About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves
The kinetic equation for plasma in two-dimensional non-uniform field of a surface wave was obtained. At the approximation of predetermined field there were found the distribution functions in dependence on the value of a coefficient of spatial attenuation. With using such distribution functions such...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2003 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/110491 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves / N.A. Azarenkov, Vl.V. Gushchin,V.V. Gushchin // Вопросы атомной науки и техники. — 2003. — № 1. — С. 92-94. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859803326127800320 |
|---|---|
| author | Azarenkov, N.A. Gushchin, Vl.V. Gushchin, V.V. |
| author_facet | Azarenkov, N.A. Gushchin, Vl.V. Gushchin, V.V. |
| citation_txt | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves / N.A. Azarenkov, Vl.V. Gushchin,V.V. Gushchin // Вопросы атомной науки и техники. — 2003. — № 1. — С. 92-94. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The kinetic equation for plasma in two-dimensional non-uniform field of a surface wave was obtained. At the approximation of predetermined field there were found the distribution functions in dependence on the value of a coefficient of spatial attenuation. With using such distribution functions such plasma characteristics as density, frequency of elementary processes, diffusion coefficients, number of particles falling down to the wall, were calculated. There was shown that in high frequency electric field transport may also have anisotropic character. Taking this into account the “correct” hydrodynamic equations were obtained. Comparison with earlier known results was carried out. As result of this work it is possible to state – taking into account the non-equilibrium and nonlocal properties is important for description of discharges sustained with surface waves.
Отримано кінетичне рівняння для плазми у двомірнонеоднорідному полі поверхневої хвилі. У наближенні сталого поля знайдено вирази для функцій розподілу у залежності від величини коефіцієнту просторового послаблення. За допомогою цих функцій розподілу підраховано такі характеристики плазми, як густина плазми, частоти елементарних процесів, коефіцієнти дифузії, кількість частинок, що потрапляють на стінки. Наведено, що у високочастотному електричному полі перенос також може носити анізотропний характер. З урахуванням цього отримано „вірні” гідродинамічні рівняння. Проведено порівняльний характер з раніше відомими результатами. Як підсумок роботи можливо стверджувати, що урахування нерівноважності та не локальності важливо, якщо описувати розряди, що підтримуються поверхневими хвилями.
Получено кинетическое уравнение для плазмы в двумернонеоднородном поле поверхностной волны. В приближении заданного поля найдены выражения для функций распределения в зависимости от величины коэффициента пространственного ослабления. С помощью этих функций распределения посчитаны такие характеристики плазмы как плотность, частоты элементарных процессов, коэффициенты диффузии, количество частиц, попадающих на стенки. Показано, что в высокочастотном электрическом поле перенос тоже может носить анизотропный характер. С учетом этого получены «правильные» гидродинамические уравнения. Проведен сравнительный анализ с ранее известными результатами. Как итог работы можно утверждать – учет неравновесности и нелокальности важен при описании разрядов, поддерживаемых поверхностными волнами.
|
| first_indexed | 2025-12-07T15:14:48Z |
| format | Article |
| fulltext |
ABOUT INFLUENCE OF EFFECTS NONEQUILIBRITY AND
NONLOCALITY ON THE PARAMETERS OF THE DISCHARGE
SUSTAINED BY SURFACE WAVES
N.A.Azarenkov, Vl.V.Gushchin,V.V.Gushchin
Kharkov National V.N. Karazin University
The kinetic equation for plasma in two-dimensional non-uniform field of a surface wave was obtained. At the
approximation of predetermined field there were found the distribution functions in dependence on the value of a
coefficient of spatial attenuation. With using such distribution functions such plasma characteristics as density,
frequency of elementary processes, diffusion coefficients, number of particles falling down to the wall, were calculated.
There was shown that in high frequency electric field transport may also have anisotropic character. Taking this into
account the “correct” hydrodynamic equations were obtained. Comparison with earlier known results was carried out.
As result of this work it is possible to state – taking into account the non-equilibrium and nonlocal properties is
important for description of discharges sustained with surface waves.
PACS: 52.80.-s
It is well known, that a field of a surface wave is two-
dimensionally non-uniform [1], for example in the
cylinder it penetrated on radius and attenuates along a
direction of propagation. Usually kinetic theory of the
discharge sustained surface waves (SW), for example,
axial – symmetric is built in approach of axial uniform of
a field [2,3]. This assumption simplified the problem. It is
valid only in approach of a “thin” waveguide, when it is
possible really to neglect by attenuation of a wave
stipulated by Coulomb collisions. However, if resonant
attenuation SW to take into account stipulated by
transformation SW in body waves [1,4-5] the situation
sharply varies.
In the kinetic equation it is necessary to take into
account addends which are proportional to lapse rates of a
distribution function. The factors facing to these addends
are proportional to coefficient of spatial attenuation α .
Generally they contain the additive contribution from
three mechanisms: Coulomb collisions, Landau’s
mechanism and transformation of waves in a point of a
plasma resonance [1].
The kind of the solution of the kinetic equation
depends on value of coefficient of spatial attenuation. At
rather small coefficients of spatial attenuation (without
the account of resonant attenuation contribution from
addends proportional to lapse rates is possible to take into
account on a perturbation theory to lapseless to the local
solution [6]. If attenuation is not a little (all three
mechanisms of attenuation), for the degree laws of
dependence of a field from coordinate both collision and
ionization frequencies from energy are taken into account
21 210 )(,)(,)(,)( l
z
l
r
q
ion
p
en rErErErE ==θ ε=ενεν=εν
2
),(
2mvzreu A =ϕ−=ε (1)
where: enν frequency of quasi-elastic collisions, ionν
frequency of ionization, 2,1E amplitudes of radial and
axial components of a field of a wave accordingly, ε a
kinetic energy of electrons, Aϕ ambipolar potential, u a
total energy of electrons, me, a charge and mass of
particles accordingly, θν ,0 - constants independing from
energy, 21,,, llqp numbers; than it is possible to find the
automodel solution of the kinetic equation:
ββ =ξξ=
u
r
r
fruf ,)(),(0 (2)
where β and 1β are numbers.
At rather small coefficients of spatial attenuation
EDF represents local distribution with distortion in the
field of major energies (in a tail part EDF), since
e
A
e
A
e T
m
EeT
e
T
eT >α
δ ω
+
ϕϕ=ε 31
2
22
0
*
1 )
3
)((
, (3)
where: eT - "temperature" of electrons, 0T temperature
of neutral gas, δ - part of energy, transmitted at one
collision, ω frequency of a field SW.
If attenuation is not a little, then "body" EDF is
subject also to distortion, and the distortion in the field of
a tail begins at smaller values of energy *
1
*
2 ε<ε<eT .
The depletion EDF is characteristic for both cases in the
field of a tail, i.e. the waning EDF goes faster, than
exponential curve. Hence, EDF becomes nonmaxwellian
and nonlocal, since depends on a field in across section.
The basic difficulty of the theory of non-uniform gas-
discharge plasma is stipulated by the following factors:
the spatial distribution of a field beforehand, as a rule, is
not known. It is determined by a lateral view of
concentration and source distribution of ionization, i.e.
shape of electrons distribution function. And the electrons
distribution function (EDF), in turn, is shaped by a field
[6]. This complexity bypass as follows. The kinetic
equation is solved in approach of a given field. In our case
it is equivalent to the task of a lateral view of ambipolar
potential (field of a surface wave obeys to Maxwell
equations, therefore it is considered as given). Its lateral
view is selected as degree function [7]. At local
distribution EDF is possible to present as:
)()(),( 00 ufrnruf = (4)
where the function 0f is normalized on unity:
1)(24
0
03 =π ∫
∞
duufu
m
(5)
92 Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 92-94
In a nonlocal case factorized EDF is impossible,
therefore it is normalized on density:
duzrufu
m
zrn ),,(24),( 0
0
3 ∫
∞
π= (6)
Now, knowing EDF and setting ambipolar potential
distribution as degree function [7]:
wall
pp
wallA R
r
L
z ϕ−−−−ϕ=ϕ )})(1)(]12[1{( 21 (7)
where: R-radius of a wave guide, L- length of the
discharge (distance on which density of plasma decreases
from the peak value 0n up to underload crn ), wallϕ -
potential of a wall (thus ambipolar potential can not
exceed potential of a wall). From this requirement we
determine spatial distributions of density (both radial, and
axial):
−
−−∝
21
1121),(
pp
R
r
L
zzrn (8)
Their analysis shows difference of radial density
distribution from the Bessel function of an order zero, and the
axial distribution has nonlinear character.
If we know EDF, the ambipolar field distribution and
transport coefficients, then we can find the kinetic coefficients,
such as frequency of ionization and excitation frequency,
complete number of inelastic collisions and quantity of
particles hitting on walls. In other words, it is possible to
obtain many parameters of the discharge within the
framework of the simplified theory and qualitatively to
estimate a role of effects of a non-equilibrium and nonlocality.
Many theories of the discharge are grounded on the
hydrodynamic approach [8,9]. It’s much easier and
consequently so attractively. On their basis the model
operation explicates also in view of two-dimensional
inhomogeneity and nonlinearity [10]. But an overwhelming
majority of these operations guess, background EDF is
nonmaxwellian. As the minimum three reasons exist in real
laboratory plasma on which EDF is declined from
equilibrium: spatial boundedness, presence of an external field
and inelastic processes. What will be with these results if to
take into account nonequilibrity? As a minimum the kinetic
coefficients the included in hydrodynamic equations can vary.
On the other hand, it is known [11], if nonequilibrity is
stipulated by a field, the hydrodynamical equations become
simpler and are reduced to one equation of a continuity
(diffusion) in which coefficients are determined equilibrium
EDF in view of a series development on lapse rates of all
quantities giving in change EDF. If nonequilibrity is stipulated
by a combined effect of inelastic processes and field, the
hydrodynamic equations in which inelastic processes
renormalized kinetic coefficients [12] is gained.
Having EDF it is easy to receive the hydrodynamic
equations for numbered kinds of nonequilibrity.
Supplementing these equations, equation for a field, we shall
receive combined equations featuring the discharge within the
framework of hydrodynamics are based on nonequilibrity
EDF. Further, already by known expedient [9] easy to receive:
axial and radial plasma density distributions, condition of an
ignition, diffusion constants and drift velocity, expression for
effective length of the discharge:
)1(ln4 01 −
ν
ω= −
cren
eff n
nRL (9)
within the framework of a field non-equilibrium and in case of
a non-equilibrium stipulated by a combined effect of a field
and inelastic processes
)1
1
(ln4 01 −
><+ν
ω= −
inel
cr
en
eff Q
n
n
RL
(10)
where inelQ is the addend corresponding for inelastic
processes.
Comparing these characteristics with results obtained on
the basis of the usual hydrodynamic equations [9] it is possible
to see a series of differences: the radial distribution of density
by more flater (it is especially strong expressed at automodel
distribution), the axial distribution becomes nonlinear (that is
according to [5]); effective length of the discharge diminishes
in relation to results of the local theory (at automodel
distribution the discharge most shorter), the condition ignition
became approximate and nonlocal. And it means that the non-
equilibrium and nonlocality is significantly changed all
discharge characteristics.
Only in approach of a “thin” waveguide, when the role
lapse rate of the terms in the kinetic equation diminishes and,
hence, EDF is close to local and the results of both
hydrodynamics are close. It means, that the existing
hydrodynamic theories are restricted to approach of a “thin”
waveguide. For wide waveguide these theories give wrong
results.
The appearance of an anisotropy of transport coefficients
is characteristic for the discharges in stationary electric fields,
but this anisotropy disappears in high-frequency (HF) field
[11]. If HF field amplitude depends on time, than it is
equivalent to the account of a time increment (decrement).
This situation is realized, for example, when the surface wave
is excited by a beam of charged particles or exterior
electromagnetic wave [13].
Picking a field in appropriate way, we shall receive the
kinetic equation extending all known and having the relevant
passages to the limit. Already at a level of the equation the
occurrence of an anisotropy of transport coefficients is visible,
since there are corresponding for a drift stream and operation
of a field above a diffusion stream. Naturally this anisotropy
will enter and the solutions for EDF and in discharge
characteristics on the basis of a kinetics.
The hydrodynamical equations become anisotropic, the
transport coefficients along a field and across are different, that
is stipulated by distinction of a field components of a surface
wave and renormalization of drift velocity.
On the basis of the evaluations done and obtained results
it is possible to state: that the account of a non-equilibrium and
nonlocality EDF renders essential influence to parameters of
the discharge sustained by a surface wave; the hydrodynamic
equations, and consequently, all discharge characteristics vary.
Anisotropy of transport coefficients in high-frequency (HF)
field occurs if it (field) amplitude depends on time.
The work is carried out within the framework of the
project № 1112 STCU.
REFERENCES:
[1] A.N.Kondratenko. Plasma wave guides. M.:
Energoatomizdat, 1976.
93
[2] U.Kortshagen, H. Schluter, A. Shivarova// J.Phys.
D:Appl. Phys. 1991, v.24, p.1571
[3] A.Kortshagen//J.Phys.D:Appl.Phys.1993,v.26,p.1691-
1699
[4] K.N.Stepanov//Sov. J.of Technic. Phys., 1965, v. 67,
p. 576
[5] Yu. M.Aliev et al.// Physical Review E, 1995, v51,
p.6091.
[6] L.D.Tsendin// Sov.J. Plasma Phys., 1982, v.8, №.1, p.
169.
[7] V.Kolobov, W.N.G.Hitchon// Physical Review E,
1995, v.52, № 1, p.972
[8] V.Atanassov, I.Zhelyazkov// Physics Reports, 1995,
v.255, p.79.
[9] Yu. M.Aliev et al.// Plasma Sources Sci. Technol.,
1993, v.2, p.145.
[10] I.Peres, M.Fortin, J.Margot.// Phys. Plasmas, 1996,
v.12, p1754.
[11] N.L.Aleksandrov, A.M.Konchakov,
A.P.Napartovich, A.N.Starostin. Chemistry of
plasma/ ed. by B.M.Smirnov. M.: Atomizdat, 1984,
p. 3.
[12] V.P. Vstovsky// Sov.J.Plasma Phys. 1986, v.12, p.
1479
[13] A.F. Aleksandrov, L.S. Bogdankevich, A.A.
Ruhadse Fundamentals an electrodynamics of
plasma. M.: Vysshaya Shkola, 1978.
ПРО ВПЛИВ ЕФЕКТІВ НЕРІВНОВАЖНОСТІ ТА НЕЛОКАЛЬНОСТІ НА ПАРАМЕТРИ РОЗРЯДУ,
ЩО ПІДТРИМУЄТЬСЯ ПОВЕРХНЕВИМИ ХВИЛЯМИ
М.О. Азаренков, Вол.В. Гущин, В.В. Гущин
Отримано кінетичне рівняння для плазми у двомірнонеоднорідному полі поверхневої хвилі. У наближенні
сталого поля знайдено вирази для функцій розподілу у залежності від величини коефіцієнту просторового
послаблення. За допомогою цих функцій розподілу підраховано такі характеристики плазми, як густина плазми,
частоти елементарних процесів, коефіцієнти дифузії, кількість частинок, що потрапляють на стінки. Наведено,
що у високочастотному електричному полі перенос також може носити анізотропний характер. З урахуванням
цього отримано „вірні” гідродинамічні рівняння. Проведено порівняльний характер з раніше відомими
результатами. Як підсумок роботи можливо стверджувати, що урахування нерівноважності та не локальності
важливо, якщо описувати розряди, що підтримуються поверхневими хвилями.
О ВЛИЯНИИ ЭФФЕКТОВ НЕРАВНОВЕСНОСТИ И НЕЛОКАЛЬНОСТИ НА ПАРАМЕТРЫ РАЗРЯДА,
ПОДДЕРЖИВАЕМОГО ПОВЕРХНОСТНЫМИ ВОЛНАМИ
Н.А. Азаренков, Вл.В. Гущин, В.В. Гущин
Получено кинетическое уравнение для плазмы в двумернонеоднородном поле поверхностной волны. В
приближении заданного поля найдены выражения для функций распределения в зависимости от величины
коэффициента пространственного ослабления. С помощью этих функций распределения посчитаны такие
характеристики плазмы как плотность, частоты элементарных процессов, коэффициенты диффузии, количество
частиц, попадающих на стенки. Показано, что в высокочастотном электрическом поле перенос тоже может
носить анизотропный характер. С учетом этого получены «правильные» гидродинамические уравнения.
Проведен сравнительный анализ с ранее известными результатами. Как итог работы можно утверждать – учет
неравновесности и нелокальности важен при описании разрядов, поддерживаемых поверхностными волнами.
94
N.A.Azarenkov, Vl.V.Gushchin,V.V.Gushchin
М.О. Азаренков, Вол.В. Гущин, В.В. Гущин
Н.А. Азаренков, Вл.В. Гущин, В.В. Гущин
|
| id | nasplib_isofts_kiev_ua-123456789-110491 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:14:48Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Azarenkov, N.A. Gushchin, Vl.V. Gushchin, V.V. 2017-01-04T14:26:22Z 2017-01-04T14:26:22Z 2003 About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves / N.A. Azarenkov, Vl.V. Gushchin,V.V. Gushchin // Вопросы атомной науки и техники. — 2003. — № 1. — С. 92-94. — Бібліогр.: 13 назв. — англ. 1562-6016 PACS: 52.80.-s https://nasplib.isofts.kiev.ua/handle/123456789/110491 The kinetic equation for plasma in two-dimensional non-uniform field of a surface wave was obtained. At the approximation of predetermined field there were found the distribution functions in dependence on the value of a coefficient of spatial attenuation. With using such distribution functions such plasma characteristics as density, frequency of elementary processes, diffusion coefficients, number of particles falling down to the wall, were calculated. There was shown that in high frequency electric field transport may also have anisotropic character. Taking this into account the “correct” hydrodynamic equations were obtained. Comparison with earlier known results was carried out. As result of this work it is possible to state – taking into account the non-equilibrium and nonlocal properties is important for description of discharges sustained with surface waves. Отримано кінетичне рівняння для плазми у двомірнонеоднорідному полі поверхневої хвилі. У наближенні сталого поля знайдено вирази для функцій розподілу у залежності від величини коефіцієнту просторового послаблення. За допомогою цих функцій розподілу підраховано такі характеристики плазми, як густина плазми, частоти елементарних процесів, коефіцієнти дифузії, кількість частинок, що потрапляють на стінки. Наведено, що у високочастотному електричному полі перенос також може носити анізотропний характер. З урахуванням цього отримано „вірні” гідродинамічні рівняння. Проведено порівняльний характер з раніше відомими результатами. Як підсумок роботи можливо стверджувати, що урахування нерівноважності та не локальності важливо, якщо описувати розряди, що підтримуються поверхневими хвилями. Получено кинетическое уравнение для плазмы в двумернонеоднородном поле поверхностной волны. В приближении заданного поля найдены выражения для функций распределения в зависимости от величины коэффициента пространственного ослабления. С помощью этих функций распределения посчитаны такие характеристики плазмы как плотность, частоты элементарных процессов, коэффициенты диффузии, количество частиц, попадающих на стенки. Показано, что в высокочастотном электрическом поле перенос тоже может носить анизотропный характер. С учетом этого получены «правильные» гидродинамические уравнения. Проведен сравнительный анализ с ранее известными результатами. Как итог работы можно утверждать – учет неравновесности и нелокальности важен при описании разрядов, поддерживаемых поверхностными волнами. The work is carried out within the framework of the project № 1112STCU en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves Про вплив ефектів нерівноважності та нелокальності на параметри розряду, що підтримується поверхневими хвилями О влиянии эффектов неравновесности и нелокальности на параметры разряда, поддерживаемого поверхностными волнами Article published earlier |
| spellingShingle | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves Azarenkov, N.A. Gushchin, Vl.V. Gushchin, V.V. Basic plasma physics |
| title | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves |
| title_alt | Про вплив ефектів нерівноважності та нелокальності на параметри розряду, що підтримується поверхневими хвилями О влиянии эффектов неравновесности и нелокальности на параметры разряда, поддерживаемого поверхностными волнами |
| title_full | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves |
| title_fullStr | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves |
| title_full_unstemmed | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves |
| title_short | About influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves |
| title_sort | about influence of effects nonequilibrity and nonlocality on the parameters of the discharge sustained by surface waves |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110491 |
| work_keys_str_mv | AT azarenkovna aboutinfluenceofeffectsnonequilibrityandnonlocalityontheparametersofthedischargesustainedbysurfacewaves AT gushchinvlv aboutinfluenceofeffectsnonequilibrityandnonlocalityontheparametersofthedischargesustainedbysurfacewaves AT gushchinvv aboutinfluenceofeffectsnonequilibrityandnonlocalityontheparametersofthedischargesustainedbysurfacewaves AT azarenkovna provplivefektívnerívnovažnostítanelokalʹnostínaparametrirozrâduŝopídtrimuêtʹsâpoverhnevimihvilâmi AT gushchinvlv provplivefektívnerívnovažnostítanelokalʹnostínaparametrirozrâduŝopídtrimuêtʹsâpoverhnevimihvilâmi AT gushchinvv provplivefektívnerívnovažnostítanelokalʹnostínaparametrirozrâduŝopídtrimuêtʹsâpoverhnevimihvilâmi AT azarenkovna ovliâniiéffektovneravnovesnostiinelokalʹnostinaparametryrazrâdapodderživaemogopoverhnostnymivolnami AT gushchinvlv ovliâniiéffektovneravnovesnostiinelokalʹnostinaparametryrazrâdapodderživaemogopoverhnostnymivolnami AT gushchinvv ovliâniiéffektovneravnovesnostiinelokalʹnostinaparametryrazrâdapodderživaemogopoverhnostnymivolnami |