Secondary streamers in the primary streamer channel
The propagation of the process with ionization and attachment in the remainder of the streamer channel is studied. From the simplified model consideration it is shown that in the conditions of the attachment instability development the spatially inhomogeneous perturbations move to anode. The conditi...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2019 |
| Main Authors: | , , , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2019
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/194715 |
| 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: | Secondary streamers in the primary streamer channel / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, S. Pugach, G. Taran, L. Zavada // Problems of atomic science and technology. — 2019. — № 1. — С. 184-186. — Бібліогр.: 6 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-194715 |
|---|---|
| record_format |
dspace |
| spelling |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Pugach, S. Taran, G. Zavada, L. 2023-11-29T09:18:45Z 2023-11-29T09:18:45Z 2019 Secondary streamers in the primary streamer channel / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, S. Pugach, G. Taran, L. Zavada // Problems of atomic science and technology. — 2019. — № 1. — С. 184-186. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.80.Hc https://nasplib.isofts.kiev.ua/handle/123456789/194715 The propagation of the process with ionization and attachment in the remainder of the streamer channel is studied. From the simplified model consideration it is shown that in the conditions of the attachment instability development the spatially inhomogeneous perturbations move to anode. The conditions, in which the perturbations move to cathode, as it is usually observed for the secondary streamers, are discussed. Вивчається поширення процесу з іонізацією та налипанням у залишку каналу стримера. З розгляду спрощеної моделі видно, що в умовах розвитку налипальної нестійкості просторово неоднорідні збурення рухаються до анода. Обговорюються умови, за яких ті збурення рухаються до катода, як це зазвичай спостерігається для вторинних стримерів. Изучается распространение процесса с ионизацией и прилипанием в остатке канала стримера. Из рассмотрения упрощенной модели видно, что в условиях развития прилипательной неустойчивости пространственно неоднородные возмущения движутся к аноду. Обсуждаются условия, при которых эти возмущения движутся к катоду, как это обычно наблюдается для вторичных стримеров. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies Secondary streamers in the primary streamer channel Вторинні стримери в каналі первинного стримера Вторичные стримеры в канале первичного стримера Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Secondary streamers in the primary streamer channel |
| spellingShingle |
Secondary streamers in the primary streamer channel Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Pugach, S. Taran, G. Zavada, L. Low temperature plasma and plasma technologies |
| title_short |
Secondary streamers in the primary streamer channel |
| title_full |
Secondary streamers in the primary streamer channel |
| title_fullStr |
Secondary streamers in the primary streamer channel |
| title_full_unstemmed |
Secondary streamers in the primary streamer channel |
| title_sort |
secondary streamers in the primary streamer channel |
| author |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Pugach, S. Taran, G. Zavada, L. |
| author_facet |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Pugach, S. Taran, G. Zavada, L. |
| topic |
Low temperature plasma and plasma technologies |
| topic_facet |
Low temperature plasma and plasma technologies |
| publishDate |
2019 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Вторинні стримери в каналі первинного стримера Вторичные стримеры в канале первичного стримера |
| description |
The propagation of the process with ionization and attachment in the remainder of the streamer channel is studied. From the simplified model consideration it is shown that in the conditions of the attachment instability development the spatially inhomogeneous perturbations move to anode. The conditions, in which the perturbations move to cathode, as it is usually observed for the secondary streamers, are discussed.
Вивчається поширення процесу з іонізацією та налипанням у залишку каналу стримера. З розгляду спрощеної моделі видно, що в умовах розвитку налипальної нестійкості просторово неоднорідні збурення рухаються до анода. Обговорюються умови, за яких ті збурення рухаються до катода, як це зазвичай спостерігається для вторинних стримерів.
Изучается распространение процесса с ионизацией и прилипанием в остатке канала стримера. Из рассмотрения упрощенной модели видно, что в условиях развития прилипательной неустойчивости пространственно неоднородные возмущения движутся к аноду. Обсуждаются условия, при которых эти возмущения движутся к катоду, как это обычно наблюдается для вторичных стримеров.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/194715 |
| citation_txt |
Secondary streamers in the primary streamer channel / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, S. Pugach, G. Taran, L. Zavada // Problems of atomic science and technology. — 2019. — № 1. — С. 184-186. — Бібліогр.: 6 назв. — англ. |
| work_keys_str_mv |
AT bolotovo secondarystreamersintheprimarystreamerchannel AT kadolinb secondarystreamersintheprimarystreamerchannel AT mankovskyis secondarystreamersintheprimarystreamerchannel AT ostroushkov secondarystreamersintheprimarystreamerchannel AT pashchenkoi secondarystreamersintheprimarystreamerchannel AT pugachs secondarystreamersintheprimarystreamerchannel AT tarang secondarystreamersintheprimarystreamerchannel AT zavadal secondarystreamersintheprimarystreamerchannel AT bolotovo vtorinnístrimerivkanalípervinnogostrimera AT kadolinb vtorinnístrimerivkanalípervinnogostrimera AT mankovskyis vtorinnístrimerivkanalípervinnogostrimera AT ostroushkov vtorinnístrimerivkanalípervinnogostrimera AT pashchenkoi vtorinnístrimerivkanalípervinnogostrimera AT pugachs vtorinnístrimerivkanalípervinnogostrimera AT tarang vtorinnístrimerivkanalípervinnogostrimera AT zavadal vtorinnístrimerivkanalípervinnogostrimera AT bolotovo vtoričnyestrimeryvkanalepervičnogostrimera AT kadolinb vtoričnyestrimeryvkanalepervičnogostrimera AT mankovskyis vtoričnyestrimeryvkanalepervičnogostrimera AT ostroushkov vtoričnyestrimeryvkanalepervičnogostrimera AT pashchenkoi vtoričnyestrimeryvkanalepervičnogostrimera AT pugachs vtoričnyestrimeryvkanalepervičnogostrimera AT tarang vtoričnyestrimeryvkanalepervičnogostrimera AT zavadal vtoričnyestrimeryvkanalepervičnogostrimera |
| first_indexed |
2025-11-26T00:09:22Z |
| last_indexed |
2025-11-26T00:09:22Z |
| _version_ |
1850593567784828928 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2019. №1(119)
184 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2019, № 1. Series: Plasma Physics (25), p. 184-186.
SECONDARY STREAMERS IN THE PRIMARY STREAMER CHANNEL
O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, S. Pugach, G. Taran,
L. Zavada
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: ostroushko-v@kipt.kharkov.ua
The propagation of the process with ionization and attachment in the remainder of the streamer channel is
studied. From the simplified model consideration it is shown that in the conditions of the attachment instability
development the spatially inhomogeneous perturbations move to anode. The conditions, in which the perturbations
move to cathode, as it is usually observed for the secondary streamers, are discussed.
PACS: 52.80.Hc
INTRODUCTION
The discharge between the needle anode and the
plane cathode is used in plasma chemistry for a long
time. In the form of cathode directed streamers [1] the
discharge is effective for the non-equilibrium plasma
production. The study of the processes, which
accompany the streamer propagation, is continued up to
now [2, 3]. In the paper [4], the numerical simulations
of the cathode directed streamer propagation in the
electronegative gases with strong attachment are carried
out for the quasi-stationary stage, far from electrodes,
and for the stage of going out to cathode. In the present
paper, the phenomenon of the secondary streamer is
studied. It is observed at the final stage of streamer
propagation in some electronegative gases, when the
streamer goes out to cathode. The secondary streamer is
the domain with intensive glow in the channel of the
primary streamer. Sufficiently convinced explanation of
the secondary streamers nature is presented in the paper
[5]. It is shown that the attachment instability leads to
monotonous increase of electron and ion density
perturbations and to appearing of the channel domains
with strong and weak field. But in the approximation
considered in [5], the boundaries of the domains are
motionless. In the present paper, it is carried out the
study of the model near to one studied in [5], with
estimation of the displacement velocity for the charge
density perturbations. It is shown that in the conditions
of the attachment instability the perturbations move to
anode, whereas the secondary streamers usually move to
cathode. So, the attachment instability may be
considered as the cause of appearing of the channel
domains with strong and weak field, but movement of
these domains to cathode may take place in the
conditions of the attachment instability absence, when
spatially inhomogeneous perturbations fade away.
1. SIMPLIFIED MODEL
In the model considered in [5], the ratio of
attachment and relaxation frequency is small parameter,
the relationships are deduced in the assumption about
such degree of plasma quasi-neutrality, which does not
prohibit the electric field strength distribution to be
inhomogeneous, and the displacement current is
neglected. Also, in fact, the assumption is made that the
emission current from cathode,
eI , is near to the ratio
0I of the applied voltage and the discharge gap
resistance. In reality, the emission current is determined
by a lot of factors, and the difference between the
entrance current and the exit current leads to change of
the total charge value inside the gap. If
e 0I I then it is
formed the comparatively thin near-cathode layer with
large non-compensated positive charge density and not
very small part of the total potential drop, and the ratio
of the other parts of the potential drop and the discharge
gap resistance should be near to
eI . To consider the
next approximations in the expansion with respect to the
mentioned small parameter, it is necessary to impose the
clear condition on the entrance current. To keep the
main results of [5], it is necessary to keep quasi-
neutrality. To ensure the absence of the non-
compensated charge in the whole discharge gap, the
entrance and exit currents should be equal. The results
obtained in consideration of such model may be applied
for more real situation of non-equal entrance and exit
currents with aid of decrease of the potential drop over
the gap on the value of the potential drop over the
mentioned near-cathode layer.
So, it is considered the plasma in the gap between
cathode ( 0x ) and anode ( 0x b ). Ion motion is
neglected. The plasma is described by the equations
e e e a e i( )t x tn n E n n , (1)
0 0 e i( )xE e n n , (2)
where with index means derivative with respect to
the variable indicated in index,
e and
en are mobility
and density of electrons,
in is the difference of the
densities of positive and negative ions, E is the
quantity opposite to the x -component of the electric
field strength (
xE E , 0E ),
0 is electric constant,
0e is elementary charge ( 0 0e ), a is difference
between the attachment and ionization frequencies. It is
assumed that
a a ( )E and
e const . It is imposed
the condition
0
b
dxE U , where U is voltage applied
to the gap, and the condition
i e
0
( ) 0
b
dx n n . (3)
Integration of the equation (2) and the equality
i e e e( ) ( )t xn n n E (following from (1)) with use
of (3) gives the equalities 0| |x x bE E and
e 0 e( ) ( )x x bn E n E , (4)
ISSN 1562-6016. ВАНТ. 2019. №1(119) 185
and then the quantities
en ,
etn ,
itn , and
e( )x n E at
the different boundaries ( 0x and x b ) also should
have equal values. The condition (4) may be imposed
instead of (3).
2. APPROXIMATE SOLUTION
For the homogeneous distribution, indicating the
quantities with the index 0 , one gets
e0 a0 e0tn n ,
e0 e0 a0( ) (0)exp( )n t n t ,
i0 e0n n , and
0E U b .
To ensure (4), the linear perturbations of the
homogeneous distribution are searched in the form of
the real parts of the products of the amplitudes
(dependent on time and indicated with the index 1 ) and
the factor exp( )ikx with 2k n b and nonzero
integer n . For the amplitudes one gets the equations
e1 e e1 0 e0 1
a0 e1 a 0 1 e0 i1
( ) [ ( ) ( ) ( )]
( ) ( ) ( ) ( )
t
E t
n t ik n t E n t E t
n t E t n t n t
, (5)
0 1 0 e1 i1( ) [ ( ) ( )]ik E t e n t n t , (6)
where
a 0E is the value of the derivative
a ( )E E at
0E E . Denoting
i1 e1( ) ( ) ( )Q t n t n t ,
e0 e 0v E ,
1
r0 0 0 e e0(0)e n , and
r r0 a0( ) exp( )t t , with use
of the equations (5) and (6) one gets the equations
1
1 0 0( ) ( ) ( )E t ik e Q t ,
e1 i1( ) ( ) ( )n t n t Q t ,
e0 i1 e0 r( ) ( ) [ ( )] ( )tikv n t Q t ikv t Q t ,
2
e0 a0 r
a 0 0 r
( ) [ ( )] ( )
( ) ( )
t t
E
Q t ikv t Q t
E t Q t
.
The function -1
r0( ) ln ( )P t Q t obeys to the equation
-1 2 2
r0
-1
e0 a0 r0 a0
-1
a 0 0 r0 a0
( ) [ ( )]
[( ) exp( )] ( )
exp( )
t t
t
E
P t P t
ikv t P t
E t
. (7)
function ( )P t may be given with the asymptotic
expansion
r00
( ) [ ( )]m
mm
P t p t
. Its substitution into
(7) gives the equation
r 00
[ ( )] 0m
mm
Z t
, with
0 0 0 a0( ) ( )[ ( ) exp( )]t tZ t p t p t t ,
2
1 0 a0 1 a 0 0
1 e0 a0 0
( ) ( ) exp( )[ ( ) ]
[2 ( ) ] ( )
t t E
t t
Z t p t t p t E
p t ikv p t
,
2
2 1 e0 a0 1 1
0 a0 2
( ) ( ) [ ( )] ( )
[2 ( ) exp( )] ( )
t t t
t t
Z t p t ikv p t p t
p t t p t
.
It is imposed the requirement ( ) 0mZ t , for each m .
For 0m one gets two different solutions:
1
0 0 a0 a0( ) (0) [1 exp( )]p t p t ,
0 0( ) (0)p t p . The
next terms for these two solutions are the following:
1 1 e0 a 0 0( ) (0) ( )Ep t p ikv E t ,
1 1 a 0 0( ) (0) Ep t p E t ,
2 2 e0 a0 a 0 0( ) (0) ( )( )Ep t p f t ikv E ,
with 1
a0 a0 a 0 0( ) [exp( ) 1] Ef t t E . It is worthy to
note that
r0exp( ) ( ) exp[ ( )]ikx Q t ikx P t , the sum
r0 ( )ikx P t contains the parameter k in the term
0[ ( )]ik x x t , with 1
0 r0 e0( ) ( )x t v f t ,
0 e0( )x t v t ,
and for
a 0 0E one gets the relationship
a 0 0 ( ) 0E t x t , which connects the direction of the
perturbation movement with the sign of
a 0E .
The solution ( )P t is characterized by the fast
decay, and the perturbations move to anode with the
electron velocity. The time evolution of the spatial
perturbations determined by the solution ( )P t is
described by the factor
a 0 0exp( )E E t . So, the stability of
the solution ( )P t depends on the sign of
a 0E . For
a 0 0E , the solution ( )P t is unstable, the
perturbations move to anode with the velocities much
less than electron velocity. Such motion direction is
typical for the attachment instability [6]. For
a 0 0E ,
the solution ( )P t is stable, and the perturbations move
to cathode. The evolution of the homogeneous electron
density is described by the factor
a0exp( )t . The cases
a0 0 and
a0 0 correspond to attachment decay
and ionization growth, respectively.
3. DISCUSSION
So, in the conditions of attachment instability, the
perturbations move to anode, whereas the secondary
streamers usually move to cathode. In the paper [5], the
motion of the leading edge of the glow domain to
cathode is obtained in assumption of gas density
decrease with time (due to streamer channel heating)
and relevant increase of the ratio of electric field
strength and the gas density, which determines the rates
of electron processes. The same effect may be obtained
with relevant increase of the potential drop on the gap.
As it is mentioned above, the electric field strength
distribution in the gap essentially depends on the
entrance current. In particular, in the limit case when the
entrance current becomes zero, the channel soon gets
the additional positive charge through the electron going
out to anode, and then the quasi-stationary field
distribution is set (if the ion motion is neglected), in
which almost all potential drop is related to the
comparatively thin near-cathode layer, and in the
plasma channel the field is very weak. When the
streamer goes out to cathode the situation is near to the
opposite one. Namely, before the streamer approach to
cathode the considerable part of the potential drop falls
on the small domain in front of streamer. During the
streamer going out to cathode, the domain dimension
decreases, and also, the electron emission from cathode
considerably increases, leading to the field strength
decrease near the cathode. As a result, the field strength
in the other part of channel increases, leading to
propagation of glow in the channel in both directions.
The velocity of the intensive glow domain boundary
propagation is very small for the boundary, near which
the spatial variation of the field strength is very sharp.
So, such field strength increase can give the secondary
streamer with propagating forward boundary and
practically motionless backward boundary situated near
the space with the comparatively large difference
186 ISSN 1562-6016. ВАНТ. 2019. №1(119)
between the positive and negative ion densities in the
channel remainder.
The propagation of the secondary streamer
backward boundary to cathode (Fig. 2 in [5]) may be the
ionization wave propagation, which starts near the
mentioned channel non-uniformity in consequence of
the field strength increase up to the level, at which the
tendency to decrease of the difference between the
positive and negative ion densities is replaced with the
tendency to its increase and the following space charge
field strengthening. And the field strength increase,
which gives the start to the ionization wave propagation,
may be the result of the increase of the potential drop on
the relevant part of streamer channel during the streamer
going out to cathode. On the other hand, the ionization
wave propagation is accompanied with recovery of high
conductivity behind the wave front, and so, with the
potential redistribution and the field strength increase
between the front and cathode, leading to the additional
propagation of the secondary streamer forward
boundary to cathode.
CONCLUSIONS
The secondary streamer is the moving glowing
domain with comparatively large field strength, in the
streamer channel. In the paper [5], it is substantiated
that the contrast in glow increases due to the attachment
instability. In the present paper, from the simplified
model consideration, it is estimated the velocity of the
spatially inhomogeneous perturbation movement in the
conditions of the attachment instability and it is
attracted the attention to the movement direction, which
is opposite to one usually observed for the secondary
streamers. Besides the gas density decrease through the
channel heating, the propagation of the forward
boundary of the large field strength domain to cathode
may be resulted from the potential redistribution during
going out of the ionization waves to cathode, which
leads to the field strength increase in the considerable
part of the discharge gap not very near to cathode.
When field strength increases near the domain with the
enlarged difference between the positive and negative
ion densities in the channel remainder, the ionization
wave may start from there, so that the wave front
becomes the backward boundary of the secondary
streamer, and the wave front propagation to cathode
leads to further field strength increase between the front
and cathode, that is, to further propagation of the
forward boundary of the large field strength domain to
cathode.
REFERENCES
1. Yu.P. Raizer. Gas discharge physics. Springer:
“Verlag”, 1991.
2. O.V. Bolotov, V.I. Golota, B.B. Kadolin, et al.
Similarity laws for cathode-directed streamers in gaps
with an inhomogeneous field at elevated air pressure //
Plasma Physics Reports. 2010, v. 36, № 11, p. 1000-
1011.
3. O.V. Manuilenko. Computer simulation of positive
streamer dynamics in uniform and non-uniform electric
fields in air. // Problems of Atomic Science and
Technology. Series “Plasma Electronics and New
Methods of Acceleration” (8). 2013, № 4, p. 194-199.
4. O. Bolotov, B. Kadolin, S. Mankovskyi, et al.
Numerical simulations of cathode directed streamer
propagation in electronegative gases // Problems of
Atomic Science and Technology. Series ”Plasma
Electronics and New Methods of Acceleration” (10).
2018, № 4, p. 172-175.
5. R.S. Sigmond. The residual streamer channel: Return
strokes and secondary streamers // Journal of Applied
Physics. 1984, v. 56, № 5, p. 1355-1370.
6. R.A. Haas. Plasma stability of electric discharges in
molecular gases // Physical Review A. 1973, v. 8, № 2,
p. 1017-1043.
Article received 23.09.2018
ВТОРИЧНЫЕ СТРИМЕРЫ В КАНАЛЕ ПЕРВИЧНОГО СТРИМЕРА
О. Болотов, Б. Кадолин, С. Маньковский, В. Остроушко, И. Пащенко, С. Пугач, Г. Таран, Л. Завада
Изучается распространение процесса с ионизацией и прилипанием в остатке канала стримера. Из
рассмотрения упрощенной модели видно, что в условиях развития прилипательной неустойчивости
пространственно неоднородные возмущения движутся к аноду. Обсуждаются условия, при которых эти
возмущения движутся к катоду, как это обычно наблюдается для вторичных стримеров.
ВТОРИННІ СТРИМЕРИ В КАНАЛІ ПЕРВИННОГО СТРИМЕРА
О. Болотов, Б. Кадолін, С. Маньковський, В. Остроушко, І. Пащенко, С. Пугач, Г. Таран, Л. Завада
Вивчається поширення процесу з іонізацією та налипанням у залишку каналу стримера. З розгляду
спрощеної моделі видно, що в умовах розвитку налипальної нестійкості просторово неоднорідні збурення
рухаються до анода. Обговорюються умови, за яких ті збурення рухаються до катода, як це зазвичай
спостерігається для вторинних стримерів.
|