Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse
Nonlinear mechanism of Langmuir wave excitation in dense plasma by intensive laser pulse has been investigated. Laser pulse has frequency ω=ω p /2 (where ω p is electron plasma frequency).
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| Дата: | 2005 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Цитувати: | Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse / V.A. Balakirev, I.V. Karas’, V.I. Karas’, Ya.B. Fainberg, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2005. — № 1. — С. 143-145. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-789452015-03-25T03:02:07Z Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse Balakirev, V.A. Karas’, I.V. Karas’, V.I. Fainberg, Ya.B. Tolstoluzhsky, A.P. Plasma electronics Nonlinear mechanism of Langmuir wave excitation in dense plasma by intensive laser pulse has been investigated. Laser pulse has frequency ω=ω p /2 (where ω p is electron plasma frequency). Досліджено нелінійний механізм збудження ленгмюровських хвиль у щільній плазмі інтенсивним лазерним імпульсом з частотою ω=ω p /2 (де ω p - електронна плазмова частота). Исследован нелинейный механизм возбуждения ленгмюровских волн в плотной плазме интенсивным лазерным импульсом c частотой ω=ω p /2 (где ω p - электронная плазменная частота). 2005 Article Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse / V.A. Balakirev, I.V. Karas’, V.I. Karas’, Ya.B. Fainberg, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2005. — № 1. — С. 143-145. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.25.Dg, 52.65.Ff, 29.17.+w http://dspace.nbuv.gov.ua/handle/123456789/78945 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Plasma electronics Plasma electronics |
| spellingShingle |
Plasma electronics Plasma electronics Balakirev, V.A. Karas’, I.V. Karas’, V.I. Fainberg, Ya.B. Tolstoluzhsky, A.P. Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse Вопросы атомной науки и техники |
| description |
Nonlinear mechanism of Langmuir wave excitation in dense plasma by intensive laser pulse has been investigated. Laser pulse has frequency ω=ω p /2 (where ω p is electron plasma frequency). |
| format |
Article |
| author |
Balakirev, V.A. Karas’, I.V. Karas’, V.I. Fainberg, Ya.B. Tolstoluzhsky, A.P. |
| author_facet |
Balakirev, V.A. Karas’, I.V. Karas’, V.I. Fainberg, Ya.B. Tolstoluzhsky, A.P. |
| author_sort |
Balakirev, V.A. |
| title |
Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse |
| title_short |
Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse |
| title_full |
Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse |
| title_fullStr |
Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse |
| title_full_unstemmed |
Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse |
| title_sort |
excitation of langmuir oscillations in a semi-infinite dense plasma by laser pulse |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2005 |
| topic_facet |
Plasma electronics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78945 |
| citation_txt |
Excitation of Langmuir oscillations in a semi-infinite dense plasma by laser pulse / V.A. Balakirev, I.V. Karas’, V.I. Karas’, Ya.B. Fainberg, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2005. — № 1. — С. 143-145. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
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| first_indexed |
2025-07-06T03:04:47Z |
| last_indexed |
2025-07-06T03:04:47Z |
| _version_ |
1836865119728959488 |
| fulltext |
EXCITATION OF LANGMUIR OSCILLATIONS
IN A SEMI-INFINITE DENSE PLASMA BY LASER PULSE
V.A. Balakirev, I.V. Karas’, V.I. Karas’, Ya.B. Fainberg, A.P. Tolstoluzhsky
NSC “Kharkov Institute of Physics & Technology”, NAS of the Ukraine, Kharkov, Ukraine,
e-mail: karas@ kipt.kharkov.ua
Nonlinear mechanism of Langmuir wave excitation in dense plasma by intensive laser pulse has been investigated.
Laser pulse has frequency ω=ω p /2 (where ω p is electron plasma frequency).
PACS: 52.25.Dg, 52.65.Ff, 29.17.+w
1. INTRODUCTION
The study of physical mechanisms of a Langmuir
wave excitation in plasma by a laser radiation is of inte-
rest for series of applications and first of all for processes
of acceleration in plasma of electrons and ions (a modern
state of this problem can see from articles [1-7], and
references therein). In the present article a nonlinear
mechanism of a Langmuir wave excitation by laser pulse
which frequency is equal to half of plasma frequency is
explored. Such pulse on the one hand have skin-depth of
penetration in plasma, and with another – currents
induced in plasma and charges on a second harmonic of
radiation are in a resonance with Langmuir oscillations.
2. A STATEMENT OF PROBLEM. THE BASIC
EQUATIONS
From vacuum on semi-infinite homogeneous plasma
normally to its boundary a laser pulse with the given
profile of intensity is incident. A frequency of laser pulse
ω is twice lower than an electron plasma frequency pω .
Such pulse have skin-depth of penetration in plasma. For
the indicated frequency a nonlinear current in plasma
(ponderomotive force) will have a plasma frequency and,
hence, in skin-layer there will be a resonance excitation of
Langmuir waves which from area of a radiant will be
propagate deep into plasmas.
The initial set of equations contains: equations of
motion of an electron component of plasma
m ∂ V
∂t
V ∇V=−e E− e
с
[ V×H ]−
V Te
2
n
∇ n , (1)
an equation of a continuity and also Maxwell equations
for an electromagnetic field ( TeV is a thermal electron
velocity, V
r
is electron velocity, n is an electron density).
After realization of an average procedure we obtain an
expression for nonlinear force.
F nl=
e 2
4mω2 ∇ E t 2 e−2iωtк .с . . (2)
The set of equations for longitudinal perturbations is
equivalent to an equation for a longitudinal electric field
of a Langmuir wave. In a situation considered by us in
plasma the laser radiation intensity damps under the law
a2=a
02 F t / tL exp −2κz , a2=
e2 E
t2
m2 c2 ω2
,.
κ=ω
c −ε ω =3
2
ω p
c
, ε=1 −
ω
p2
ω2
(3)
ε is an permittivity of plasmas. Function F t / t L
describes a laser pulse profile, t L - the reference duration
of laser pulse. With the account (3) equation for a
Langmuir wave field can be noted as follows
∂2 E l
∂ t 2 ωp 2 E l−vTe 2
∂2 E l
∂ z2 =
=−ω p2
mc2
e
κa0 2 F t / tL сosω p te−2κz
(4)
For the further analysis, it is convenient, to insert the
dimensionless variables
τ=ω p t , ς=zω p/ vTe , ψ=E l /E ¿ ,
E¿=
3
2
Em a
02 , Em=
mc ω p
e
.
In these variables the equation (4) takes an form
∂2ψ
∂ τ 2 ψ−∂2ψ
∂ς 2 =−F τ /τL сosτe−ας , (5)
where. τ L=ω p tL , α=3 vTe /c .
3. ANALYTICAL STUDY OF A PROBLEM
Thus, excitation of a Langmuir wave is described by
Klein-Gordon equation with a right part relevant to a
ponderomotive force on a second harmonic of laser
radiation. A frequency of a second harmonic coincides
with a plasma frequency.
Let's consider in the beginning a case of "cold" plasma.
A Langmuir oscillation excitation in this case is described
by an inhomogeneous equation of an oscillator. For
simplicity we shall consider, that laser pulse has the
symmetric profile. After a termination of a laser pulse
action on plasmas the Langmuir oscillations with some
structure of a field are excited. The plasma oscillations are
concentrated in skin-layer. In case of a laser pulse with
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 143-145 143
the Gaussian profile of a laser pulse temporal envelope of
electric field amplitude depends on duration under a
linear law.
The account of thermal energy of plasma electrons will
decrease a plasma oscillations energy in a narrow skin-
layer. The solution of the Klein - Gordon equation,
describing this effect, has been obtained by a method of a
Green function. Expression for a Green function looks
like
G ς*, τ∗=1
2
θ τ∗θ τ∗−ς∗׿
¿¿ J 0τ∗2−ς∗2¿ ,
¿
(6)
where ( )xθ is Heviside function, J0(x) is the Bessel
(cylindrical) function, * , * .ζ ζ ζ τ τ τ′ ′= − = −
Accordingly, the solution of an inhomogeneous equation
of Klein-Gordon can be noted as follows:
¿
ψ τ , ς =−∫
−∞
τ
dτ∗∫
−∞
ζ
dς∗θ τ∗−ς∗cos τ− τ∗
¿ J 0 τ∗2−ς∗2¿ e−α ζ−ς∗F∗ τ− τ∗¿
τ L
,
¿
F*=F/2 (7)
4. ANALYTICAL AND NUMERICAL
RESULTS AND DISCUSSIONS
Let's consider behaviour of a Langmuir wave amplitude
at times essentially exceeding a pulse duration.
It is shown, at high times τ >> ς
p2 ( ς p=ω p L /vTe ,
L is a plasma layer thickness) the plasma oscillation
amplitude diminishes as 1/ 2τ − .
The spatial and temporal distribution of a Langmuir wave electric field excited by laser pulse In dense plasma at
following dimensionless parameters t L=12 , α=0 . 433
For deriving of the complete pattern of nonlinear
process of a Langmuir oscillation excitation by laser pulse
in a dense plasma the Langmuir oscillation elect-ric field
has been calculated numerically with help formula (7) at
the following dimensionless parameters:
12, 0.43Lτ α= = . The profile of laser pulse was
simulated by function F τ /τ L =cos π
2
τ
τ L . For
the laser with a wave length λ =1.05 mµ to the indicated
dimensionless parameters there correspond the following
values of physical quantities: a plasma density
21
0 4.5 10n = ⋅ cm-3, a plasma frequency
15 13.77 10 ,p sω −= ⋅ a plasma electron temperature
T=32 keV. The figure illustrates a detailed pattern of a
Langmuir wave excitation. It is visible, that the Langmuir
wave disturbance is propagated into plasmas. The field in
plasma has oscillation character with the amplitude that
grows from a wave disturbance head to a plasma
boundary. After wave disturbance front propagation past
given space point the electric field oscillates with a
plasma frequency. A dispersion spread of a Langmuir
perturbation reduces in a diminution of a Langmuir
oscillation maximum amplitude. In the dimensional
unities a longitudinal electric field strength is determined
by formula 2
0 03 / 4lE a nψ= (V/cm), where n0 is
plasma density, a0 is laser pulse dimensionless amplitude,
ψ is efficiency coefficient of Langmuir wave excitation.
144
5. SUMMARY
Nonlinear mechanism of Langmuir wave excitation
in dense plasma by intensive laser pulse has been
investigated. A laser pulse that has frequency
ω=ω p /2 propagate normally to boundary of semi-
infinite plasma from vacuum. It is shown, this wave from
source region propagate in plasma volume. In plasma a
field have an oscillator character. Its amplitude increases
from head of wave disturbance to plasma boundary. In
each disturb point of space this field oscillate on plasma
frequency.
The Langmuir disturbance dispersion reduction ensures
the Langmuir oscillation maximum amplitude decreasing.
The longitudinal electric field magnitude have been
determined by relation
2
0 03 / 4lE a nψ= (V/cm),
. It is important note, that in recent article [3] have place
direct experimental evidence of accelerated electron
bunches separated by half the period of the laser light at
irradiation of thick solid targets by laser beam at
relativistic intensities.
The work was supported in part by INTAS project
#01-233 and Foundation of Fundamental Researches of
the Ukraine project # 02.07/213.
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ВОЗБУЖДЕНИЕ ЛEНГМЮРОВСКИХ КОЛЕБАНИЙ В ПОЛУОГРАНИЧЕННОЙ ПЛОТНОЙ ПЛАЗМЕ
ЛАЗЕРНЫМ ИМПУЛЬСОМ
В.A. Балакирев, И.В. Карась, В.И. Карась, Я.Б. Файнберг, А.П. Толстолужский
Исследован нелинейный механизм возбуждения ленгмюровских волн в плотной плазме интенсивным
лазерным импульсом c частотой ω=ω p /2 (где ω p - электронная плазменная частота).
ЗБУДЖЕННЯ ЛEНГМЮРОВСЬКИХ КОЛИВАНЬ У НАПІВОБМЕЖЕНІЙ ЩІЛЬНІЙ ПЛАЗМІ
ЛАЗЕРНИМ ІМПУЛЬСОМ
В.A. Балакірeв, І.В. Карась, В.І. Карась, Я.Б. Файнберг, О.П. Толстолужський
Досліджено нелінійний механізм збудження ленгмюровських хвиль у щільній плазмі інтенсивним лазерним
імпульсом з частотою ω=ω p /2 (де ω p - електронна плазмова частота).
145
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