Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air
The results of numerical simulations of the propagation of a positive streamer in air in the uniform and strongly non - uniform electric fields are presented. It is shown that the dynamics of the streamer propagation in air retains the main features characteristic of a negative streamer in nitrogen....
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Cite this: | Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air / O.V. Manuilenko // Вопросы атомной науки и техники. — 2013. — № 4. — С. 194-199. — Бібліогр.: 14 назв. — англ. |
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Manuilenko, O.V. 2017-01-17T20:09:19Z 2017-01-17T20:09:19Z 2013 Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air / O.V. Manuilenko // Вопросы атомной науки и техники. — 2013. — № 4. — С. 194-199. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.80.Mg, 52.80.Tn https://nasplib.isofts.kiev.ua/handle/123456789/112182 The results of numerical simulations of the propagation of a positive streamer in air in the uniform and strongly non - uniform electric fields are presented. It is shown that the dynamics of the streamer propagation in air retains the main features characteristic of a negative streamer in nitrogen. It is shown that the velocity of the streamer in a non - uniform electric field is higher than its velocity in an uniform field at given voltages on electrodes. It is shown that with decreasing needle radius the velocity of the streamer is increased at given voltages on electrodes. This growth continues until a critical radius, after which the growth of the positive streamer velocity practically stops. Наведено результати числового моделювання поширення позитивного стримера в повітрі в однорідних і сильно неоднорідних електричних полях. Показано, що динаміка поширення стримера в повітрі зберігає основні риси, характерні для негативного стримера в азоті. Показано, що швидкість розповсюдження стримера в неоднорідному полі більше за його швидкість в однорідному полі при заданих потенціалах на електродах. Показано, що швидкість стримера зростає із зменшенням радіусу кривизни голки при заданих потенціалах на електродах. Це зростання триває до деякого критичного радіусу, після якого зростання швидкості позитивного стримера практично припиняється. Приведены результаты численного моделирования распространения положительного стримера в воздухе в однородных и сильно неоднородных электрических полях. Показано, что динамика распространения стримера в воздухе сохраняет основные черты, характерные для отрицательного стримера в азоте. Показано, что скорость распространения стримера в неоднородном поле больше его скорости в однородном поле при заданных потенциалах на электродах. Показано, что скорость стримера растет с уменьшением радиуса кривизны иглы при заданных потенциалах на электродах. Этот рост продолжается до некоторого критического радиуса, после которого рост скорости положительного стримера практически прекращается. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Плазменно-пучковый разряд, газовый разряд и плазмохимия Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air Числове моделювання динаміки позитивного стримера в однорідних і неоднорідних електричних полях у повітрі Численное моделирование динамики положительного стримера в однородных и неоднородных электрических полях в воздухе Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air |
| spellingShingle |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air Manuilenko, O.V. Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| title_short |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air |
| title_full |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air |
| title_fullStr |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air |
| title_full_unstemmed |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air |
| title_sort |
сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air |
| author |
Manuilenko, O.V. |
| author_facet |
Manuilenko, O.V. |
| topic |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| publishDate |
2013 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Числове моделювання динаміки позитивного стримера в однорідних і неоднорідних електричних полях у повітрі Численное моделирование динамики положительного стримера в однородных и неоднородных электрических полях в воздухе |
| description |
The results of numerical simulations of the propagation of a positive streamer in air in the uniform and strongly non - uniform electric fields are presented. It is shown that the dynamics of the streamer propagation in air retains the main features characteristic of a negative streamer in nitrogen. It is shown that the velocity of the streamer in a non - uniform electric field is higher than its velocity in an uniform field at given voltages on electrodes. It is shown that with decreasing needle radius the velocity of the streamer is increased at given voltages on electrodes. This growth continues until a critical radius, after which the growth of the positive streamer velocity practically stops.
Наведено результати числового моделювання поширення позитивного стримера в повітрі в однорідних і сильно неоднорідних електричних полях. Показано, що динаміка поширення стримера в повітрі зберігає основні риси, характерні для негативного стримера в азоті. Показано, що швидкість розповсюдження стримера в неоднорідному полі більше за його швидкість в однорідному полі при заданих потенціалах на електродах. Показано, що швидкість стримера зростає із зменшенням радіусу кривизни голки при заданих потенціалах на електродах. Це зростання триває до деякого критичного радіусу, після якого зростання швидкості позитивного стримера практично припиняється.
Приведены результаты численного моделирования распространения положительного стримера в воздухе в однородных и сильно неоднородных электрических полях. Показано, что динамика распространения стримера в воздухе сохраняет основные черты, характерные для отрицательного стримера в азоте. Показано, что скорость распространения стримера в неоднородном поле больше его скорости в однородном поле при заданных потенциалах на электродах. Показано, что скорость стримера растет с уменьшением радиуса кривизны иглы при заданных потенциалах на электродах. Этот рост продолжается до некоторого критического радиуса, после которого рост скорости положительного стримера практически прекращается.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112182 |
| citation_txt |
Сomputer simulation of positive streamer dynamics in uniform and non-uniform electric fields in air / O.V. Manuilenko // Вопросы атомной науки и техники. — 2013. — № 4. — С. 194-199. — Бібліогр.: 14 назв. — англ. |
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2025-11-25T12:17:27Z |
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2025-11-25T12:17:27Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2013. №4(86) 194
COMPUTER SIMULATION OF POSITIVE STREAMER DYNAMICS
IN UNIFORM AND NON-UNIFORM ELECTRIC FIELDS IN AIR
O.V. Manuilenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: ovm@kipt.kharkov.ua
The results of numerical simulations of the propagation of a positive streamer in air in the uniform and strongly
non - uniform electric fields are presented. It is shown that the dynamics of the streamer propagation in air retains
the main features characteristic of a negative streamer in nitrogen. It is shown that the velocity of the streamer in a
non - uniform electric field is higher than its velocity in an uniform field at given voltages on electrodes. It is shown
that with decreasing needle radius the velocity of the streamer is increased at given voltages on electrodes. This
growth continues until a critical radius, after which the growth of the positive streamer velocity practically stops.
PACS: 52.80.Mg, 52.80.Tn
INTRODUCTION
Papers [1 - 7] are devoted to the numerical modeling
of the positive (cathode-directed) streamer in air within
the drift-diffusion approximation. These works are used
both structured and unstructured meshes to solve the
continuity and Poisson equations. Streamer is a nonlin-
ear structure with a sharp edge. Therefore, for its correct
resolution in numerical simulations were used the expo-
nential representation for the current density in the drift-
diffusion approximation − the Scharfetter-Gummel al-
gorithm [8], or flux − corrected transport schemes [9].
In [1 - 7], for different values of the applied voltage,
different radii of curvature of the needle, and different
distances between the electrodes, the velocity of the
streamer obtained in the range of 107…108 cm/s, which
is in good agreement with experiment. A systematic
study of the influence of radius of the needle on the
speed of the positive streamer is not conducted. This is
the subject of the paper.
The computer simulations of the negative (anode -
directed) streamers in nitrogen in the uniform (plane - to
- plane geometry) and non - uniform (needle - to - plane
geometry) fields are presented in [10, 11]. It is shown
that the behavior of the streamer velocity versus time
has four specific regions: a sharp drop at the beginning
of the movement, a propagation with a constant veloc-
ity, an area of the first (low) acceleration, and a region
of the second (strong) acceleration at the approach of
the streamer head to an anode. It is shown that the ve-
locity of the negative streamer in a non - uniform elec-
tric field is always higher than its velocity in an uniform
field at the same potentials on the electrodes. It is shown
in [11] that with decreasing radius of the needle, the
streamer velocity is increased. The growth of the
streamer speed, with decreasing of the needle radius, is
stopped when the needle curvature radius reaches a cer-
tain critical size.
Below the results of numerical simulations, using
the finite element method (SUPG, CWDPG), of positive
streamer dynamics in air are presented. The computer
simulations have been performed for uniform and for
non - uniform electric fields. It is shown that the dynam-
ics of the streamer propagation in air retains the main
features characteristic of a negative streamer in nitro-
gen.
1. MODEL
The coupled continuity equations for electrons, posi-
tive ions, negative ions, and Poisson equation for simu-
lation of positive streamer dynamics in air are:
( ) epattphize
e LSSS
t
n
−−+=Γ⋅∇+
∂
∂ r
, (1)
pnepphiz
p LLSS
t
n
−−+=
∂
∂
, (2)
pnatt
n LS
t
n
−=
∂
∂
, (3)
oV ερ /2 −=∇ , (4)
where en , pn , nn are the number densities for electrons,
positive ions and negative ions, eeeee nDEn ∇−−=Γ
rr
μ
is the electron flux in the drift-diffusion approximation,
eμ , eD are the electron mobility and diffusion coeffi-
cients, V is the potential of the electric field,
,VE −∇=
r
( )nep nnne −−=ρ , e is the electron
charge, oε is the permittivity of free space. In Eqs. (1) -
(3), S and L stand for sources and losses of charged
particles. izS is the rate of charged particle generation
due to collisional ionization, phS is the rate of
photoionization, attS is the rate of electron attachment,
epL is the rate of electron-ion recombination, and pnL
is the rate of ion-ion recombination. Ions in (2), (3) are
considered as immovable since their mobility several
orders of magnitude smaller than the electron mobility,
which allows, for the simulation time, neglect their dis-
placement. In the calculations was used a set of trans-
port coefficients and rate constants given in [12, 13].
The rate of photoionization in air is [14]:
( ) ( ) ( )∫
′
′′=
V
ph VdRRgrIrS 24/ πrr
, (5)
where rrR ′−=
rr
, ( ) )/()( qqiz ppprSrI +′=′
rr ξ ,
( ) ( ) ( )
( )minmax
maxmin
/ln
expexp
22
χχ
χχ
R
RpRp
Rg OO −−−
= . Here
ξ =0.1, qp =30 Torr, p is the total pressure of the gas
mixture, minχ =3.5⋅10-2 cm-1Torr-1, maxχ =2.0, cm-1⋅Torr-1.
ISSN 1562-6016. ВАНТ. 2013. №4(86) 195
Fig. 1 shows the simulation domain and boundary
conditions. Initially electrons and ions are located at the
anode with number densities:
( )2 2
, , , , exp / ( ) /e p n e p n r z zn r z Lδ σ σ= − − − , eδ =9⋅1013 cm-3,
pδ = 1⋅1014 cm-3, nδ = 1⋅1013 cm-3, rσ = 1⋅10-4 cm2,
zσ = 6.25⋅10-4 cm2. Anode voltage is 0V = 8 kV, zL = 0.2 cm,
rL = 0.05 cm, needle radius is one of R ={0.25, 0.5,
1.0, 2.0}⋅ ndlH , needle height is ndlH = 0.3125 mm. In
the case of plane - to - plane geometry R + ndlH = 0.
Fig. 1. Simulation domain and boundary conditions
2. UNIFORM ELECTRIC FIELDS
Figs. 2, 3 show the dynamics of positive streamer in
the homogeneous fields. The initial conditions are cho-
sen to avoid the avalanche stage, when the Laplacian
electric field is not disturbed by the field of the gener-
ated space charge field - ∝pe,δ 1014 cm-3.
Fig. 2 shows distribution of the space charge density
);,( tzrρ in { }zr, at different times. Fig. 3 presents
the distribution of the absolute value of the electric field
);,( tzrE
r
at the same time points. The arrows in
Figs. 2 and 3 show the electric field );,( tzrE
r
. After a
short initial stage (< 1⋅10-10 s), a positive streamer is
formed. It moves in the direction of the applied Lapla-
cian field. For t > 1⋅10-9 s the electric field is substan-
tially enhanced in front of the streamer head, and at-
tenuated behind it. After an initial rise, the electric field
in front of the streamer head slightly decreases as it
moves toward the cathode. It is clear from Fig. 2 that
after the formation of the streamer head, the radius first
decreases and then increases as it moves to the cathode,
creating a constriction on the body of the streamer.
Fig. 4 shows the distributions in { }zr, of the impact
ionization rate );,( tzrSiz at different times, and the
corresponding distributions of the photoionization
rate );,( tzrS ph . It is clear from Fig. 4 that the generatin
of the electrons due to photoionization has a maximum
in the vicinity of the streamer head, where is maximal
impact ionization. The photoionization region is always
wider than the area of impact ionization, which leads to
the birth of the electrons in front of the positive streamer
head, and is one of the conditions of its movement.
Fig. 2. Space charge density );,( tzrρ
Fig. 3. Absolute value of the electric field );,( tzrE
r
ISSN 1562-6016. ВАНТ. 2013. №4(86) 196
Fig. 5 shows the space charge density );,0( tzr =ρ
and the absolute value of the electric field
);,0( tzrE =
r
on the axis at different times during the
movement of the streamer. After a rapid rise in the ini-
tial stage, the space charge density );,0( tzr =ρ and
the electric field );,0( tzrE =
r
at the streamer head
decrease. When the head of the streamer approaches the
cathode, the local electric field in front of the streamer
head is increased. This leads to the growing impact
ionization rate and the rate of photoionization. This, in
turn, leads to an increase in the densities of charged
particles, and the rise of the space charge density
);,0( tzr =ρ .
Fig. 4. Left column - );,( tzrSiz .
Right column - );,( tzrS ph
Fig. 5. Space charge density );,0( tzr =ρ and electric
field );,0( tzrE =
r
on the axis at different times
As the streamer moves to the cathode, the positive
streamer head is broadened in the longitudinal direction,
which is associated with the presence of photoioniza-
tion. It is clearly seen from the space charge density
distributions on the axis at different times (see Fig. 5).
This behavior differs from the movement of the nega-
tive streamer in nitrogen, where there is no photoioniza-
tion, and the head of the negative streamer, as it moves
towards the anode, shrinks and increases in magnitude.
Fig. 6 shows the z-coordinate of the maximum of
the electric field max|);,0(| tzrE =
r
on the axis versus
time, and the velocity of max|);,0(| tzrE =
r
versus
time, which is the positive streamer propagation veloc-
ity through the discharge gap - )(tVs .
The behavior of this velocity has, as in the case of
the negative streamer in nitrogen [11], the characteristic
regions: (1) the sharp drop of the velocity at the begin-
ning of the movement, (2) the propagation with a con-
stant velocity, (3) the area of the first (low) acceleration,
and (4) the region of the second (strong) acceleration at
the approach of the streamer head to the cathode. In
contrast to the negative streamer in nitrogen [11], the
region of constant velocity can not be identified as the
initial linear stage of the avalanche development, when
the space charge is small, and the external electric field
is practically not distorted by the space charge.
Fig. 6. z-coordinate of the maximum of the electric field
max|);,0(| tzrE =
r
on the axis versus time,
and streamer velocity )(tVs versus time
3. NON-UNIFORM ELECTRIC FIELDS
Figs. 7, 8 show, as an example, the simulation results
of the positive streamer propagation through the dis-
charge gap with non - uniform electric fields. 0V = 8 kV,
R = 1.0⋅Hndl. The initial and boundary conditions are
the same as in Section 3. Fig. 7 presents the space
charge density );,( tzrρ at different time points. Fig. 8
shows the the absolute value of the electric field
);,( tzrE
r
at the same time points. The arrows indicate
the electric field.
ISSN 1562-6016. ВАНТ. 2013. №4(86) 197
The dynamics of the streamer passage through the
discharge gap is changed in comparison with the case of
the uniform field. These changes are due to increased
vacuum (Laplacian) electric field on the needle and the
appearance of the radial electric field. The increased
Laplacian electric field on the tip causes movement of
the streamer, at least at the initial stage, in higher fields
as compared with the plane - to - plane case. Which in
turn, leads to an increase in its speed (see also Figs. 9,
10), and a decrease the time of the streamer formation.
The radial electric field increases the transverse dimen-
sion of the streamer in comparison with the plane - to -
plane case.
After a short initial stage (< 1⋅10-10 s), a positive
streamer is formed. For t > 1⋅10-9 s the electric field is
enhanced in front of the positive streamer head, and
attenuated behind it.
Fig. 7. Space charge density );,( tzrρ
After an initial growth, the electric field in front of
the streamer head decreases as it moves through the
discharge gap, and then increases when the head of
streamer comes close to the cathode. It is clear from
Fig. 7 that after the formation of the streamer head, the
radius first decreases and then increases as it moves to
the cathode, creating a constriction on the body of the
streamer. As in the plane case, the generation of the
electrons due to photoionization has a maximum in the
vicinity of the streamer head, where is maximal impact
ionization. Photoionization region is always wider than
the area of impact ionization, which leads to the birth of
the electrons in front of the positive streamer head.
Fig. 9 shows the z-coordinates of the maximum of
the electric field max|);,0(| tzrE =
r
on the axis as func-
tion of time, and velocities of the positive streamers
)(tVs for different values of the radii of the needle
R = {0.25, 0.5, 1.0, 2.0, inf}⋅ ndlH at anode potential
0V = 8 kV. The R = inf means uniform electric field,
or plane - to - plane computational domain.
Fig. 8. Absolute value of the electric field );,( tzrE
r
As seen from Fig. 9, the velocity of the positive
streamer versus time )(tVs behaves as a speed of the
negative streamer in nitrogen [11]. There are four char-
acteristic regions: (1) the sharp drop of the velocity at
the beginning of the movement, (2) the propagation
with a constant velocity, (3) the area of the first (weak)
acceleration, and (4) the region of the second (strong)
acceleration at the approach of the streamer head to the
cathode. As seen from Fig. 9, the streamer velocity in-
creases with decreasing radius of curvature of the needle
at a predetermined potential on the anode. This increase
in the velocity goes up to a certain radius (in this case
R = 0.5⋅ ndlH ), after which the growth of the streamer
speed is cuted off.
Fig. 10 shows the streamer mean velocity >< sV as a
function of the needle radius. Mean velocity is defined
as trzs LV τ/>=< , where zL is the discharge gap
length, trτ is the passage time of the streamer through
the discharge gap. The dashed line in Fig. 10 shows the
ISSN 1562-6016. ВАНТ. 2013. №4(86) 198
speed >< sV for uniform field. It can be seen that the
>< sV increases with decreasing R . Starting from
some R , the growth of the speed stops. It is also seen
that the velocity in a non - uniform field is higher than
the speed in an uniform field.
Fig. 9. Positive streamer dynamics for different radii of
the needle R = {0.25, 0.5, 1.0, 2.0, inf}. ndlH . Applied
voltage 0V = 8 kV. ndlH = 0.3125 mm. Top -
z-coordinate of the maximum of the electric field
max|);,0(| tzrE =
r
on the axis versus time.
Bottom - streamer velocity )(tVs versus time
Fig. 10. The dependence of the positive streamer
average speed >< sV on the radius of the needle
R = {0.25, 0.5, 1.0, 2.0, inf}. ndlH for applied voltage
0V = 8 kV. ndlH = 0.3125 mm
CONCLUSIONS
The results of numerical simulations of the propaga-
tion of a positive streamer in the atmospheric pressure
air in the uniform and strongly non - uniform electric
fields are presented. It is shown that the velocity of the
positive streamer versus time behaves as a speed of the
negative streamer in nitrogen [11]. There are four char-
acteristic regions: the sharp drop of the velocity at the
beginning of the movement, the propagation with a
nearly constant velocity, the area of the first (low) ac-
celeration, and the region of the second (strong) accel-
eration at the approach of the streamer head to the cath-
ode.
It is shown that the propagation velocity of the posi-
tive streamer in a non - uniform electric field is higher
than its velocity in an uniform field at given voltages on
electrodes.
It is shown that with decreasing needle radius veloc-
ity of the streamer is increased at given voltages on
electrodes. This growth continues until a critical radius,
after which the growth of the positive streamer velocity
practically stops.
REFERENCES
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ISSN 1562-6016. ВАНТ. 2013. №4(86) 199
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ ПОЛОЖИТЕЛЬНОГО СТРИМЕРА
В ОДНОРОДНЫХ И НЕОДНОРОДНЫХ ЭЛЕКТРИЧЕСКИХ ПОЛЯХ В ВОЗДУХЕ
О.В. Мануйленко
Приведены результаты численного моделирования распространения положительного стримера в воздухе
в однородных и сильно неоднородных электрических полях. Показано, что динамика распространения
стримера в воздухе сохраняет основные черты, характерные для отрицательного стримера в азоте. Показано,
что скорость распространения стримера в неоднородном поле больше его скорости в однородном поле при
заданных потенциалах на электродах. Показано, что скорость стримера растет с уменьшением радиуса кри-
визны иглы при заданных потенциалах на электродах. Этот рост продолжается до некоторого критического
радиуса, после которого рост скорости положительного стримера практически прекращается.
ЧИСЛОВЕ МОДЕЛЮВАННЯ ДИНАМІКИ ПОЗИТИВНОГО СТРИМЕРА В ОДНОРІДНИХ
І НЕОДНОРІДНИХ ЕЛЕКТРИЧНИХ ПОЛЯХ У ПОВІТРІ
О.В. Мануйленко
Наведено результати числового моделювання поширення позитивного стримера в повітрі в однорідних і
сильно неоднорідних електричних полях. Показано, що динаміка поширення стримера в повітрі зберігає
основні риси, характерні для негативного стримера в азоті. Показано, що швидкість розповсюдження стри-
мера в неоднорідному полі більше за його швидкість в однорідному полі при заданих потенціалах на елект-
родах. Показано, що швидкість стримера зростає із зменшенням радіусу кривизни голки при заданих потен-
ціалах на електродах. Це зростання триває до деякого критичного радіусу, після якого зростання швидкості
позитивного стримера практично припиняється.
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