Nonlinear analysis of the plasma wave decay
Distortions of drift waves form connected with nonlinear processes agreed upon by influence of plasma shear flows on wave are considered. Plasma velocities are directed along line of wave propagation. It is shown that result of such an influence is strong transformation of wave. The overturn is ac...
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irk-123456789-882272015-11-11T03:01:43Z Nonlinear analysis of the plasma wave decay Khvesyuk, V.I. Karbushev, D.N. Фундаментальная физика плазмы Distortions of drift waves form connected with nonlinear processes agreed upon by influence of plasma shear flows on wave are considered. Plasma velocities are directed along line of wave propagation. It is shown that result of such an influence is strong transformation of wave. The overturn is achieved. It leads to wave decay. Розглянуто перекривлення форми дрейфових хвиль, пов’язане з нелінійними процесами, які визвано впливом неоднорідних швидкостей плазми, направленими вздовж лінії розповсюдження хвилі. Показано, що внаслідок такого впливу хвиля істотно перекривлюється аж до перекидання. Це призводить до розпаду хвилі. Рассматриваются искажения формы дрейфовых волн, связанные с нелинейными процессами, вызываемыми воз- действием неоднородных скоростей плазмы, направленных вдоль линии распространения волны. Показано, что в ре- зультате такого воздействия волна существенно искажается, вплоть до опрокидывания. Это ведёт к распаду волны. 2009 Article Nonlinear analysis of the plasma wave decay / V.I. Khvesyuk, D.N. Karbushev // Вопросы атомной науки и техники. — 2009. — № 1. — С. 72-73. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 52.35.Qz; 52.55.Lf; 52.25.Fi http://dspace.nbuv.gov.ua/handle/123456789/88227 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Фундаментальная физика плазмы Фундаментальная физика плазмы |
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Фундаментальная физика плазмы Фундаментальная физика плазмы Khvesyuk, V.I. Karbushev, D.N. Nonlinear analysis of the plasma wave decay Вопросы атомной науки и техники |
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Distortions of drift waves form connected with nonlinear processes agreed upon by influence of plasma shear flows
on wave are considered. Plasma velocities are directed along line of wave propagation. It is shown that result of such an
influence is strong transformation of wave. The overturn is achieved. It leads to wave decay. |
| format |
Article |
| author |
Khvesyuk, V.I. Karbushev, D.N. |
| author_facet |
Khvesyuk, V.I. Karbushev, D.N. |
| author_sort |
Khvesyuk, V.I. |
| title |
Nonlinear analysis of the plasma wave decay |
| title_short |
Nonlinear analysis of the plasma wave decay |
| title_full |
Nonlinear analysis of the plasma wave decay |
| title_fullStr |
Nonlinear analysis of the plasma wave decay |
| title_full_unstemmed |
Nonlinear analysis of the plasma wave decay |
| title_sort |
nonlinear analysis of the plasma wave decay |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2009 |
| topic_facet |
Фундаментальная физика плазмы |
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http://dspace.nbuv.gov.ua/handle/123456789/88227 |
| citation_txt |
Nonlinear analysis of the plasma wave decay / V.I. Khvesyuk, D.N. Karbushev // Вопросы атомной науки и техники. — 2009. — № 1. — С. 72-73. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T15:59:17Z |
| last_indexed |
2025-07-06T15:59:17Z |
| _version_ |
1836913849117179904 |
| fulltext |
NONLINEAR ANALYSIS OF THE PLASMA WAVE DECAY
V.I. Khvesyuk, D.N. Karbushev
Bauman Moscow State Technical University, Moscow, Russia, E-mail: khves@power.bmstu.ru
Distortions of drift waves form connected with nonlinear processes agreed upon by influence of plasma shear flows
on wave are considered. Plasma velocities are directed along line of wave propagation. It is shown that result of such an
influence is strong transformation of wave. The overturn is achieved. It leads to wave decay.
PACS: 52.35.Qz; 52.55.Lf; 52.25.Fi
1. INTRODUCTION
Voluminous literature devotes problem of suppression
of plasma instabilities by shear flows [1-6] etc. In order to
solve this problem different approaches are proposed. In
this work firstly approach based on analysis of distortion
of drift wave shape is considered.
It is well-known variety of nonlinear wave processes
and methods of them investigations. One of directions of
analysis these phenomena is investigation of transforma-
tion of wave form and possible following them decay [7,
8, 9] also [10] and the references quoted therein. Within
the framework of such analysis finite waves amplitudes
and transformations of forms of waves are taken into ac-
count. In much in the same way sonic waves, sea waves
and ion – sonic waves were investigated [7-10]. Taking
into account of finite value of wave amplitude leads to
distortion of originally harmonic wave and increasing
steepness of wave shape. This statement is correctly both
for waves in gases and waves in plasmas [9].
In this work similar task is considered in connection
with drift waves in plasma under influence velocity shear
plasma along wave velocity. It is necessary to keep in
view important features of drift waves. Firstly motion of
plasma particles in drift waves is transverse with respect
to velocity propagation of wave. Secondly drift waves are
unstable consequently it is necessary to take into account
exponential increase of wave amplitude. The last feature
did not consider till now. It is shown that distortion of
originally harmonic form leads to overturn and decay of
waves. Similar decay of drift waves was observed in ex-
perimental work [11].
This task is solved using two differ variety of approxi-
mations.
2. METHOD OF INDEPENDENT PAR-
TICLES
This method is very simple and convenient in order to
solve such a task. But it provides correct solution for
weak deviations from sinusoidal wave shape in original
linear state. Therefore it is possible to obtain only qualita-
tive solution in such an approach.
It is considered propagation of drift wave mode inside
slab parallel yOz plate. Axis Ox is directed along gradient of
plasma density and plasma temperature. Magnetic field is di-
rected along Oz axis. Transverse with respect to magnetic
field component of drift wave is propagated along axis Oy.
First of all some results of analysis of particles motion in
drift wave is presented using a simple method based on solu-
tion of 2D set equations. Coordinate system is connected
Fig. 1. The trajectory of charged particle inside drift
wave having constant amplitude a
Fig. 2. The trajectory of charged particle inside drift
wave having exponential increasing amplitude
with moving wave. Then for wave of constant amplitude a
trajectory of every charged particle is ellipse (Fig. 1)
1
)( 2
2
2
2
=+
aA
y
a
x
.
Here A is constant in formula Axv y = . For wave with
exponential increasing amplitude trajectory of particle is
spiral (Fig. 2). In parametric form equations of spiral are
)()exp()( tSintatx ωγ= ,
[ ]{ }γωωωγγ
γω
−−
+
= )()()exp()( 22 tSintCostAaty
Lower hydrodynamic approach is considered.
72 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1.
Series: Plasma Physics (15), p. 72-73.
3. HYDRODYNAMIC METHOD
Hydrodynamic approach is based on the following
starting points. Velocity distribution along direction of
wave propagation (Oy axis) is given. Plasma density is
taken as compressible. In cross direction with respect to
the wave propagation (Ox axis) the particles motion is
taken into account as electrical drift. One is determined
by electric field arising because of density gradients along
Oy axis.
The main advantage this model is possibility of to
consider essentially nonlinear stages wave existence.
Then the overturn is achieved. Corresponding numerical
results are presented in Fig. 3, 4. On these Figs. compari-
son harmonic and perturbed waves is presented.
1tt =
2tt =
3tt =
Fig. 3. Dynamics of drift wave mode under influence of
velocity shear, Axv y = . Moment 3t corresponds to
condition equality infinity of derivative perturbed wave
)2(3 At < )(3 At
Fig. 4. Dynamics of drift wave mode under influence of
velocity shear, Axv y 2= . In moment of achievement of
overturn amplitude value of wave less than in the case
when Axv y =
4. CONCLUSIONS
It is shown that influence of shear flow on drift wave
leads to wave overturn. It means following decay of
wave. Added analysis shows that wave decay can take
place before achievement overturn namely when gradient
density in wave yn ∂∂ / and gradient density in plasma
xn ∂∂ /0 will become equal. From estimations follows that
this equality appears earlier than overturn.
REFERENCES
1. H. Biglari, H.D. Diamond, P.W. Terry // Phys. Fluids.
1990, v. B2, p. 1.
2. S. Hamaguchi, W. Horton // Phys. Fluids, 1992, v. B4,
p.319.
3. J.Q. Dong, W. Horton// Phys. Fluids.1993, v.B5, p.1581.
4. K.H. Burrel, E.J. Doyl, P. Gohil et al // Phys. Plasmas.
1994, v. 1, p. 1536.
5. K.H. Burrel // Phys. Plasmas. 1997, v. 1, 4, p. 1499.
6. W.X. Wang, T.S. Hahm, W.W. Lee et al // Phys.
Plasmas. 2007, v. 14, p. 072306.
7. L.D.Landau, E.M.Lifshits. Hydrodynamics. Moscow:
“Nauka”, 2006.
8. G.B.Whithem. Linear and nonlinear waves. New York,
Toronto, London, Sydney: “John Wiley & Sons”, 1974.
9. R.Z.Sagdeev// Voprosy teorii plasmy. 1964, v. 4, p. 20.
10. G.M.Zaslavsky, R.Z.Sagdeev. Introduction to
nonlinear physics. Moscow: “Nauka”, 1988.
11.A.E. Petrov, K.A. Sarksyan, N.N. Skvortsova,
N.K. Kharchev // Fizika plasmy. 2001, v. 27, p. 58.
Article received 22.09.08
НЕЛИНЕЙНЫЙ АНАЛИЗ РАСПАДА ПЛАЗМЕННОЙ ВОЛНЫ
В.И. Хвесюк, Д.Н. Карбушев
Рассматриваются искажения формы дрейфовых волн, связанные с нелинейными процессами, вызываемыми воз-
действием неоднородных скоростей плазмы, направленных вдоль линии распространения волны. Показано, что в ре-
зультате такого воздействия волна существенно искажается, вплоть до опрокидывания. Это ведёт к распаду волны.
НЕЛІНІЙНИЙ АНАЛІЗ РОЗПАДУ ПЛАЗМОВОЇ ХВИЛІ
В.І. Хвесюк, Д.М. Карбушев
Розглянуто перекривлення форми дрейфових хвиль, пов’язане з нелінійними процесами, які визвано
впливом неоднорідних швидкостей плазми, направленими вздовж лінії розповсюдження хвилі. Показано, що
внаслідок такого впливу хвиля істотно перекривлюється аж до перекидання. Це призводить до розпаду хвилі.
73
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