Azimuthal stability of trichel pulses and cathode directed streamers
The numerical simulations of negative corona discharge in Trichel pulse mode are carried out with the calculation of evolution of azimuthal perturbations. It is found the azimuthal instability with increment corresponding to avalanche development. This instability is suppressed at the nonlinear stag...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Azimuthal stability of trichel pulses and cathode directed streamers / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Problems of atomic science and technology. — 2019. — № 4. — С. 130-134. — Бібліогр.: 3 назв. — англ. |
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Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. 2023-12-03T14:51:23Z 2023-12-03T14:51:23Z 2019 Azimuthal stability of trichel pulses and cathode directed streamers / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Problems of atomic science and technology. — 2019. — № 4. — С. 130-134. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.80.Hc https://nasplib.isofts.kiev.ua/handle/123456789/195194 The numerical simulations of negative corona discharge in Trichel pulse mode are carried out with the calculation of evolution of azimuthal perturbations. It is found the azimuthal instability with increment corresponding to avalanche development. This instability is suppressed at the nonlinear stage and does not lead to the process branching. The result is also applicable to the azimuthal instability of the cathode directed streamer, found earlier. The difference in their increments is followed from the difference in courses of the processess, which is discussed. Виконане числове моделювання негативної корони в режимі імпульсів Тричела з розрахунком еволюції азимутальних збурень. Виявлено азимутальну нестійкість з інкрементом, відповідним розвитку лавини. Ця нестійкість пригнічується на нелінійній стадії і не веде до галуження процесу. Результат також застосовується до виявленої раніше азимутальної нестійкості спрямованого до катода стримера. Різниця в їхніх інкрементах випливає з різниці в ході процесів, які обговорюються. Выполнено численное моделирование отрицательной короны в режиме импульсов Тричела с расчетом эволюции азимутальных возмущений. Выявлена азимутальная неустойчивость с инкрементом, соответствующим развитию лавины. Эта неустойчивость подавляется на нелинейной стадии и не ведет к ветвлению процесса. Результат также применим к выявленной ранее азимутальной неустойчивости направленного к катоду стримера. Разница в их инкрементах следует из разницы в ходе процессов, которые обсуждаются. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Gas and plasma-beam discharges and their applications Azimuthal stability of trichel pulses and cathode directed streamers Азимутальна стійкість імпульсів тричела та спрямованих до катодa стримерів Азимутальная устойчивость импульсов тричела и направленных к катоду стримеров Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Azimuthal stability of trichel pulses and cathode directed streamers |
| spellingShingle |
Azimuthal stability of trichel pulses and cathode directed streamers Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Gas and plasma-beam discharges and their applications |
| title_short |
Azimuthal stability of trichel pulses and cathode directed streamers |
| title_full |
Azimuthal stability of trichel pulses and cathode directed streamers |
| title_fullStr |
Azimuthal stability of trichel pulses and cathode directed streamers |
| title_full_unstemmed |
Azimuthal stability of trichel pulses and cathode directed streamers |
| title_sort |
azimuthal stability of trichel pulses and cathode directed streamers |
| author |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_facet |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| topic |
Gas and plasma-beam discharges and their applications |
| topic_facet |
Gas and plasma-beam discharges and their applications |
| 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 |
Азимутальна стійкість імпульсів тричела та спрямованих до катодa стримерів Азимутальная устойчивость импульсов тричела и направленных к катоду стримеров |
| description |
The numerical simulations of negative corona discharge in Trichel pulse mode are carried out with the calculation of evolution of azimuthal perturbations. It is found the azimuthal instability with increment corresponding to avalanche development. This instability is suppressed at the nonlinear stage and does not lead to the process branching. The result is also applicable to the azimuthal instability of the cathode directed streamer, found earlier. The difference in their increments is followed from the difference in courses of the processess, which is discussed.
Виконане числове моделювання негативної корони в режимі імпульсів Тричела з розрахунком еволюції азимутальних збурень. Виявлено азимутальну нестійкість з інкрементом, відповідним розвитку лавини. Ця нестійкість пригнічується на нелінійній стадії і не веде до галуження процесу. Результат також застосовується до виявленої раніше азимутальної нестійкості спрямованого до катода стримера. Різниця в їхніх інкрементах випливає з різниці в ході процесів, які обговорюються.
Выполнено численное моделирование отрицательной короны в режиме импульсов Тричела с расчетом эволюции азимутальных возмущений. Выявлена азимутальная неустойчивость с инкрементом, соответствующим развитию лавины. Эта неустойчивость подавляется на нелинейной стадии и не ведет к ветвлению процесса. Результат также применим к выявленной ранее азимутальной неустойчивости направленного к катоду стримера. Разница в их инкрементах следует из разницы в ходе процессов, которые обсуждаются.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195194 |
| citation_txt |
Azimuthal stability of trichel pulses and cathode directed streamers / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Problems of atomic science and technology. — 2019. — № 4. — С. 130-134. — Бібліогр.: 3 назв. — англ. |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2019. №4(122) 130
AZIMUTHAL STABILITY OF TRICHEL PULSES AND CATHODE
DIRECTED STREAMERS
O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: ostroushko-v@kipt.kharkov.ua
The numerical simulations of negative corona discharge in Trichel pulse mode are carried out with the calcula-
tion of evolution of azimuthal perturbations. It is found the azimuthal instability with increment corresponding to
avalanche development. This instability is suppressed at the nonlinear stage and does not lead to the process branch-
ing. The result is also applicable to the azimuthal instability of the cathode directed streamer, found earlier. The dif-
ference in their increments is followed from the difference in courses of the processess, which is discussed.
PACS: 52.80.Hc
INTRODUCTION
Negative corona discharge is widely used in plasma-
chemical techniques, in particular, in ozone synthesis.
To intensify required reactions, it is worthy to use nega-
tive corona in Trichel pulse mode at relatively high
voltage value but to keep discharge from turn to station-
ary mode, which destructs ozone through the gas heat-
ing.
In a discharge with a very large voltage, which reali-
zation requires rapid voltage application, during a few
nanoseconds, a branching of the ionization process is
observed, which can affect the gas heating rate, but
which is not observed for the quasi-stationary voltage
application, with a characteristic time of change, much
larger than the time of Trichel pulse development up to
the maximum value of total current. In order to find the
possibility of branching realization, the numerical simu-
lations of negative corona discharge in Trichel pulse
mode are carried out.
The real possibilities of the modern computers allow
the detailed simulations of the axially symmetric pro-
cesses. For some three-dimensional processes, such as
branching of streamers, the initial, linear stage of their
development can also be simulated on a two-
dimensional mesh [1, 2]. In the present paper, this ap-
proach is applied to the Trichtel pulses. Strictly speak-
ing, the concepts of stability and instability are related
to the perturbations of the stationary mode. It is near to
the stationary one the intermediate stage of the cathode-
directed streamer propagation when its head is already
far removed from the anode, but has not yet approached
the cathode. Any pulse process in general is unsteady,
and the formal calculation of the development of its
small perturbations may give characteristics somewhat
corresponding to reality only when the characteristic
time of development of those perturbations will be
much less than the characteristic time of development of
the main axially symmetric pulse.
1. SIMULATION MODEL
In the present numerical simulations, it is taken into
account the drift and diffusion of electrons and ions and
the processes of impact ionization, attachment, detach-
ment, electron-ion and ion-ion recombination. The
equations used are similar to those given in [3].
In conditions of the atmospheric pressure gas dis-
charge, the electron and ion motion may be considered
in the drift-diffusion approximation, and the field may
be calculated as electrostatic. The time evolution of the
particle densities and the field potential distribution may
be determined with the equations
t div( )
( )
e e e e e
i a e d n ep e p
N D N N E
N N N N
µ
n n n β
∂ − ∇ + =
= − + −
d
,
t div( )p p p p p
i e ep e p np n p
N D N N E
N N N N N
µ
n β β
∂ − ∇ − =
= − −
d
,
t div( )n n n n n
a e d n np n p
N D N N E
N N N N
µ
n n β
∂ − ∇ + =
= − −
d
,
2 1
0 ( )p e nq N N Ne −∇ Φ = − − − .
Here the indexes e , p , and n indicates electrons,
positive and negative ions, µ are relevant mobilities,
β are recombination coefficients, in , an , dn are fre-
quencies of ionization, attachment, and detachment
(numbers of the events per time caused by single elec-
tron or negative ion, respectively), i e En αµ= , where
α is ionization coefficient, | |E E=
d
, E = −∇Φ
d
, q is
elementary charge, 0e is electric constant.
The calculations are carried out for the volume re-
stricted with the ellipsoid of revolution having the fo-
cuses on the axis of revolution and with the hyperbo-
loids of revolution having the same axis of revolution
and the focuses. At the electrodes-hyperboloids it is
imposed the conditions of absence of diffusion flow,
absence of ion emission, and existence of electron emis-
sion from the cathode determined by positive ions flow,
e e i p pN E N Eµ γ µ= ,
where iγ is the coefficient of ion-electron emission. At
the boundary surface formed with ellipsoid, it is im-
posed the condition of absence of any charged particle
flow to the surface or from the surface. To avoid the
accumulation of the charged particles near this bounda-
ry it is assumed that in the elementary volumes nearest
to this surface the charged particles have artificially
large mobility. Potential is calculated in assumption of
its fixed values at infinite hyperboloids-electrodes (one
of them may be plane), and so, calculated field distribu-
tion corresponds to the case of infinite space between
hyperboloids with charge in the volume bounded by
ellipsoid. The calculations are carried out in the hyper-
boloid coordinates ( , )σ τ connected with the cylindrical
coordinates ( , )zρ by the equalities
ISSN 1562-6016. ВАНТ. 2019. №4(122) 131
2 2 1 2[( 1)(1 )]aρ σ τ= − − and z aστ= , where a is half
of distance between focuses. To calculate the potential
distribution the expansion in the terms of eigenfunctions
with respect to the coordinate τ is made, and the ob-
tained ordinary differential equation with respect to the
coordinate σ is solved with run method.
The evolution of the azimuthally inhomogeneous
distribution is calculated in the linear approximation.
For the particle densities and potential, it is taken
0 1 cos( )N N N mϕ= + , 0 1 cos( )mϕΦ = Φ +Φ ,
where ϕ is azimutal angle (so that cosx ρ ϕ= ,
siny ρ ϕ= ), m is natural number (the indexes epn
here are not written). The sinuous streamer path may be
connected with the development of the process at
1m = , and the processes at 2m ≥ , in particular, may
describe the streamer bifurcation. It is worthy to write
some equalities used in linear approximation: for the
absolute value of field strength, 0 1 cos( )E E E mϕ= + ,
where 0 0| |E E=
d
, 1 0 1( , )E e E=
d
d , 0 0 0e E E=
d
d ; for the
perturbations (namely, for the corresponding factors at
cos( )mϕ ) of mobilities, (1)
1 1Eµ µ= , where (1)µ is the
derivative of the function ( )Eµ ; for the perturbation of
ionization frequency, 1 0 0 1 0 1 0 1 0 0i E E En α µ α µ α µ= + + ,
where (1)
1 1Eα α= ; for the perturbation of the quantity
div( )N Eµ
d
, which has the form
1 0 0 0 1 0 1 0 0 0 0 1div( ) ( , ( ))N E N E E N N Qµ µ µ µ+ + ∇ +
d d d
,
where 1
1 0 1 1 1( )p e nQ q N N Ne −= − − ; for the perturbation
of summands connected with recombination,
1 0 0 0 1 0 0 0 1p p pN N N N N Nβ β β+ + . The equation for the
perturbation of potential has the form
2 2 2
1 1 1m Qρ−∇ Φ − Φ = − . The diffusion coefficients are
taken constant. With the approach to the symmetry axis
the ratios of the perturbation and the quantity mρ ap-
proaches the bounded values, so, it is worthy to remove
the factor 2 / 2( 1)mσ − and to rewrite the equations for
the coefficients at it. In particular, for the perturbation
of potential the solution is searched in the form of the
expansion 1 1 ( ) F ( )m
n nn
σ τΦ = Φ∑ (with unknown
1 ( )n σΦ ) over the eigenvalues n and the corresponding
eigenfunctions F ( )m
n τ of the Dirichlet problem for the
Legendre equation,
2 2 2 1[(1 ) F ( )] [ ( 1) (1 ) ]F ( ) 0m mmτ τ n nτ τ n n τ τ−∂ − ∂ + + − − = .
Using the Poisson equation in hyperboloid coordinates
one can obtain the equation
2
1
2 2 1
1 1
[( 1) ( )]
[ ( 1) ( 1) ] ( ) ( )m Q
σ σ n
n n
σ σ
n n σ σ σ−
∂ − ∂ Φ +
+ − + − − Φ = − ,
where the quantities 1 ( )Q n σ may be obtained from the
expansion 2 2 2
1 1( ) ( ) F ( )mQ a Q n nn
σ τ σ τ− = ∑ . Assumed
that 2 / 2
1 1( ) ( )( 1)m
n nσ σ σΦ = Φ − , one can get the equa-
tion,
2 2
1 1
1 1
( 1) ( ) 2( 1) ( )
[ ( 1) ( 1)] ( ) ( )
m
m m Q
σ n σ n
n n
σ σ σ σ
n n σ σ
− ∂ Φ + + ∂ Φ +
+ + − + Φ = − ,
and the boundary condition at the symmetry axis,
1 1
1 1
lim {2( 1) ( )
[ ( 1) ( 1)] ( ) ( )} 0
m
m m Q
σ σ n
n n
σ
n n σ σ
→ + ∂ Φ +
+ + − + Φ + = .
As the initial distribution for the basic, axially sym-
metric mode, the uniform distribution with a number
density of electrons and positive ions of 103 cm−3 is tak-
en, and for azimuthal harmonics (the amplitudes of
which are normalized at each step), it is taken the distri-
bution cos( )mϕ .
2. SIMULATION RESULTS
If the increment of a small azimuthal perturbation
development is near (by the order of magnitude) to the
inverse time of the main pulse development then the
results of calculations of the perturbation evolution
would depend to a large extent on the choice of the ini-
tial distribution. But it is revealed that the rate of azi-
muthal perturbations development significantly exceeds
the rate of the main pulse development. In the Fig. 1, it
is shown the typical time dependence for the total cur-
rent ( I ) and for the logarithmic derivatives of the max-
imum density in the axially symmetric mode ( 0κ ) and
in the azimuthal perturbation (κ ). It should be empha-
sized that for the different azimuthal harmonics (the
calculations are carried out for m =1…6) the increments
are approximately equal. The value 1 on the ordinate
axis corresponds to the following values: 10 mA for the
total current, 1010 s−1 for the increment of the axially-
symmetric mode, 2.5⋅1012 s−1 for the increment of the
perturbation.
5 10 15 20
0,0
0,5
1,0 κ0 κ
t,ns
I
Fig. 1. Total current ( I ) and time derivatives of maxi-
mum density logarithm, in axially-symmetric mode ( 0κ )
and in azimuthal perturbation (κ ); units in text
So, the instability of azimuthal perturbations with a
large increment has been formally revealed, while in
reality the branching of the process during the Trichel
pulse is not observed. And it is noteworthy the fact that
the obtained value of increment in order of magnitude
corresponds to the characteristic frequency of ionization
in a strong field. Therefore, it is natural to suppose that
the obtained magnitude of the perturbation increase rate
characterizes the linear stage of the electron avalanches
development, up to the stage of the space charge field
relaxation caused by conductivity. The ability of the
avalanche to develop remains high at the stage of Trich-
el pulse dumping, but each avalanche, having been de-
veloped to the stage of field relaxation, reduces the rate
ISSN 1562-6016. ВАНТ. 2019. №4(122) 132
of its development. This azimuthal instability of the
Trichtel pulse mode does not lead to the ionization pro-
cess branching. Some random heterogeneity of the
structure, in particular, the advantage in the ion-electron
emission coefficient of one areas of the cathode surface
on others, leads to more intensive development of the
ionization process in the corresponding direction, but
the subsequent random perturbations complicate the
details of this development almost imperceptibly.
Fig. 2. Perturbation growth increments
for the azimuthal harmonics in cathode-directed
streamer quasi-stationary propagation
In connection with the above, a question arises about
the instability found in numerical simulation of the
cathode-directed streamer [1, 2]. There the development
of azimuthally-inhomogeneous fluctuations was studied
for a formally stationary (within the model) mode of a
streamer propagation with constant velocity in an exter-
nal field close to the homogeneous one. The increment
of instability found there was much less than the ioniza-
tion frequency and somewhat dependent on the harmon-
ic number, as shown in the Fig. 2, corresponding to the
Fig. 2 of the paper [2]. Here one should pay attention to
the difference in the processes of the streamer propagation
to cathode in positive corona, and Trichel pulse develop-
ment in the negative corona. In the case of Trichel pulse,
the electrons move in the direction of the ionized space
propagation, and those ionization acts, due to which this
propagation occurs, are performed by a significant part of
electrons, so that the average number of successive acts of
ionization performed by one of those electrons is relatively
small. In the case of cathode directed streamer, the propa-
gation of the ionized space takes place through an ava-
lanche multiplication of electrons, the initial density of
which in the air is 108…109 times less than one character-
istic of the streamer channel. The electrons move to-
wards the streamer, becoming part of the streamer after
performing about 30 acts of impact ionization
(9⋅log 2 10 ≈ 30). The first acts occur in a relatively
weak field, where the time between successive acts of
impact ionization performed by one electron is larger.
As a result, the increment of perturbation density in-
crease for cathode directed streamer is not 30, but ap-
proximately 100 times less than one for Trichel pulse, as
it follows from the comparison of the Figs. 1 and 2. And
the dependence of increment on the perturbation har-
monic number in the Fig. 2 is related to the difference in
the field strength of different harmonics at the distance
from the streamer head near to its transverse dimension,
for the same charge perturbation amplitude at the head.
Whereas just on the head, in front of cathode directed
streamer channel, the field strength of different harmon-
ics for the same charge perturbation amplitude almost
does not differ, but depends on the sizes related to the
zone of intense ionization in front of the plasma space.
Similarly, in negative corona, the field strength in the
zone of intense ionization near the needle cathode dur-
ing Trichel pulse development is almost the same for
different harmonics, at the same amplitude of space
charge perturbation.
It should be emphasized that the fact of realization
of negative corona at the quasi-stationary voltage in the
form of Trichel pulses, and not streamers, is closely
related to the directions of the propagation of processes
and the motion of electrons. The processes caused by
ionization, developing faster in a strong field near the
needle electrode, start up there and propagate to a plane
electrode, whereas the electrons necessary for ionization
move from cathode to anode, regardless of the shape of
the electrodes. It is worthwhile to describe in more de-
tail how the tendency to transverse localization of the
process in streamer mode of positive corona and the
absence of such tendency in Trichel pulse mode of neg-
ative corona is related to the directions of motion.
3. TRANSVERSE LOCALIZATION
For a positive streamer, which propagates from an-
ode to cathode and is charged positively, transverse lo-
calization is a consequence of correlation of some pa-
rameters inherent to such a streamer.
First, the field strength level in the zone of intensive
ionization in front of the streamer head is largely deter-
mined by the type of dependence of the ionization coef-
ficient on the field strength value. Approximately, the
dependence has the form 0 aexp( )E Eα α= − , where
aE ~ 200 kV / cm. At aE E<< the dependence α on
E is very steep, and at aE E>> it gradually goes to
saturation. When the streamer propagates inside the gap
at the given value of the potential of the streamer head
relative to cathode, the value of the product s md E of the
streamer transverse dimension sd and the maximum
intensity of the field strength mE near the streamer head
is approximately fixed. This assertion is connected with
the fact that the potential, with respect to infinity, of the
sphere with diameter sd and the field strength mE on
its surface is equal to s m 2d E . The streamer propaga-
tion velocity sυ is estimated by the relation
sυ ∼ 1
s id n −Λ , where in is the characteristic frequency
of impact ionization, in ~ e mEαµ , α and eµ are char-
acteristic values of the ionization coefficient and the
electron mobility in the intensive ionization zone, Λ is
the number of ionization acts necessary to increase the
electron density from the initial one to that which is
characteristic for the streamer channel ( Λ ~ 25…30).
This assertion is based, in particular, on the assumption
that the streamer propagation velocity is much greater
than electron drift velocity, and intensive ionization,
ISSN 1562-6016. ВАНТ. 2019. №4(122) 133
with frequency in , begins at a distance sd from the
current position of the streamer head. Under these as-
sumptions, after Λ successive ionization acts with time
intervals i1n , that is, in time inΛ , the forward part of
the streamer channel propagates to a distance, which is
slightly smaller than sd (on the length of the electron
drift during the time inΛ ). As a result,
sυ ∼ 1
s m ed E αµ−Λ , and the streamer velocity is roughly
proportional to the product eαµ . When the field
strength increases, the electron mobility decreases, and
the dependence of the product of ionization coefficient
and electron mobility on the field strength has maxi-
mum at E ~ aE . That is, the streamer propagation ve-
locity is maximal when mE ~ aE , and this value of mE
corresponds to some value s0d of the transverse stream-
er dimension sd , as the value of the product s md E is
approximately fixed. If the streamer dimension sd at
the given value of head potential relative to cathode was
considerably larger than s0d , then from the streamer
head, the new, smaller streamer, with sd ~ s0d , would
begin to propagate with a higher speed, whereas if the
condition s s0d d<< was executed then the streamer
would increase its transverse dimension and velocity
until the condition mE ~ aE is established.
Secondly, the electron density in the positive
streamer channel is also, by the order of magnitude,
determined by the values of the ionization coefficient
and mobility of electrons at E ~ aE . Namely, through
the avalanches multiplication the density of electrons
increases, and therefore, the characteristic time rτ of
the field relaxation, 1
r 0τ σ e−= , where σ is the conduc-
tivity, e eqNσ µ= , decreases. When rτ becomes less
than the characteristic time i1n between two succes-
sive ionization acts carried out by one electron, the field
after the last ionization act has time to weaken, and the
next ionization act does not occur. Thus, the maximum
electron density, attainable in an avalanche, is estimated
by the ratio eN ∼ 1
e 0 i( )qµ e n− , in which the value in
and eµ should be taken for the field strength near to
aE . For the atmospheric air, one gets
eN ∼ (1014...1015) cm −3.
Thirdly, the source of initial electrons for the propa-
gation of avalanches in the atmospheric air is mainly
ionization by photons emitted from such excited states
of the nitrogen molecule, for which the photon energy
exceeds the ionization energy of the oxygen molecule.
The density of electrons obtained due to such ionization
when the streamer propagates reaches the value
(106...107) cm −3. The number of acts of impact ioniza-
tion required to increase the density of electrons from
this value to the value (1014...1015) cm −3 characteristic
for the streamer channel is estimated to be 25…30 and it
depends on the values of those densities logarithmically.
As a result, such a large number of successive acts
of impact ionization in front of the streamer, coupled
with the steep dependence α of E when aE E<< ,
lead to a transversal localization of the streamer propa-
gation process. For example, the difference of only
2.5% in the ionization coefficients for two close ava-
lanche development paths after 30 acts of ionization
gives approximately twice difference in the attained
electron density, with the corresponding consequences
for the prospect of streamer propagation in the corre-
sponding direction. So, the transverse localization of
propagation is an intrinsic feature of positive streamers.
The above considerations relate just to positive
streamers, in which the development of avalanches be-
gins at the points far from the streamer head, and propa-
gates towards the head. On the contrary, in the ioniza-
tion process, which propagates in the direction of the
electron motion, the propagation starts from the volume
with already attained high electron density. Then for the
corresponding movement of the ionization front it is
sufficient only one ionization act, and the small differ-
ence in the ionization coefficient for the different direc-
tions gives a small difference in the rate of the ioniza-
tion front propagation for those directions. That is, it
turns out that the negative streamers, directed to anode,
cannot exist.
But the presented description of the ionization pro-
cess propagation does not take into account the possibil-
ity of its branching, and refers to the case of the quasi-
stationary voltage application and a slight excess of
quasi-stationary voltage over the relevant streamer
mode threshold. The discharge is realized at such volt-
age value in the case when voltage is increased slowly
and the intensive ionization process development occurs
just after the voltage exceeds the threshold. If the volt-
age is applied for the time of the order of nanoseconds,
then the process goes on just in the field corresponding
to the instantaneous value of the applied voltage, which
can significantly exceed the threshold. And then the
points, in which E ~ aE , can be located far from the
current position of the negative streamer head. And be-
fore the streamer head approaches those points through
ionization, along with the displacement of electrons
from the former location of the head, from those points
it has time to develop an avalanche, the backward end
of which largely has the properties of the streamer
channel. And for the old head, to become the part of that
channel it is sufficient to reach it. In addition, from that
channel, it may begin the process of the positive stream-
er propagation, directed to the head. In any case, the
connection of the old head with the high conductive
plasma corresponds to the formation of a continuous
channel of the streamer, which has already propagated
further. But there may be a lot of the points, from which
the development of avalanches begins, and then, with a
high probability, the streamer branching may occur.
The positive streamer, directed to the cathode, also
can propagate at the voltage value significantly greater
than the streamer mode threshold in the case of the qua-
si-stationary voltage application. And then the devel-
opment of avalanches starts from many points, more
distant from the head, than it is in the case of voltage
close to the threshold. And after the avalanche coming
to the head, a few remnants of their traces can turn into
ISSN 1562-6016. ВАНТ. 2019. №4(122) 134
channels of the branched positive streamer. However,
positive streamers can exist and branch out also at a
voltage close to the threshold.
CONCLUSIONS
In the numerical simulations of negative corona dis-
charge in Trichel pulse mode with the calculation of the
evolution of azimuthal perturbations, it is found the az-
imuthal instability with the value of increment corre-
sponding to electron avalanche multiplication through
the impact ionization. This formally obtained instability
does not lead to the branching of the process in reality,
because it is suppressed at the nonlinear stage of the
avalanche development. It becomes obviously that the
azimuthal instability of the cathode directed streamer
propagation in positive corona discharge obtained earli-
er has the same nature. The difference of these instabili-
ties in the increment values is connected with the direc-
tions of the electron motion and the process propaga-
tion: in the negative corona the direction is the same,
whereas in the positive corona the directions are oppo-
site. It is discussed, how the difference in the process
courses is connected with the absence of the streamer
mode in the negative corona at the quasi-stationary volt-
age application.
REFERENCES
1. O. Bolotov, B. Kadolin, S. Mankovskyi, et al. Quasi-
stationary streamer propagation // Problems of
Atomic Science and Technology. Series “Plasma
Electronics and New Methods of Acceleration”.
2015, № 4, p. 185-188.
2. O. Bolotov, B. Kadolin, S. Mankovskyi, et al. Nu-
merical simulations of quasi-stationary streamer
propagation // Problems of Atomic Science and
Technology. Series “Nuclear Physics Investiga-
tions”. 2016, № 5, p. 121-125.
3. O. Bolotov, V. Golota, B. Kadolin, et al. Develop-
ment of azimuthally not uniform processes in corona
discharge in axially symmetric gap // Problems of
Atomic Science and Technology. Series “Plasma
Electronics and New Methods of Acceleration”.
2013, № 4, p. 161-165.
Article received 02.06.2019
АЗИМУТАЛЬНАЯ УСТОЙЧИВОСТЬ ИМПУЛЬСОВ ТРИЧЕЛА И НАПРАВЛЕННЫХ К КАТОДУ
СТРИМЕРОВ
О. Болотов, Б. Кадолин, С. Маньковский, В. Остроушко, И. Пащенко, Г. Таран, Л. Завада
Выполнено численное моделирование отрицательной короны в режиме импульсов Тричела с расчетом
эволюции азимутальных возмущений. Выявлена азимутальная неустойчивость с инкрементом, соответ-
ствующим развитию лавины. Эта неустойчивость подавляется на нелинейной стадии и не ведет к ветвлению
процесса. Результат также применим к выявленной ранее азимутальной неустойчивости направленного к
катоду стримера. Разница в их инкрементах следует из разницы в ходе процессов, которые обсуждаются.
АЗИМУТАЛЬНА СТІЙКІСТЬ ІМПУЛЬСІВ ТРИЧЕЛА ТА СПРЯМОВАНИХ ДО КАТОДA
СТРИМЕРІВ
О. Болотов, Б. Кадолін, С. Маньковський, В. Остроушко, І. Пащенко, Г. Таран, Л. Завада
Виконане числове моделювання негативної корони в режимі імпульсів Тричела з розрахунком еволюції
азимутальних збурень. Виявлено азимутальну нестійкість з інкрементом, відповідним розвитку лавини. Ця
нестійкість пригнічується на нелінійній стадії і не веде до галуження процесу. Результат також застосо-
вується до виявленої раніше азимутальної нестійкості спрямованого до катода стримера. Різниця в їхніх ін-
крементах випливає з різниці в ході процесів, які обговорюються.
E-mail: ostroushko-v@kipt.kharkov.ua
INTRODUCTION
1. SIMULATION MODEL
2. SIMULATION RESULTS
3. TRANSVERSE LOCALIZATION
CONCLUSIONS
REFERENCES
О. Болотов, Б. Кадолін, С. Маньковський, В. Остроушко, І. Пащенко, Г. Таран, Л. Завада
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