Accelerating field excitation, occurrence and evolution of electron beam near Jupiter
When electron beam, formed Io-Jupiter penetrates into Jupiter plasma the beam-plasma instability develops.
 Then electron distribution function becomes wider by excited fields. These electrons cause UV polar light. The conditions of formation, properties, stability and evolution of a formed...
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| Zitieren: | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter / V.I. Maslov, A.P. Fomina, R.I. Kholodov, I.P. Levchuk, S.A. Nikonova, O.P. Novak, I.N. Onishchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 106-111. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860211141661163520 |
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| author | Maslov, V.I. Fomina, A.P. Kholodov, R.I. Levchuk, I.P. Nikonova, S.A. Novak, O.P. Onishchenko, I.N. |
| author_facet | Maslov, V.I. Fomina, A.P. Kholodov, R.I. Levchuk, I.P. Nikonova, S.A. Novak, O.P. Onishchenko, I.N. |
| citation_txt | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter / V.I. Maslov, A.P. Fomina, R.I. Kholodov, I.P. Levchuk, S.A. Nikonova, O.P. Novak, I.N. Onishchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 106-111. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | When electron beam, formed Io-Jupiter penetrates into Jupiter plasma the beam-plasma instability develops.
Then electron distribution function becomes wider by excited fields. These electrons cause UV polar light. The conditions of formation, properties, stability and evolution of a formed intensive double layer have been described.
Beam reflection leads to semi-vortex formation.
Когда электронный пучок, образованный Ио-Юпитера, проникает в плазму Юпитера, развивается пучково-плазменная неустойчивость. Тогда функция распределения электронов становится шире, благодаря возбужденным полям. Эти электроны вызывают ультрафиолетовое свечение. Описаны условия формирования,
свойства, устойчивость и эволюция сформировавшегося интенсивного двойного слоя. Отражение пучка
приводит к образованию полувихря.
Коли електронний пучок, утворений Іо-Юпітера, проникає в плазму Юпітера, розвивається пучковоплазмова нестійкість. Тоді функція розподілу електронів стає ширше завдяки збудженим полям. Ці електрони викликають ультрафіолетове світіння. Описано умови формування, властивості, стійкість і еволюція інтенсивного подвійного шару, що формується. Відбиття пучка призводить до утворення напіввихору.
|
| first_indexed | 2025-12-07T18:14:36Z |
| format | Article |
| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №4(116) 106
COLLECTIVE PROCESSES IN SPACE PLASMAS
ACCELERATING FIELD EXCITATION, OCCURRENCE
AND EVOLUTION OF ELECTRON BEAM NEAR JUPITER
V.I. Maslov1,4, A.P. Fomina2, R.I. Kholodov3, I.P. Levchuk1, S.A. Nikonova4, O.P. Novak3,
I.N. Onishchenko1
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2Bogolyubov Institute of Theoretical Physics NAS of Ukraine, Kiev, Ukraine;
3Institute of Applied Physics NAS of Ukraine, Sumy, Ukraine;
4Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: vmaslov@kipt.kharkov.ua
When electron beam, formed Io-Jupiter penetrates into Jupiter plasma the beam-plasma instability develops.
Then electron distribution function becomes wider by excited fields. These electrons cause UV polar light. The con-
ditions of formation, properties, stability and evolution of a formed intensive double layer have been described.
Beam reflection leads to semi-vortex formation.
PACS: 29.17.+w; 41.75.Lx
INTRODUCTION
In this paper, the dynamics of an electron beam,
which leads to polar light of Jupiter [1 - 13], in the vicini-
ty of Jupiter has been investigated, which according to
model [14] is accelerated in the Io vicinity. Electron
bunches move along a magnetic tube from Io to Jupiter.
Since the magnetic field lines of Jupiter meet at its poles,
the beam is focused while moving toward Jupiter, and the
density of the beam electrons increases. When the beam
penetrates into the plasma to a certain depth, the beam-
plasma instability (BPI) develops. In this case, the excited
oscillations expand the electron distribution function. Thus,
from their energy distribution function, a tail grows, which
determines the observed aurora in the UV range.
Since BPI in an inhomogeneous plasma develops lo-
cally, it can at some height lead to the formation of a
double layer (DL). The conditions for the formation of
this DL have been formulated, its properties have been
obtained, the dynamics of plasma particles and the re-
flection of the beam back in its field have been de-
scribed. After reflection from Jupiter upper ionosphere
electron bunches change the direction of motion [15].
The effect of the space charge of a decelerated beam
and its collision with particles of partially ionized plas-
ma lead to a gradual expansion of the decelerating
beam. Thus, the reflected beam moves back on a larger
radius, leading to vortex dynamics.
1. BEAM-PLASMA INSTABILITY
The energy of the beam electrons is too high to
cause UV auroras. However, the BPI [16], caused by
them, forms the tail of the electron distribution function
up to the UV range (Fig. 1).
Fig. 1. The distribution functions of the beam and plas-
ma electrons formed at t2>t1>t0 as a result of the elec-
tron beam interaction with the Jovian plasma
Thus, when a beam penetrates into the plasma to
such depth that the plasma electron density n0e becomes
large and at a significant focusing of the electron beam,
so that its density nb becomes larger than some thresh-
old, the BPI develops [16]. Growth rate γb of BPI
equals.
1 3
1 3 1 6b
bq pe b oe4 3
0e
n3 n n
2 n
γ = ω ∝
, (1)
at a rapid stage of evolution and
b
bs pe
0e
n
n
γ ≈ ω
, (2)
at a slow stage of evolution. If the beam is initially wide
in energy, then BPI from the very beginning begins with
a slow stage of evolution. As growth rate γb is propor-
tional to nb and to the plasma electron density, the insta-
bility develops at a certain height, where the electron
density n0e of the inhomogeneous plasma is large and
beam density due to focusing is large.
2. PROPERTIES OF DOUBLE ELECTRIC
LAYER, REFLECTING ELECTRON BEAM
Since the current must be closed, the beam at some
height should be reflected and go back. Let us consider
a possible mechanism of beam reflection. The reflection
mechanism from the ionosphere is associated with the
formation of double layers at entering the bunches of
fast electrons with density nb≈104 cm-3 in the ionosphere
at heights where the density of ionosphere ions ni ap-
proximately equals to nb [15].
1D numerical simulation [17] has shown that at in-
jection of an electron beam into a plasma, DL can be
formed. Let us show that at an electron beam injection
from a source into the plasma with a density comparable
to the plasma density nb=ni, the formation of DL is pos-
sible, which reflects the beam from the plasma [18 - 22].
Let us study the phenomena, accompanying injec-
tion from a certain time from a source (for example,
from a natural satellite of Jupiter) to Jupiter plasma an
electron beam with a density nb which is comparable to
the plasma density, ni.
mailto:vmaslov@kipt.kharkov.ua
ISSN 1562-6016. ВАНТ. 2018. №4(116) 107
At a beam injection from an isolated source into the
plasma, the plasma electrons are accelerated towards the
source of the electron beam in the field of the potential
drop arising between the source and the beam. At nb≈ni,
the plasma electron current to the source is small com-
pared to the injected beam current, jb=nbVb. The result-
ing reverse plasma current is small, since plasma elec-
trons close to the boundary are accelerated insignificant-
ly, and those plasma electrons, located in the interior of
the plasma near the beam reflection region, are acceler-
ated to velocities reaching the injection velocity, but
their density becomes much smaller than the beam den-
sity. Thus, the reverse plasma current does not compen-
sate the accumulation of a positive source charge.
Therefore, the potential drop reaches the kinetic energy
of the beam. The beam returns to the source, being re-
flected from the potential jump and compensating the
accumulation of a positive charge on the source. Then
the potential can separate from the source and move
inside the plasma with a certain velocity Vdl. So DL is
formed (the potential jump from φo=φ(x=0) on the in-
jection boundary to zero on Δx).
Let us consider DL that the perturbation of the ion
density in its field is insignificant
o
i i i2
i dl
e
n n n
m V
φ
d = << . (3)
The appearance of charge separation in the form of
two oppositely charged regions is necessary for the DL
formation. For an electron DL formation at an electron
beam injection into the plasma, two groups of injected
electrons are necessary for this charge separation. The
second group, in contrast to the beam, should be slow.
The second group cannot be plasma electrons that fly
into the DL region and are accelerated in its field to
velocity (Vdl
2+2eφo/m)1/2, since their density deceases in
DL to a small value n(Vth/Vb). Vth is the thermal veloci-
ty of the plasma electrons. A slow group is formed by
trapping a part of the plasma electrons by DL, which is
rapidly formed, or it is injected together with a fast
beam. First we consider the case of injection of two
groups.
Let us consider a semi-infinite plasma, x>0, into
which, high-energy, Vb>>Vth, Vthb, and slow,
Vsl<Vtho<<Vb, beams are injected with densities nb and
no. Vthb=(Tb/m)1/2, Vtho=(To/m)1/2 − thermal velocities of
electron beams. Since the distribution function of the
slow group of electrons after reflection from the DL
becomes symmetric with respect to the velocity of the
DL Vdl, the average velocity of the slow group Vsl can
be set equal to Vsl=Vdl<<c.
First, we find from the kinetic equation and the
equations of the balance of energy and momentum flux-
es the stationary characteristics of Dl.
Electrons move along trajectories
2mc ( 1) e constγ − − ϕ = . (4)
In this case, plasma electrons in the DL rest system
are accelerated in its field from -Vdl to -c(1-γo
-2)1/2, γo=
[1-(Vb-Vdl+Vthb)2/c2]-1/2. At the same time, their density
changes as
( )
1
2 21
2 2
dl dl
e e 02
0
V Vn (x) n 1 1 1
c c
−−
−
ϕ = − − + γ − ϕ
. (5)
decreasing from
ne(φ=0)=ne to ne(φ=φo)=ne(Vdl/c)(1-γo
-2)-1/2 .
Dynamics of the slow electron group is nonrelativ-
istic, and their density varies according to
( )0
0 0
0
e
n (x) n exp
T
ϕ−ϕ
=
. (6)
One can see from (6) that the density of the slow
group decreases exponentially and forms a positive
charge at φa<φ<φo. Densities of fast beam
1
2 2
b b 2 2
0
1 en (z) n 1 1 1
mc
−− ϕ = − − + γ
. (7)
and of the plasma electrons (5) increase in a power law,
which leads to a negative charge at 0<φ<φa. φa is deter-
mined from δn(φa)=0
0 0
a
0
1 1
1 2
ϕ γ + ϕ = − γ −
. (8)
One can derive that at φc=φo(2Vbth/c)γo
2 the beam re-
flection begins. As a result, quasineutrality is restored
after DL.
Since the nonresonant beam electrons, passing
through DL, penetrate into the plasma, where they are
decelerated, their density increases. Therefore, the qua-
sineutrality condition behind DL (for x>>Δx) requires
that Vdl be less than the thermal velocity of the plasma
electrons Vdl<Vth, and the density of the beam electrons,
penetrating through the DL, should be small nbo<<ne.
Consequently
( )
2
0 0
mc 1
e
ϕ ≈ γ − . (9)
All electrons transmit a momentum to DL. The flux-
es of momenta transmitted to the DL by beam electrons,
passing through DL, by electrons of the slow group and
by beam, which are reflected from DL, are equal to
cmneVdl(γo
2-1)1/2, nbomc2(γo
2-1)/γo, noTo, 2(nb-
nbo)mc2(γo
2-1)/γo
2. In DL field only ions receive a mo-
mentum whose flux is equal to nieφo. Electrons and
plasma ions take energy from DL, whose fluxes are
neeφoVdl, nieφoVdl. The electrons of the beam and the
slow group lose energy when interacting with DL. The
energy fluxes, which are transmitted to DL by slow
group, which are reflected from DL, and by passing
through DL beam electrons, are equal to VdlnoTo,
(nb-nbo)mc22Vdl(γo
2-1)/γ, nboeφoc(1-γo
-2)1/2. Using the
equations for the balance of the energy and momentum
fluxes, as well as the quasi-neutrality condition on the
beam injection boundary, one can obtain:
dl b0
2
e 0
V n 11 1
c n
= − <<
γ
, (10)
0 0i
b0 0
0 0
Tnn n
2 2e 1
γ
= − ϕ γ +
,
0 0 i
0
0 0 0
T nn 1
e 1 1
γ
= + ϕ γ + γ +
.
ISSN 1562-6016. ВАНТ. 2018. №4(116) 108
Let us find the DL profile and estimate its width.
From (6) we find that in the reflection region of the
slow group δn(φb)≈-no, φb is determined from
dn(φb)/dφ=0 and equal to φb/φo=1-To/eφo. I.e. in a re-
gion, where the perturbation of the charge density is
determined by the change in the density of the slow
group, the potential drop is insignificant. In a region,
where the perturbation of the charge density is deter-
mined by the change in the density of a fast beam upon
its deceleration, δn increases to φ=φdl. The maximum δn
is reached in the region of strong deceleration of the
beam and it is equal to δn(φdl)=nb(2Vb/Vthb)1/2/γ3/2. In
neglecting small intervals (widths of φc and φo-φb) near
φ=0 and φ=φo, we obtain
( ) ( )
( )
2
0 0
i 0
0 0
1 2x
n
3 e 1
γ + ϕ ϕ +∂ϕ ∂ ϕ
= ϕϕ −
π γ + ϕ
. (11)
From here
p
0 0
x 2
1
c
ωϕ
= −
ϕ γ
. (12)
Let us determine the width D:
( )
a
0 0
i
0
( 1)c 2mx
4e nx 21
1
ϕ=ϕ
ϕ γ −
∆ = ≈
π∂ϕ ∂
−
γ +
. (13)
And at γo>>1 Δx=(c/ωp√2)γo, ωp=(4πnіe2/m)1/2 .
We now consider the case of injection from a source
into the plasma of only a fast beam. It follows from (13)
that for γo>>1 the double layer is formed during the time
γo/ωp√2. And the response time of plasma electrons to
the formed field, according to (11), is equal to
( ) ( )( )1/4
o o p o ot 2 t= γ ω φ φ . (14)
Hence it can be concluded that during the formation
time DL the plasma electrons do not have time to react
to the formed field. Before the beam is reflected and
reaches the boundary, the plasma electrons close to it
are thrown out to the source under the action of the aris-
en field. When the plasma density is reached, which
satisfies the inequality ne(t)<nі-nb, the self-consistent
potential ceases to be monotonic. The potential grows
inside the plasma from φo(t) to φ1(t). Further, inside the
plasma the potential falls sharply from φ1(t) to zero.
This distribution of the potential keeps from the ejection
to the source of the part of the plasma electrons which
were during the DL formation in its vicinity, to neutral-
ize, together with the charge beam, plasma ions. These
trapped plasma electrons form the slow group necessary
for DL formation. After completion of DL formation,
the plasma electrons, fly into DL region, are accelerated
toward the beam.
Let us consider the stability of the relative motion of
electron fluxes. From (4), (5) - (7) we have an equation
describing the excitation of HF perturbations in the DL
neighborhood:
( ) ( ) ( )2 2
2 3
0
1
1 z y z y 0
z 2
− −− αα − − − + + = γ
, (15)
α=no/nі, z=ω/ωp, y=kb/ωp. It follows from (15) that HF
noise is generated in the DL region due to the develop-
ment of BPI. They lead, as noted above, to the spread-
ing of the electron distribution function. In [17, 23],
noise does not lead to a significant DL destruction due
to: spreading of the electron distribution function; in-
homogeneity of the potential, which ensures the viola-
tion of the wave-particle resonance condition and the
large relative noise velocity and DL.
Since DL moves slowly inside the plasma, the densi-
ty of trapped electrons no decreases in the case of non-
monotonic DL, since the localization region of these
electrons increases. The study of the stability of electron
fluxes with respect to LF perturbations on the basis of
equation
( )
( ) ( ) ( )2 2
2 3
00
1
1 z y z y 0
2kd
− −− αα + − − + + = γ
, (16)
do=(To/4πne
2)1/2 , shows that when the density of the
trapped electrons falls below the critical value
( ) ( )
2
2tho b
03
0
V V
kd> α +
γ
. (17)
DL becomes unstable with respect to perturbations
with the phase velocity equal to Vdl. Numerical simula-
tion [17] has shown that in this case DL, which has
shifted into the plasma, decays, forming a vortex in the
electron phase space and a new DL appears on the
boundary.
It was shown in [18 - 22] that DL can be formed in a
beam-plasma system only, as observed, when nb≈ni.
Thus, it has been shown that injection from a source
into a plasma of an electron beam with nb≈ni can lead to
the DL formation.
DL reflects the beam from the plasma, so the electron
velocity distribution function at the injection boundary
has three maxima, which was observed in [17].
If the beam and plasma parameters differ from those,
necessary for the formation of a monotonous DL, then
within some limits of such a deviation near the DL in its
low potential region a potential dip can be formed. The
depth of the dip is self-consistently adjusted to the pa-
rameters of the beam and plasma, facilitating the DL
formation and the beam reflection. In particular, the
potential well, reducing the fraction of the beam passing
to the low potential region, ensures quasi-neutrality in
this region. The potential well in the region of low po-
tential of DL is also formed due to 3D beam dynamics
and the limited radius of the beam.
A similar spatial distribution of the electrostatic po-
tential and the behavior of the beam were observed in
the experiment and in numerical simulation [17]. The
injection of an electron beam into the plasma in numeri-
cal simulation [17] leads under certain conditions to the
DL formation.
So, DL is formed at a fast beam density, which takes
values in a small interval near nb/n=1/4. The considered
DL moves with a velocity much less than the beam ve-
locity. The DL width is comparable to the wavelength
of the most unstable mode of beam instability. The per-
turbation of the ion density in the double-layer field is
small.
It should be noted that the electron distribution func-
tion remains unstable. Indeed, in [17], excitation in the
DL region of weak electron oscillations has been ob-
served.
ISSN 1562-6016. ВАНТ. 2018. №4(116) 109
3. NUMERICAL MODELING
OF DOUBLE LAYER GENERATION
Generation of a quasistationary double layer result-
ing from interaction of an electron beam with plasmas
was numerically simulated using particle-in-cell method
in the nonrelativistic case. For the sake of simplicity 1D
electrostatic model was used. This approximation ap-
pears to be justified, since the transverse motion of elec-
trons is suppressed by external magnetic field and the
intrinsic plasma magnetic field is assumed to be small.
The simulation was performed in the spatial region
of the size of 100λD with open boundary conditions. In
this case, the particles that leave the considered region
are excluded from the calculations. In the initial mo-
ment the considered region was filled with equilibrium
plasma of the temperature kT and the electron number
density of n0. The ion component was assumed to be
‘freezed in’ and spatially uniformly distributed. A con-
tinuous electron beam was injected into the plasma from
the left, having the drift velocity of 10vT and the veloci-
ty distribution equal to that of the plasma. The number
density of the beam is chosen to be equal to 0.4n0.
Fig. 2. Phase portrait of a double layer in plasma
Fig. 3. The electrostatic potential and the electric field
strength as functions of coordinate.
Here E0 = 4πσ, where σ is the surface charge density
of a spatial cell of a size λD
After a relatively short period of time of about 30/ωp
from the beginning of the simulation, a quasistationary
picture is formed in the phase space of the system, con-
taining small plasma oscillations and a double layer that
reflects some part of the beam. Typical instantaneous
phase portrait is shown in Fig. 2.
The double layer contains a typical drop of the elec-
trostatic potential. Fig. 3 shows plots of the potential
and electric field strength as functions of the coordinate.
These dependencies have been obtained by averaging of
the potential and the field strength over a time interval
that is much greater than the period of plasma oscilla-
tions. Note that instantaneous values can be substantial-
ly distorted by plasma waves. It can be seen from Fig. 3
that the double layer has the width of about 20λD. The
drop of the potential is determined by the energy of the
beam particles according to E = eφdl.
Fig. 4 depicts distribution functions of the electron
component in the regions before and behind the double
layer when the quasistationary flow is established,
t > 30/ωp. The solid blue line depicts the distribution
function before the double layer near the coordinate
x = 0. The right maximum corresponds to the injected
beam with a fixed normal velocity distribution and the
left one combines the reflected part of the beam and the
plasma electrons extracted and accelerated by the field
of the double layer. The dashed green line depicts the
distribution function behind the double layer. Note that
the interaction with the beam results in distortion of the
initial distribution and the appearance of a high-energy
tail, in accordance with aforesaid.
Fig. 4. The velocity distribution function of the electron
component in the regions before (solid blue line) and
after (green dashed line) the double layer. The vertical
lines shows the interval of velocities where the electron
energy is not enough to penetrate the double layer
4. NONLINEAR EQUATION, DESCRIBING
EXCITATION AND PROPERTIES
OF SEMI-VORTEX
The radial defocusing effect of the space charge of a
decelerating beam and its collision with particles of par-
tially ionized plasma lead to a gradual expansion of the
decelerating beam. Thus, the reflected beam moves
back on a larger radius, leading to a vortex-type dynam-
ics (Fig. 5).
In an unperturbed plasma, an electron beam of finite
radius br moves with velocity bV along the magnetic
field 0H of Jupiter in the direction of its surface.
ISSN 1562-6016. ВАНТ. 2018. №4(116) 110
α is the vorticity, vortical characteristic of elec-
trons.
Fig. 5. A vortex dynamics of decelerated and reflected
by double layer electron beam near Jupiter
z r r ze rotV V Vθα ≡ = ∂ − ∂
. (18)
We use hydrodynamic equations for electrons taking
into account collisions with the frequency eν
( )e
2
th
He e
e e
V V V V
t
Ve , V n ,
m n
∂
+ ν + ∇ =
∂
= ∇φ+ ω − ∇
. (19)
( )e
e
n n V 0
t
∂
+∇ =
∂
, (20)
and Poisson equation for the electric potential, ϕ ,
( )e i i4 en q n∆φ = π − . (21)
Here V
, en are the velocity and density of elec-
trons, thV is the thermal velocity of electrons, iV
, in ,
iq , im are the velocity, density, charge and mass of
ions.
Since the dimensions of the vortex perturbations are
much larger than the electron Debye radius, th
de
pe
Vr ≡
ω
,
and beam velocity, directed along z, is much more than
thermal velocity of electrons b thV V>> , one can neglect
the last term in (19).
( )e He
e
V eV V V , V
t m
∂ + ν + ∇ = ∇φ+ ω ∂
, (22)
1/22
oe
pe
e
4 n e
m
π
ω ≡
is the electron plasma frequency.
Since in the region of formation of the described
half-vortex the density of the decelerated beam is much
larger than the density of the electrons of the surround-
ing plasma, then in the first approximation we neglect
the density of the electrons of the surrounding plasma in
comparison with the beam density.
From (20) - (22) we obtain a nonlinear equation, de-
scribing the vortex dynamics of the electrons.
( )( )He e
t He
e e e
1d V
n n n
α −ω ν α
+ = α−ω ∇
. (23)
Since the problem is symmetric along the azimuth θ, α
is directed along θ, and Heω
is homogeneous and sta-
tionary, then
( )e
t He
e e e
1d V
n n n
ν αα
+ = − ω ∇
. (24)
Thus, we have derived the nonlinear vector equation,
describing the vortex dynamics of electrons, without
any approximations.
At Vθ=0
e
t
e e
d 0
n n
ν αα
+ =
. (25)
In the state of a stationary semi-vortex, we have
( ) e
e e
V 0
n n
ν αα
∇ + =
. (26)
In the linear stationary case, assuming that the elec-
tron flux is inhomogeneous in the transverse direction,
one can obtain
( ) ( )r r 0e e
0e
V n V 0
n
α
− ∂ + ∇ α+ ν α =
. (27)
In the linear nonstationary case, assuming that the
electron flux is inhomogeneous in the transverse direc-
tion, one can obtain
( ) ( )r r 0e t 0 z e
0e
V n V 0
n
α
− ∂ + ∂ + ∂ α+ ν α = . (28)
CONCLUSIONS
So, the electron beam dynamics, formed near Io, the
Jupiter natural satellite, and moved to Jupiter, has been
described analytically. When a beam penetrates into the
Jupiter plasma to a certain depth, the beam-plasma in-
stability develops. Due to this the electron distribution
function becomes wider by excited fields. These elec-
trons, when their energy reaches a certain value, cause
UV polar light. For closing of a current a double electric
layer is formed. The necessary conditions for the for-
mation and properties of the double layer of an electric
potential large amplitude, its stability, evolution and
beam reflection in its field have been described. It has
been shown that reflection of the beam leads to semi-
vortex formation. The equation, describing the semi-
vortex, has been derived.
ACKNOWLEDGMENTS
The present work was partially supported by the Na-
tional Academy of Sciences of Ukraine (project
№ 0118U003535).
REFERENCES
1. G.R. Gladstone, J.H. Waite, Jr.D. Grodent, et al. A
pulsating auroral X-ray hot spot on Jupiter // Nature.
2002, v. 415, p. 1000-1003.
2. J.T. Clarke, J. Ajello, G. Ballester, et al. Ultraviolet
emissions from the magnetic footprints of Io, Gan-
ymede and Europa on Jupiter // Nature. 2002,
v. 415, p. 997-1000.
3. J.E.P. Connerney et al. Images of excited H+
3 at the
foot of the Io flux tube in Jupiter's atmosphere // Sci-
ence. 1993, v. 262, p. 1035-1038.
4. J.T. Clarke et al. Far-ultraviolet imaging of Jupiter's
aurora and the Io “footprint” // Science. 1996,
v. 274, p. 404-409.
https://www.nature.com/articles/415997a#auth-1
https://www.nature.com/articles/415997a#auth-2
https://www.nature.com/articles/415997a#auth-3
ISSN 1562-6016. ВАНТ. 2018. №4(116) 111
5. R. Prangé et al. Rapid energy dissipation and varia-
bility of the Io-Jupiter electrodynamic circuit // Na-
ture. 1996, v. 379, p. 323-325.
6. P. Goldreich, D. Lynden-Bell. Io, a Jovian unipolar
inductor // Astrophys. J. 1969, v. 156, p. 59-78.
7. J.W. Belcher. The Jupiter–Io connection, an Alfven
engine in space // Science. 1987, v. 238, p. 170-176.
8. F.M. Neubauer. Nonlinear standing Alfven wave
current system at Io: theory // J. Geophys. Res. 1980,
v. 85, p. 1171-1178.
9. B.H. Mauk, D.K. Haggerty, C. Paranicas, et al. Dis-
crete and broadband electron acceleration in Jupi-
ter’s powerful aurora // Nature. 2017, v. 549, p. 66-
69.
10. W.R. Dunn, G. Branduardi-Raymont, L.C. Ray, et
al. The independent pulsations of Jupiter’s northern
and southern X-ray auroras // Nature. Astronomy.
2017, v. 1, p. 758-764.
11. D.J. McComas, N. Alexander, F. Allegrini, et al.
The Jovian Auroral Distributions Experiment
(JADE) on the Juno Mission to Jupiter // Space Sci
Rev. 2017, v. 213, p. 547-643.
12. J.E.P. Connerney et al. Jupiter's magnetosphere and
aurorae observed by the Juno spacecraft during its
first polar orbits. Science. 2017, v. 356, p. 826.
13. B.H. Mauk et al. Juno observation of energetic
charged particles over Jupiter's polar regions: Analy-
sis of monodirectional and bidirectional electron
beams // Geophysical Research Letters. 2017, v. 44,
p. 4410.
14. S. Jacobsen, J. Saur, F.M. Neubauer. Location and
spatial shape of electron beams in Io’s wake // J.
Geophys. Res. 2010, v. 115, p. A04205.
15. P.I. Fomin, A.P. Fomina, V.N. Mal’nev. Superradia-
tion of magnetized electrons and the power of deca-
meter radiation of the Jupiter – IO-system //
Ukrayins'kij Fyizichnij Zhurnal. 2004, v. 49, № 1, p.
3-8 (in Ukrainian).
16. A.I. Akhiezer, Ya.B. Fainberg. On the interaction of
a charged particle beam with an electron plasma //
DAN SSSR. 1949, v. 69, № 4, p. 555-556.
17. N. Singh, R.W. Schunk. Plasma response to the in-
jection of an electron beam // Plasma Phys. and
Contr. Fus. 1984, v. 26, № 7, p. 359-390.
18. V.I. Maslov. Double layer formed by relativistic
electron beam // Plasma Physics and Fusion Tech-
nology. 1992, v. 13, № 10, p. 676-679.
19. V.I. Maslov. Electron beam reflection from the
plasma due to double layer formation // Proc. of 4th
Int. Workshop on Nonlinear and Turbulent Process-
es in Physics. Singapore. 1990, p. 898-909.
20. V.I. Maslov. Double layer formed by relativistic
electron beam // Sov. Plasma Physics. 1992, v. 18,
№ 10, p. 676-679.
21. V.I. Maslov. Properties and evolution of nonstation-
ary double layers in nonequilibrium plasma // Proc.
of 4th Symposium on Double Layers and Other Non-
linear Structures in Plasmas. Innsbruck, 1992, p. 82-
92.
22. V.I. Maslov. Analytical Description of T.Sato's
Mechanism of Transformation of Ion-Acoustic Dou-
ble Layer into Strong Bunemann's One in Cosmic
and Laboratory Nonequilibrium Plasmas // Journal
of Plasma and Fusion Research. 2001, v. 4, p. 564-
569.
23. H. Okuda, R. Horton, M. Ono, M. Ashour-Abdalla.
Propagation of nonrelativistic electron beam in a
plasma in a magnetic field // Phys. Fluids. 1987,
v. 30, № 1, p. 200-203.
Article received 12.06.2018
ВОЗБУЖДЕНИЕ УСКОРЯЮЩЕГО ПОЛЯ, ПОЯВЛЕНИЕ
И ЭВОЛЮЦИЯ ЭЛЕКТРОННОГО ПУЧКА ВБЛИЗИ ЮПИТЕРА
В.И. Маслов, А.П. Фомина, Р.И. Холодов, И.П. Левчук, С.A. Никонова, А.П. Новак, И.Н. Онищенко
Когда электронный пучок, образованный Ио-Юпитера, проникает в плазму Юпитера, развивается пучко-
во-плазменная неустойчивость. Тогда функция распределения электронов становится шире, благодаря воз-
бужденным полям. Эти электроны вызывают ультрафиолетовое свечение. Описаны условия формирования,
свойства, устойчивость и эволюция сформировавшегося интенсивного двойного слоя. Отражение пучка
приводит к образованию полувихря.
ЗБУДЖЕННЯ ПРИСКОРЮЮЧОГО ПОЛЯ, ПОЯВА
І ЕВОЛЮЦІЯ ЕЛЕКТРОННОГО ПУЧКА ПОБЛИЗУ ЮПІТЕРА
В.І. Маслов, А.П. Фоміна, Р.І. Холодов, І.П. Левчук, С.O. Ніконова, О.П. Новак, І.М. Оніщенко
Коли електронний пучок, утворений Іо-Юпітера, проникає в плазму Юпітера, розвивається пучково-
плазмова нестійкість. Тоді функція розподілу електронів стає ширше завдяки збудженим полям. Ці електро-
ни викликають ультрафіолетове світіння. Описано умови формування, властивості, стійкість і еволюція ін-
тенсивного подвійного шару, що формується. Відбиття пучка призводить до утворення напіввихору.
https://www.nature.com/articles/nature23648#auth-1
https://www.nature.com/articles/nature23648#auth-2
https://www.nature.com/articles/nature23648#auth-3
https://www.nature.com/articles/s41550-017-0262-6#auth-1
https://www.nature.com/articles/s41550-017-0262-6#auth-2
https://www.nature.com/articles/s41550-017-0262-6#auth-3
INTRODUCTION
1. BEAM-PLASMA INSTABILITY
2. PROPERTIES OF DOUBLE ELECTRIC LAYER, REFLECTING ELECTRON BEAM
ACKNOWLEDGMENTS
references
ВОЗБУЖДЕНИЕ УСКОРЯЮЩЕГО ПОЛЯ, ПОЯВЛЕНИЕ И ЭВОЛЮЦИЯ ЭЛЕКТРОННОГО ПУЧКА ВБЛИЗИ ЮПИТЕРА
|
| id | nasplib_isofts_kiev_ua-123456789-147328 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:14:36Z |
| publishDate | 2018 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Maslov, V.I. Fomina, A.P. Kholodov, R.I. Levchuk, I.P. Nikonova, S.A. Novak, O.P. Onishchenko, I.N. 2019-02-14T14:04:04Z 2019-02-14T14:04:04Z 2018 Accelerating field excitation, occurrence and evolution of electron beam near Jupiter / V.I. Maslov, A.P. Fomina, R.I. Kholodov, I.P. Levchuk, S.A. Nikonova, O.P. Novak, I.N. Onishchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 106-111. — Бібліогр.: 23 назв. — англ. 1562-6016 PACS: 29.17.+w; 41.75.Lx https://nasplib.isofts.kiev.ua/handle/123456789/147328 When electron beam, formed Io-Jupiter penetrates into Jupiter plasma the beam-plasma instability develops.
 Then electron distribution function becomes wider by excited fields. These electrons cause UV polar light. The conditions of formation, properties, stability and evolution of a formed intensive double layer have been described.
 Beam reflection leads to semi-vortex formation. Когда электронный пучок, образованный Ио-Юпитера, проникает в плазму Юпитера, развивается пучково-плазменная неустойчивость. Тогда функция распределения электронов становится шире, благодаря возбужденным полям. Эти электроны вызывают ультрафиолетовое свечение. Описаны условия формирования,
 свойства, устойчивость и эволюция сформировавшегося интенсивного двойного слоя. Отражение пучка
 приводит к образованию полувихря. Коли електронний пучок, утворений Іо-Юпітера, проникає в плазму Юпітера, розвивається пучковоплазмова нестійкість. Тоді функція розподілу електронів стає ширше завдяки збудженим полям. Ці електрони викликають ультрафіолетове світіння. Описано умови формування, властивості, стійкість і еволюція інтенсивного подвійного шару, що формується. Відбиття пучка призводить до утворення напіввихору. The present work was partially supported by the National
 Academy of Sciences of Ukraine (project
 № 0118U003535). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Коллективные процессы в космической плазме Accelerating field excitation, occurrence and evolution of electron beam near Jupiter Збудження прискорюючого поля, поява і еволюція електронного пучка поблизу Юпітера Возбуждение ускоряющего поля, появление и эволюция электронного пучка вблизи Юпитера Article published earlier |
| spellingShingle | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter Maslov, V.I. Fomina, A.P. Kholodov, R.I. Levchuk, I.P. Nikonova, S.A. Novak, O.P. Onishchenko, I.N. Коллективные процессы в космической плазме |
| title | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter |
| title_alt | Збудження прискорюючого поля, поява і еволюція електронного пучка поблизу Юпітера Возбуждение ускоряющего поля, появление и эволюция электронного пучка вблизи Юпитера |
| title_full | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter |
| title_fullStr | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter |
| title_full_unstemmed | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter |
| title_short | Accelerating field excitation, occurrence and evolution of electron beam near Jupiter |
| title_sort | accelerating field excitation, occurrence and evolution of electron beam near jupiter |
| topic | Коллективные процессы в космической плазме |
| topic_facet | Коллективные процессы в космической плазме |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147328 |
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