Solitary precursor of large amplitude
In this paper the results of investigations of properties of solitary perturbation of large amplitude, propagating with light velocity at small angle to strong magnetic field in plate plasma-filled waveguide, are presented. This solitary perturbation is the hollow of electric potential. The hump of...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 1999 |
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| Language: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
1999
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| Cite this: | Solitary precursor of large amplitude / A.M. Egorov, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 1999. — № 4. — С. 84-85. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860140087003578368 |
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| author | Egorov, A.M. Maslov, V.I. Onishchenko, I.N. |
| author_facet | Egorov, A.M. Maslov, V.I. Onishchenko, I.N. |
| citation_txt | Solitary precursor of large amplitude / A.M. Egorov, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 1999. — № 4. — С. 84-85. — Бібліогр.: 10 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | In this paper the results of investigations of properties of solitary perturbation of large amplitude, propagating with light velocity at small angle to strong magnetic field in plate plasma-filled waveguide, are presented. This solitary perturbation is the hollow of electric potential. The hump of electric potential can be excited as a wake-field by electron bunch, but the hollow of electric potential, considered in this paper, is excited as a precursor of electron bunch. Because this hollow forms the positive spike of electron density, it can be excited as a precursor of laser pulse.
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| first_indexed | 2025-12-07T17:48:38Z |
| format | Article |
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SOLITARY PRECURSOR OF LARGE AMPLITUDE
A.M.Egorov, V.I.Maslov, I.N.Onishchenko
NSC KIPT, Kharkov, Ukraine
INTRODUCTION
In this paper the results of investigations of
properties of solitary perturbation of large amplitude,
propagating with light velocity at small angle to strong
magnetic field in plate plasma-filled waveguide, are
presented. This solitary perturbation is the hollow of
electric potential. The hump of electric potential can be
excited as a wake-field by electron bunch, but the
hollow of electric potential, considered in this paper, is
excited as a precursor of electron bunch. Because this
hollow forms the positive spike of electron density, it
can be excited as a precursor of laser pulse.
The velocity of the solitary precursor grows
with amplitude growth. At large amplitude the velocity
of the solitary precursor in the nonrelativistic case can
exceed more than two times the velocity of electron
bunch, which excites this precursor.
The electron bunch, which excites solitary
precursor, deforms the shape of this precursor and the
latter becomes nonsymmetric.
PROPERTIES OF THE SOLITARY PRECURSOR
Main attention in [1] at research of excitation of
the plasma wake-fields is given to process of
electromagnetic soliton formation, which can not been
described in approximation of envelope. The soliton is
formed in wake of electromagnetic pulse. The soliton is
the nonlinear superwide in frequency space
electromagnetic pulse. Last years the papers, devoted to
solitary wave pulses and their applications are published
(see, for example, [2, 3]).
At large intensities of laser radiation qualitative
change of interaction of such radiation with plasma can
take place. In particular, there is a capability of
formation of solitary perturbations. Really, the
experiments demonstrate, that if there is in dispersion
law of excited oscillations linear interval, then solitary
perturbations can be excited.
There were many attempts of obtaining of the
analytical solution as soliton, propagating with light
velocity in unlimited plasma (see, for example, [2]). In
this paper similar solitary perturbation is investigated
analytically, propagating in plasma-filled waveguide.
Solitary perturbation, propagating with velocity
Vc ≈ c under angle θ to the magnetic field Ho → ∞
in plane metallic waveguide filled by plasma, is
investigated analitically.
This solitary perturbation is the hollow of
electric potential. The properties of small amplitude
solitary perturbation one can obtain from equation
( )
( )
∆
E V E c
e n V nv c
c
c
− ∇ +
+ ∇ − ∇ =
2 2
24 0π [ ]
Using E zz = − ∂ ϕ ∂ , we have
′ ′ =
=
− −
−
−
⊥
ϕ
ϕ
ω θ θ ϕ θ
k
V
V
c
e
m V
V
c
p
c
c
e c
c
2
2 2
2
2 2
2
2
2
2
2
1 1
1 5
1
cos cos , cos
"`" is the space derivative. Integrating the latter we have
equation for the solitary perturbation shape
( )′ = + − +⊥ ⊥φ φ ω
ω
θ φ
ω
2 2 2
2
2 2
2
2
2
2
1
p
p c p
k
c V
k
[
cos
],
φ ϕ θ= e m Ve ccos2 2 .
From this equation at ′ =
= −
φ
φ φ o
0 we have nonlinear
expression for solitary perturbation velocity
( )[ ]
V
c c k c k
c kc
o p
p
≈
+ +
+
⊥ ⊥
⊥
cos θ φ ω
ω
1 2
1
2 2 2 2 2
2 2
2
From equation for the solitary perturbation shape one
can find the width of the perturbation
( ) ( )
( )
∆ ξ
ϕ ω ω θ
ω
=
+
+
⊥ ⊥
⊥ ⊥
2 2
1 2 2 2 2 2 1 2
2 2 2
m e c c k k
k c k
e o p p
p
/ /
sin .
From here at sin θ ω< < < <⊥ck p 1 follows
( )∆ ξ ϕ ω≈ 2 22 1 2
c m ee o p
/
.
There are three parameters for control of the
solitary perturbation properties: k p⊥ , ω , θ .
The solitary perturbation shape is described by
expression
( )[ ]φ φ ξ φ η= − o och2 1 2
2
/
,
( ) ( )η ω ω θ= + +⊥ ⊥ ⊥k c k c kp p
2 2 2 2 2 2 2 2sin .
For the excitation of this perturbation by electron
beam one can derive equation
∂ φ φt bo o on n V3 32= − ′′ ′( / ) ,
φ φ µ τ δ φ τ( , ) ( ) [ ( ( ))],z t t z d Vo o
t
o= −
− ∞
∫
µ φ( ) / ( / ( ))z ch z z o= 1 22 ∆ .
From here expression for growth rate of
perturbation’s amplitude follows
γ ω φ≈ p bo o o on n e mV( / ) ( , / )/ /2 1 51 3 2 1 2 .
Thus, the interaction of the electron beam with
solitary perturbation leads to growth of its amplitude in
a goodness with similar results, obtained in [4-10].
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 84-85.
84
The hump of electric potential can be excited as
a wake-field by electron bunch, but the hollow of
electric potential, considered here, is excited as a
precursor of electron bunch. Because this hollow forms
the positive spike of electron density, it can be excited
as a precursor of laser pulse.
The velocity Vc of the solitary precursor grows
with amplitude growth ϕo. At large amplitude the
velocity of the solitary precursor in the nonrelativistic
case can exceed more than two times the velocity of
electron bunch, which excites this precursor.
In relativistic case the soliton is described by
equation
′ ′ + − +
+ − + =
= − − +
= −
⊥
− −
−
ϕ π
γ γ ϕ
γ γ ϕ
γ θ
4
3 0
1 1
1
3 2 3 2 2
2 2 2
2 2 2 1 2
e n n
e mc mc k e
n n e mc
V c
o
o o
o o o
o c
( )
[ ( / ) ] / ,
/ ( / ) ,
( / cos ) /
Its shape is determined by equation
( ) ( / ){
( / )[( / ) ]}
{ ( / )[
( / ) ]}
′ = − +
+ − +
− − +
+ − + −
⊥
−
ϕ γ ϕ
γ ϕ γ
π ϕ γ
γ γ ϕ
2 2 2 3
2 2 4 4
2
2 2 2
2 3
4
8
1 1
mc k e
mc e e mc
en mc e
e mc
o
o o
o o
o o
From condition ′ = −ϕ ϕ ϕ o
follows that the
maximum velocity of solitary perturbation is realized at
e mco oϕ γ≈ −2 1( ) and is determined by equation
γ γ ωo o p c k4 3 2 2 24 3 1 3 4 0− + + =⊥/ / /
The electron bunch, which excites solitary
precursor, deforms the shape of this precursor. The
latter becomes nonsymmetric.
REFERENCES
1. S.Bulanov, T.Esirkepov, F.Kamenethz, N.Naumova.
// Plasma Physics Reports, 1995. V. 21, p. 584.
2. R.W.Ziolkowski. Phys. Rev. A. 1991. v. 44. p. 3960.
3. B.I.Cohen, B.B.Afeyan, A.E.Chou and
N.C.Luhmann, Jr. Computational study of ultra-
short-pulse reflectometry. Preprint UCRL-JC-
117947. 1994.
4. H.Schamel, Phys. Rep. 1986. V. 140. P. 163.
5. K.Nishihara, H.Sakagami, T.Taniuti, amd
A.Hasegawa, Riso Nat. Lab. R. 472. 1982. P. 41.
6. V.I.Maslov, Proc. of 4th Symp. on double layers.
Innsbruck. Austria. 1992. P. 82.
7. J.P.Lynov, P.Michelsen, H.L.Pecseli, J.J.Rasmussen,
K.Saeki and V.A.Turikov, Phys. Scr. 1979. V. 20. P.
328.
8. H.Ikezi, P.J.Barrett, R.B.White and A.Y.Wong, Phys.
Fluids. 1971. V. 14. P. 1997.
9. V.I.Maslov, Phys. Lett. 1992. V. A165. P. 63.
10. Y.Takeda and K.Yamagiwa, Phys. Fluids. 1991. V.
B3. P. 288.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 84-85.
85
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| id | nasplib_isofts_kiev_ua-123456789-81501 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:48:38Z |
| publishDate | 1999 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Egorov, A.M. Maslov, V.I. Onishchenko, I.N. 2015-05-17T15:30:21Z 2015-05-17T15:30:21Z 1999 Solitary precursor of large amplitude / A.M. Egorov, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 1999. — № 4. — С. 84-85. — Бібліогр.: 10 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/81501 In this paper the results of investigations of properties of solitary perturbation of large amplitude, propagating with light velocity at small angle to strong magnetic field in plate plasma-filled waveguide, are presented. This solitary perturbation is the hollow of electric potential. The hump of electric potential can be excited as a wake-field by electron bunch, but the hollow of electric potential, considered in this paper, is excited as a precursor of electron bunch. Because this hollow forms the positive spike of electron density, it can be excited as a precursor of laser pulse. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Solitary precursor of large amplitude Солитонный предвестник больших амплитуд Article published earlier |
| spellingShingle | Solitary precursor of large amplitude Egorov, A.M. Maslov, V.I. Onishchenko, I.N. |
| title | Solitary precursor of large amplitude |
| title_alt | Солитонный предвестник больших амплитуд |
| title_full | Solitary precursor of large amplitude |
| title_fullStr | Solitary precursor of large amplitude |
| title_full_unstemmed | Solitary precursor of large amplitude |
| title_short | Solitary precursor of large amplitude |
| title_sort | solitary precursor of large amplitude |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81501 |
| work_keys_str_mv | AT egorovam solitaryprecursoroflargeamplitude AT maslovvi solitaryprecursoroflargeamplitude AT onishchenkoin solitaryprecursoroflargeamplitude AT egorovam solitonnyipredvestnikbolʹšihamplitud AT maslovvi solitonnyipredvestnikbolʹšihamplitud AT onishchenkoin solitonnyipredvestnikbolʹšihamplitud |