Surface wave control in plasma-metal structures with perpendicular magnetic field
The nonlinear interaction of high-frequency potential surface waves at a dense magnetized plasma-metal interface with a low-frequency plasma density modulation is considered in the point of view to control the surface waves. The influence of an external steady magnetic field directed perpendicularly...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | Surface wave control in plasma-metal structures with perpendicular magnetic field / Yu.A. Akimov, N.A. Azarenkov, V.P. Olefir // Вопросы атомной науки и техники. — 2005. — № 1. — С. 69-71. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859886442739662848 |
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| author | Akimov, Yu.A. Azarenkov, N.A. Olefir, V.P. |
| author_facet | Akimov, Yu.A. Azarenkov, N.A. Olefir, V.P. |
| citation_txt | Surface wave control in plasma-metal structures with perpendicular magnetic field / Yu.A. Akimov, N.A. Azarenkov, V.P. Olefir // Вопросы атомной науки и техники. — 2005. — № 1. — С. 69-71. — Бібліогр.: 9 назв. — англ. |
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| description | The nonlinear interaction of high-frequency potential surface waves at a dense magnetized plasma-metal interface with a low-frequency plasma density modulation is considered in the point of view to control the surface waves. The influence of an external steady magnetic field directed perpendicularly to the interface and plasma parameters on temporal dynamics of the waves is studied.
Розглянуто нелінійну взаємодію високочастотних поверхневих хвиль, що розповсюджуються вздовж межі густої магнітоактивної плазми з металом, із низькочастотними збуреннями густини плазми з точки зору контро лю за поверхневими хвилями. Вивчено вплив зовнішнього магнітного поля, перпендикулярного до межі розподілу, та параметрів плазми на часову динаміку хвиль.
Рассмотрена возможность использования нелинейного взаимодействия высокочастотных поверхностных волн, распространяющихся на границе “плотная магнитоактивная плазма-металл”, c низкочастотными возмущениями плотности плазмы для управления поверхностными волнами. Исследовано влияние постоянного магнитного поля, перпендикулярного границе, и параметров плазмы на временную динамику волн.
|
| first_indexed | 2025-12-07T15:53:00Z |
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SURFACE WAVE CONTROL IN PLASMA-METAL STRUCTURES
WITH PERPENDICULAR MAGNETIC FIELD
Yu.A. Akimov, N.A. Azarenkov, V.P. Olefir
Department of Physics and Technology, Institute of High Technologies,
Kharkiv National University, Kharkiv, Ukraine,
E-mail: olefir@pht.univer.kharkov.ua; Fax: (057) 3353977; Tel: (057) 3350509
The nonlinear interaction of high-frequency potential surface waves at a dense magnetized plasma-metal interface
with a low-frequency plasma density modulation is considered in the point of view to control the surface waves. The in
fluence of an external steady magnetic field directed perpendicularly to the interface and plasma parameters on tempo
ral dynamics of the waves is studied.
PACS: 52.35.Mw
1. INTRODUCTION
At the present time plasma-metal waveguides are
widely used in plasma and semiconductor electronics, gas
discharges, and various plasma technologies [1]. It causes
the intensive theoretical and experimental studies of wave
processes in plasma-metal structures.
In practice many types of waveguide structures oper
ate with a magnetic field oriented perpendicularly to a
plasma-metal boundary [2-5]. Such waveguides are typi
cal of RF and microwave discharge, magnetrons, Penning
sources, magnetic discharge pumps, Hall detectors, diver
tor- and limiter-equipped fusion systems, and so on. Espe
cially such configuration of magnetic field is very impor
tant for plasma processing, because the best macroscopic
processing uniformity is achieved when the magnetic
field is perpendicular to the substrate.
As well known, the propagation of SWs at a cold plas
ma-metal interface with a perpendicular magnetic field is
impossible, whereas it is possible in a warm plasma. The
linear theory of potential SWs at a plane boundary of a
warm plasma with a metal in such magnetic field configu
ration has been considered in [2, 3]. Some nonlinear
mechanisms of these SWs at a dense plasma have been
investigated, for example, in [6, 7].
In order to control the SWs, their nonlinear attenua
tion due to the nonlinear dynamics of the plasma particles
can be used. In this paper we pay attention to the control
of the high-frequency SW at the presence of a normal to
the plasma-metal interface steady magnetic field by
means of a low-frequency plasma density modulation.
2. FORMULATION
Let us consider a planar waveguide structure consist
ing of a nonisothermal ( T e >>T i , where T e and T i
are the electron and ion plasma temperatures, respective
ly) magnetized plasma that occupies the half-space
x0 and is bounded in the plane x=0 by a perfect
conducting metal. An external steady magnetic field is
supposed to be directed along the axis x .
According to paper [2], a finiteness of the electron
thermal velocity V Te in such planar waveguide struc
tures causes the existence of high-frequency (HF) poten
tial SWs in the frequency region greater than the electron
cyclotron frequency. Below we will consider the HF SW
in a high-density plasma, when the SW frequency is into
the range ωce
2 ω1
2 << ω pe
2 , where ωce , ω pe are the
electron cyclotron and plasma frequencies, accordingly.
Hereinafter all quantities corresponding to the HF SW of
a finite amplitude we will note with the index 1, so in this
frequency region the HF SW potential can be written in
the following form:
ϕ 1=A1[ exp−λ1
' x −exp −λ1
'' x ]exp[ i k 1 y−ω1 t ]
, (1)
where A1 is the HF SW amplitude, λ1
' and λ1
'' de
termine penetration depth of the wave fields into the plas
ma. The wavenumber k1 is given by:
k1=ω1/V Teω1
2−ωce
2 /ω pe
2 . (2)
In order to study a possibility of the SW control, let us
consider the nonlinear interaction of HF SW with a low-
frequency (LF) plasma density modulation
δn r , t =δn x exp [ i k 2 y−ω2 t ] . The LF
wave frequency ω2 and its wavenumber k2 are sup
posed to be such that ∣ω2∣<<∣ω1∣ , ∣k 2∣<<∣k 1∣ . It is
well known that a plasma density modulation can essen
tially influence on SW stability. Below we will consider
the following three low-frequency regions:
1) ω2
2 << ωci
2 , ω pi
2 ; 2) ωci
2 << ω2
2 << ω pi
2 ;
3) ωci
2 , ω pi
2 << ω2
2 << ωce
2
( ωci , ω pi are the ion cyclotron and plasma frequen
cies). An interaction of those modulations with the HF
wave results in the excitation of long-wave (
k−=k 1−k 2 , ω−=ω1−ω2 ) and short-wave (
k=k 1k 2 , ω=ω1ω2 ) satellites of the HF
SW. In such system two kinds of interaction of HF, LF
waves and satellites are possible [8]. The resonant interac
tion is realized, when one of the satellites and the LF per
turbation are eigen waves of the waveguide structure. An
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 69-71 69
0,0 0,5 1,0 1,5 2,0 2,5
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
IA2I/IA20I
tν
1
0.0
2.0
3.0
4.0
IIm QI IA10I
2/ ν1 =5.0
Fig. 1. Time evolution of the LF perturbation amplitude
for different values of the parameter ∣Q∣∣A10∣
2 /ν1
other kind of interaction is non-resonant, when only the
satellites are eigen.
One can show that in such structure the conditions of
resonant interaction are not fulfilled, whereas the non-res
onant type of interaction is possible. It takes place, when
the LF wave has a phase velocity which is close to the HF
SW wave group velocity V gr=∂ω1/∂ k 1 :
ω2=∑
n=0
∞
[ k 2
2n1/ 2n1 ! ]∂2n V gr k1 /∂ k 1
2n≈k 2V gr
. (3)
One can show, the LF wave with dispersion relation (3)
can be represented as a superposition of the forced oscilla
tions of surface and volume types. Thus, in the structure un
der consideration the nonlinear dissipation of the HF wave
energy takes place. It is caused by HF wave energy transport
from the interaction region near the plasma-metal interface
deep into plasma by the radiation part of the LF wave.
3. HF SW INSTABILITY CRITERION
The volume part of the LF plasma density
perturbations results in an additional attenuation of the
HF surface wave. In order to study this phenomenon, let
us, following to [8], write the nonlinear equation set for
the HF SW and its satellites, which corresponds to the
nonlinear dispersion relation:
i∂ A1
∂ t
V gr
∂ A1
∂ y iν1 A1=Q¿ A1 A
¿ A1
¿ A− A
Q A1
¿ AA1 A−
¿ A−,
i∂A
∂ t V gr
∂ A
∂ y iν1 A=Q A1
¿ AA1 A−
¿ A1 ,
i∂ A−
∂ t V gr
∂ A−
∂ y iν1 A−=Q¿ A1 A
¿ A1
¿ A− A1 ,
¿}¿ }¿}¿
¿¿
(4)
where ν1 is a linear decrement of the collision attenua
tion of the HF surface wave and its satellites; parameter
Q is complex and defined by considered LF regions:
1) Q=− i
16
e2
me
2 V Te
4
ω2
2∣ωci∣
ω pi
3
ω1
2−ωce
2 3/2
ω1ω pe
;
2) 222
11
6
2/322
1
4
2
5
42
2
)2(
)(
16 cepi
cepe
TeeVm
eiQ
ω−ωωω
ω−ωωω
−= ; (5)
3) Q=−i 5
3
e2
me
2 V Te
4
ω1
3∣ωce∣ω1
2−ωce
2 3/2
ω2
22ω1
2−ωce
2 2
.
Due to the complication of this equation set, it can be
investigated only numerically. Below we will consider the
temporal variation of the HF SW and its satellites ampli
tudes in the case, when ∂ A1 ± /∂ y=0 . The results of
numerical solution of the LF perturbation amplitude are
represented in fig. 1.
In a case of rather small initial values of the HF SW
amplitude, when ∣Q∣∣A10∣
2 /ν1<< 1 (hereinafter the
index 0 corresponds to the initial values of the wave am
plitudes), the LF wave attenuation can be described by
∣A2∣=∣A20∣exp −2ν1 t . It means, the HF SW and
its satellites attenuation is caused only by electron colli
sions. But, if the following condition
∣Q∣∣A10∣
2 /ν14 (6)
is fulfilled then at initial stage of the waves interaction a
growth of the LF perturbations and satellites with a simul
taneous decrease of the HF SW amplitude takes place.
Thus, an increase of the parameter ∣Q∣∣A10∣
2 /ν1
leads to a more intensive growth of the LF wave ampli
tude and to a more intensive attenuation of the HF SW,
consequently. The condition (6) corresponds to the case,
when a growth of the satellites due to their nonlinear in
teraction with the HF and LF waves exceeds their colli
sion decrease. This condition determines an amplitude
threshold value of the HF SW, at which the instability is
possible.
The carried out analysis has shown that the SWs of a
small amplitude are stable with respect to the low-fre
quency plasma density modulation for the frequency re
gion ω2
2 << ω pi
2 , ωci
2 and unstable for
ωci
2 << ω2
2 << ω pi
2 and ωci
2 , ω pi
2 << ω2
2 << ωce
2 .
In the second range, ωci
2 << ω2
2 << ω pi
2 , the HF
SW amplitude threshold ∣A10∣cr , at excess of which the
SW instability appears, grows with an increase of the
electron temperature and the plasma density and decreas
es with frequency ω2 : ∣A10∣cr∝ω2
−2no
1 /4V Te
2 . An
increase of the external magnetic field results in growth of
value ∣A10∣cr . Thus, the most influence of the plasma
density modulation is achieved at rather high frequencies
ω2≈0, 3 ω pi in the limit of unmagnetized plasma
with rather small density and weak electrons thermal mo
tion.
70
1 10 100
0,0
0,5
1,0
1,5
2,0
2,5
|A10|cr, V
ω2/(2π), МHz
Fig.2. Influence of ω2 on ∣A10∣cr
In the third LF range, ωci
2 , ω pi
2 << ω2
2 << ωce
2 , the
SW initial amplitude threshold ∣A10∣cr grows with the
electron temperature and the LF plasma density modula
tion frequency as ∣A10∣cr∝ω2V Te
2 . The analysis of
magnetic field influence on ∣A10∣cr shows, the thresh
old value has a minimum at ωce=2 /5 ω1 . Thus, the
most influence of the plasma density modulation takes
place in the region of rather high frequencies when
ω2≈3 ω pi , as well as in the case of a weak electron
thermal motion of the plasma immersed in a steady mag
netic field with intensity close to 2 /5 ω1 me c /e .
Below we will estimate the initial HF SW amplitude
threshold in the case of etching of tungsten films in a
magnetoplasma sustained by microwaves. Under the ex
perimental conditions [9] the low-pressure pure SF6
discharge for electron cyclotron resonance etching is
characterized by the pressure p =5 mTorr, plasma densi
ty no≈1 .3 ⋅1012 см-3, average electron temperature
3.2 eV and electron collision frequency ν1 =50 MHz,
immersed into the magnetic field H o≈875 Oe. In that
case the instability of HF SW with
ω1/2π =ω pe /4π = 5 GHz relatively to the LF
perturbations from the range ω2/ 2π =(1 ¿ 7) MHz
appears at small enough amplitudes: ∣A10∣ > (2.25 ¿
0.045) V (see fig.2). It corresponds to ∣E10∣ >(1.11 ¿
0.023) kV/cm for the HF SW electric field at the plasma-
metal interface. Relatively to the LF modulation from the
range ω2/ 2π =(65 ¿ 825) MHz, the FH SW is unsta
ble at ∣A10∣ >(0.021 ¿ 0.3) V or ∣E10∣ >(0.11 ¿ 0.144)
kV/cm.
These estimates show that, under the etching condi
tions [9], the low-frequency plasma density modulation
from the ranges ωci
2 << ω2
2 << ω pi
2 and
ωci
2 , ω pi
2 << ω2
2 << ωce
2 can be effectively used for
the HF SWs control, in contrast to the case of
ω2
2 << ωci
2 , ω pi
2 .
REFERENCES
[1] M. Moisan, J. Hurbert, J. Margot, Z. Zakrzewski. The
Development and Use of Surface-Wave Sustained
Discharges for Applications // Advanced Technologies
Based on Wave and Beam Generated Plasmas / Aca
demic Publisher, Kluwer, Amsterdam, 1999, pp. 1-49.
[2] N.A. Azarenkov, A.N. Kondratenko, Yu.O. Tishetskiy
// Tech. Phys. (69). 1999, p. 30.
[3] Yu.A. Akimov, N.A. Azarenkov, V.P. Olefir // Phys.
Scr. (70). 2004, p. 33.
[4] D.P. Schmidt, N.B. Meezan, W.A. Hargus Jr, M.A.
Cappelli // Plasma Sources Sci. Technol. (9). 2000, p.
68.
[5] A.V. Nedospasov, M.Z. Tokar' // Sov. Voprosy teorii
plasmy. (18). 1990, p. 68.
[6] N.A. Azarenkov, Yu.A. Akimov, V.P. Olefir // Tech.
Phys. (49). 2004, p. 39.
[7] N.A. Azarenkov, Yu.A. Akimov, V.P. Olefir // Plas
ma Phys. Reports. (29). 2003, p. 669.
[8] J.C. Weiland, H. Wilhelmsson. Coherent non-linear
interaction of waves in plasma. Oxford: “Pergamon
press”, 1977.
[9] F. Bounasri et al. // J. Appl. Phys. (77). 1995, p. 4030.
УПРАВЛЕНИЕ ПОВЕРХНОСТНЫМИ ВОЛНАМИ В ПЛАЗМЕННО-МЕТАЛЛИЧЕСКИХ
СТРУКТУРАХ С ПЕРПЕНДИКУЛЯРНЫМ МАГНИТНЫМ ПОЛЕМ
Ю.А. Акимов, Н.А. Азаренков, В.П. Олефир
Рассмотрена возможность использования нелинейного взаимодействия высокочастотных поверхностных
волн, распространяющихся на границе “плотная магнитоактивная плазма-металл”, c низкочастотными возму
щениями плотности плазмы для управления поверхностными волнами. Исследовано влияние постоянного маг
нитного поля, перпендикулярного границе, и параметров плазмы на временную динамику волн.
КЕРУВАННЯ ПОВЕРХНЕВИМИ ХВИЛЯМИ У ПЛАЗМОВО-МЕТАЛЕВИХ СТРУКТУРАХ ІЗ
ПЕРПЕНДИКУЛЯРНИМ МАГНІТНИМ ПОЛЕМ
Ю.О. Акімов, М.О. Азаренков, В.П. Олефір
Розглянуто нелінійну взаємодію високочастотних поверхневих хвиль, що розповсюджуються вздовж межі
густої магнітоактивної плазми з металом, із низькочастотними збуреннями густини плазми з точки зору контро
лю за поверхневими хвилями. Вивчено вплив зовнішнього магнітного поля, перпендикулярного до межі роз
поділу, та параметрів плазми на часову динаміку хвиль.
71
|
| id | nasplib_isofts_kiev_ua-123456789-78657 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:53:00Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Akimov, Yu.A. Azarenkov, N.A. Olefir, V.P. 2015-03-19T18:04:12Z 2015-03-19T18:04:12Z 2005 Surface wave control in plasma-metal structures with perpendicular magnetic field / Yu.A. Akimov, N.A. Azarenkov, V.P. Olefir // Вопросы атомной науки и техники. — 2005. — № 1. — С. 69-71. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.35.Mw https://nasplib.isofts.kiev.ua/handle/123456789/78657 The nonlinear interaction of high-frequency potential surface waves at a dense magnetized plasma-metal interface with a low-frequency plasma density modulation is considered in the point of view to control the surface waves. The influence of an external steady magnetic field directed perpendicularly to the interface and plasma parameters on temporal dynamics of the waves is studied. Розглянуто нелінійну взаємодію високочастотних поверхневих хвиль, що розповсюджуються вздовж межі густої магнітоактивної плазми з металом, із низькочастотними збуреннями густини плазми з точки зору контро лю за поверхневими хвилями. Вивчено вплив зовнішнього магнітного поля, перпендикулярного до межі розподілу, та параметрів плазми на часову динаміку хвиль. Рассмотрена возможность использования нелинейного взаимодействия высокочастотных поверхностных волн, распространяющихся на границе “плотная магнитоактивная плазма-металл”, c низкочастотными возмущениями плотности плазмы для управления поверхностными волнами. Исследовано влияние постоянного магнитного поля, перпендикулярного границе, и параметров плазмы на временную динамику волн. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Surface wave control in plasma-metal structures with perpendicular magnetic field Керування поверхневими хвилями у плазмово-металевих структурах із перпендикулярним магнітним полем Управление поверхностными волнами в плазменно-металлических структурах с перпендикулярным магнитным полем Article published earlier |
| spellingShingle | Surface wave control in plasma-metal structures with perpendicular magnetic field Akimov, Yu.A. Azarenkov, N.A. Olefir, V.P. Basic plasma physics |
| title | Surface wave control in plasma-metal structures with perpendicular magnetic field |
| title_alt | Керування поверхневими хвилями у плазмово-металевих структурах із перпендикулярним магнітним полем Управление поверхностными волнами в плазменно-металлических структурах с перпендикулярным магнитным полем |
| title_full | Surface wave control in plasma-metal structures with perpendicular magnetic field |
| title_fullStr | Surface wave control in plasma-metal structures with perpendicular magnetic field |
| title_full_unstemmed | Surface wave control in plasma-metal structures with perpendicular magnetic field |
| title_short | Surface wave control in plasma-metal structures with perpendicular magnetic field |
| title_sort | surface wave control in plasma-metal structures with perpendicular magnetic field |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78657 |
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