasma density in the lightning
channel. This Alfven current value is very close to the
current in the dart leader phase of the lightning, which
was measured in the initial stage of the rocket-triggered
lightning [5]. In this case, the estimate of the Hall
potential in the filament UHall = B2/ 4π ene by the
account of the above-mentioned approximate relation
B2≈4πne me c2 gives the relativistic value UHall ≈
mec2/e = 0.511 MeV. This means that already for the
electron density greater than ne > 1012 cm-3 the radial
electric field in the current channel is greater than 1
MV/cm. In the filament with the strong radial electric
field Er and the azimuth magnetic field Bθ, the electron
drift velocity is on the order of the light velocity c. The
calculation of the maximum relativistic factor of the
drifting electrons at the axis within the framework of the
presented theory gives for the measured current value J ≈
11kA in the dart leader stage γ0 ∼ 2. This value is in a
reasonable accordance with the measured x-ray emission
in the 30 − 250 keV. By the domination of the collision
term in the second Eq. (5) the characteristic time of the
filament dynamics connected with the neutralization of
the electric potential is about t0 ∼ 0.1 µs what is in
accordance with the characteristic time of the x-ray bursts
in [5]. One can calculate the total energy of the filament
related to the unit length. This value is about 10-2 J/cm for
the above-mentioned dart leader phase of the lightning
and can increase up to 1 J/cm for the main phase with the
current about 100 kA. The dissipation of this energy
depends on the collision of the relativistic electron with
the neutral component and can be neglected by νen t0 <<
1, where νen − the electron-neutral collision frequency.
This condition may by fulfilled by t0 ∼ 0.1 µs. Here one
76
should stress that the total energy of such a filament is on
the order of the several hundred keV by the current J =
100 kA for the clouds remote from the Earth surface on
the several km, however, this energy constitutes only a
small fraction of the total energy of the charged cloud.
Also it is useful to mention the return stroke stage of the
lightning phenomena, when the inverse propagation of
the lightning occurs. It is known that by the investigation
of the lightning propagation one can consider the
processes in the current channel within the framework of
the telegraph equation. Now, in the introduced approach
the wave processes in the current channel correspond
rather to the propagation of the magnetic self-insulation
wave [6]. In the presented approach, the return stroke
phase of the lightning must be the reflected magnetic self-
insulation wave that propagates in the reversed direction
from the Earth surface as the surface potential is equal to
zero. Therefore, in the propagation of the reflected
magnetic self-insulation wave the potential difference of
the filament essentially diminished or disappeared, so the
filament energy is released in the filament plasma. This
energy deposition must result in the radiation from the
filament plasma and in the forming of the shock waves.
CONCLUSIONS
The conducted investigations reveal the existence of the
filament equilibria with the different space - time scales,
where the magnetic field plays a decisive role. In
addition, in this equilibrium the current flow is carried out
by the relativistic electrons. The full similarity of the
physical processes for the nonquasineutral current
filaments in the different space-time scales at the definite
ranges of the magnetic field and the plasma density is
obtained. Estimates within the framework of the current
filament model show that the account of the magnetic
field, connected with the current of the lightning channel,
results in the appearance of the strong electric field and
the relativistic electrons, which energy and life time
increase with the current and the radius of the channel,
respectively.
ACKNOWLEDGEMENTS
This paper is supported in part within the framework of
the system of the initiative projects in Russian Research
Center “Kurchatov Institute”.
We thank I.V. Nemtchinov for bringing Ref.5 to our
attention.
REFERENCES
1. A.Pukhov// Rep. Progr. Phys. (66). 2003 , p.47.
2. D.D.Ryutov, M.S.Derzon, M.K.Matzen//Rev. Mod.
Phys.(72). 2000, N1, p.167.
3. A.V.Gordeev, T.V.Losseva//JETP Lett.(70), 1999,
p.684.
4. A.V. Gordeev, T.V.Losseva//Plasma Physics Reports,
(29), 2003, N 9, p. 748.
5. J.R. Dwyer et al.// Geophys.Res.Lett.(31), 2004,
L05118; L05119; L12102.
6. L.I.Rudakov, M.V. Babykin, A.V. Gordeev, et al. The
generation and focusing of the high-current relativistic
electron beams./ ed. L.I.Rudakov. Moscow:
“Energoatomizdat”, 1990, pp. 181-122.
ДИНАМИКА НЕКВАЗИНЕЙТРАЛЬНЫХ ТОКОВЫХ ФИЛАМЕНТОВ НА РАЗЛИЧНЫХ
ПРОСТРАНСТВЕННО-ВРЕМЕННЫХ МАСШТАБАХ
Александр В. Гордеев, Татьяна В. Лосева
Полученные ранее результаты по равновесию и динамике неквазинейтральных токовых филаментов для
пространственного масштаба порядка одного микрона и временного масштаба порядка одной пикосекунды
применяются к объектам в атмосфере, ионосфере и в межзвёздном пространстве. Основной чертой нового
равновесия для электронного токового филамента является присутствие электрического поля, которое
появляется как результат разделения зарядов на магнитном дебаевском радиусе rB. Произведены численные
расчёты ионной динамики, связанной с электрическим полем филамента. Получено, что одни и те же уравнения
могут описывать равновесие и динамику филаментов от микронного масштаба до длины порядка миллиона км.
Представлены аргументы, которые вводят новый подход для феномена молнии, где магнитное поле в канале
молнии может играть решающую роль.
ДИНАМІКА НЕКВАЗІНЕЙТРАЛЬНИХ ТОКОВИХ ФІЛАМЕНТІВ НА РІЗНИХ ПРОСТОРОВО-
ТИМЧАСОВИХ МАСШТАБАХ
Олександр В. Гордєєв, Тетяна В. Лосєва
Отримані раніше результати по рівновазі і динаміці неквазінейтральних токових філаментів для просторового
масштабу порядку одного мікрона і тимчасового масштабу порядку однієї пікосекунди застосовуються до
об'єктів в атмосфері, іоносфері й у міжзоряному просторі. Основною рисою нової рівноваги для електронного
токового філамента є присутність електричного поля, що з'являється як результат поділу зарядів на магнітному
дебаєвському радіусі r. Зроблено чисельні розрахунки іонної динаміки, зв'язаної з електричним полем
філамента. Отримано, що ті ж самі рівняння можуть описувати рівновагу і динаміку філаментів від мікронного
масштабу до довжини порядку мільйона км. Представлено аргументи, що вводять новий підхід для феномена
блискавки, де магнітне поле в каналі блискавки може відігравати вирішальну роль.
77
78
|
| id | nasplib_isofts_kiev_ua-123456789-78896 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:01:30Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Gordeev, A.V. Losseva, T.V. 2015-03-22T10:47:43Z 2015-03-22T10:47:43Z 2005 Dynamics of nonquasineutral current filaments on different space - time scales / A.V. Gordeev, T.V. Losseva // Вопросы атомной науки и техники. — 2005. — № 1. — С. 75-77. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.58.Lq, 52.59.Px, 52.65.Kj, 52.80.Mg https://nasplib.isofts.kiev.ua/handle/123456789/78896 The earlier obtained results on the equilibrium and dynamics of the nonquasineutral current filaments for the size scale on the order of 1 µm and the time on the order of 1 ps are being applied to the objects in the atmosphere, the ionosphere and in the interstellar space. The main feature of the equilibrium for the electron current filament consists in the presence of the strong electric field that appears as a result of the charge separation at the magnetic Debye radius rB. The numerical calculations of the ion dynamics due to the electric field of the filament are performed. It was obtained that the same equations can describe the equilibria and dynamics of the filaments from the micron size scale to the length of about millions km. Some arguments are presented in order to introduce a new approach for the lightning phenomena, where the magnetic field of the current in the lightning channel may play a decisive role. Отримані раніше результати по рівновазі і динаміці неквазінейтральних токових філаментів для просторового масштабу порядку одного мікрона і тимчасового масштабу порядку однієї пікосекунди застосовуються до об'єктів в атмосфері, іоносфері й у міжзоряному просторі. Основною рисою нової рівноваги для електронного токового філамента є присутність електричного поля, що з'являється як результат поділу зарядів на магнітному дебаєвському радіусі r. Зроблено чисельні розрахунки іонної динаміки, зв'язаної з електричним полем філамента. Отримано, що ті ж самі рівняння можуть описувати рівновагу і динаміку філаментів від мікронного масштабу до довжини порядку мільйона км. Представлено аргументи, що вводять новий підхід для феномена блискавки, де магнітне поле в каналі блискавки може відігравати вирішальну роль. Полученные ранее результаты по равновесию и динамике неквазинейтральных токовых филаментов для пространственного масштаба порядка одного микрона и временного масштаба порядка одной пикосекунды применяются к объектам в атмосфере, ионосфере и в межзвёздном пространстве. Основной чертой нового равновесия для электронного токового филамента является присутствие электрического поля, которое появляется как результат разделения зарядов на магнитном дебаевском радиусе rB. Произведены численные расчёты ионной динамики, связанной с электрическим полем филамента. Получено, что одни и те же уравнения могут описывать равновесие и динамику филаментов от микронного масштаба до длины порядка миллиона км. Представлены аргументы, которые вводят новый подход для феномена молнии, где магнитное поле в канале молнии может играть решающую роль. This paper is supported in part within the framework of the system of the initiative projects in Russian Research Center “Kurchatov Institute”. We thank I.V. Nemtchinov for bringing Ref.5 to our attention. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Space plasma Dynamics of nonquasineutral current filaments on different space - time scales Динаміка неквазінейтральних токових філаментів на різних просторово- тимчасових масштабах Динамика неквазинейтральных токовых филаментов на различных пространственно-временных масштабах Article published earlier |
| spellingShingle | Dynamics of nonquasineutral current filaments on different space - time scales Gordeev, A.V. Losseva, T.V. Space plasma |
| title | Dynamics of nonquasineutral current filaments on different space - time scales |
| title_alt | Динаміка неквазінейтральних токових філаментів на різних просторово- тимчасових масштабах Динамика неквазинейтральных токовых филаментов на различных пространственно-временных масштабах |
| title_full | Dynamics of nonquasineutral current filaments on different space - time scales |
| title_fullStr | Dynamics of nonquasineutral current filaments on different space - time scales |
| title_full_unstemmed | Dynamics of nonquasineutral current filaments on different space - time scales |
| title_short | Dynamics of nonquasineutral current filaments on different space - time scales |
| title_sort | dynamics of nonquasineutral current filaments on different space - time scales |
| topic | Space plasma |
| topic_facet | Space plasma |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78896 |
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