Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity
The results of numerical simulations of the propagation of a negative streamer in nitrogen in the uniform and strongly non-uniform electric fields are presented. It is shown that the propagation velocity of the streamer in a nonuniform electric field is always higher than its velocity in an uniform...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity / O.V. Manuilenko, V.I. Golota // Вопросы атомной науки и техники. — 2013. — № 4. — С. 189-193. — Бібліогр.: 8 назв. — англ. |
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Manuilenko, O.V. Golota, V.I. 2017-01-17T19:55:37Z 2017-01-17T19:55:37Z 2013 Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity / O.V. Manuilenko, V.I. Golota // Вопросы атомной науки и техники. — 2013. — № 4. — С. 189-193. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.80.Mg, 52.80.Tn https://nasplib.isofts.kiev.ua/handle/123456789/112169 The results of numerical simulations of the propagation of a negative streamer in nitrogen in the uniform and strongly non-uniform electric fields are presented. It is shown that the propagation velocity of the streamer in a nonuniform electric field is always higher than its velocity in an uniform field at given voltages on electrodes. It is shown that as the needle radius decreases, the velocity of the streamer increases. The growth of streamer velocity, with decrease of the needle radius, is stopped when the needle curvature radius reaches a certain critical size. It is shown that in the region of the strong nonlinearity, when the streamer dynamics is determined by the charge of the streamer head, its velocity as a function of the longitudinal coordinate is independent of the needle radius. It is shown that the velocity of the streamer increases with growth of the applied voltage. Наведено результати числового моделювання поширення негативного стримера в азоті в однорідних і сильно неоднорідних електричних полях. Показано, що швидкість поширення стримера в неоднорідному полі завжди більша його швидкості в однорідному полі при однакових потенціалах на електродах. Показано, що при зменшенні радіуса голки швидкість стримера збільшується при заданій напрузі на електродах. Зростання швидкості стримера, із зменшенням радіуса голки, припиняється, коли радіус кривизни голки досягає деякого критичного розміру. Показано, що в області сильної нелінійності, коли динаміка поширення стримера визначається його об'ємним зарядом, його швидкість, як функція поздовжньої координати не залежить від радіуса голки. Показано, що швидкість стримера зростає з ростом напруги, що прикладена до електродів. Приведены результаты численного моделирования распространения отрицательного стримера в азоте в однородных и сильно неоднородных электрических полях. Показано, что скорость распространения стримера в неоднородном поле всегда больше его скорости в однородном поле при одинаковых потенциалах на электродах. Показано, что при уменьшении радиуса иглы скорость стримера увеличивается при заданном напряжении на электродах. Рост скорости стримера, с уменьшением радиуса иглы, прекращается, когда радиус кривизны иглы достигает некоторого критического размера. Показано, что в области сильной нелинейности, когда динамика распространения стримера определяется его объемным зарядом, его скорость, как функция продольной координаты не зависит от радиуса иглы. Показано, что скорость стримера возрастает с ростом напряжения, приложенного к электродам. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity Числове моделювання негативних стримерів у сильних неоднорідних електричних полях в азоті. Вплив радіуса голки і прикладеної напруги на швидкість стримера Численное моделирование отрицательных стримеров в сильных неоднородных электрических полях в азоте. Влияние радиуса иглы и приложенного напряжения на скорость стримера Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity |
| spellingShingle |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity Manuilenko, O.V. Golota, V.I. Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| title_short |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity |
| title_full |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity |
| title_fullStr |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity |
| title_full_unstemmed |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity |
| title_sort |
numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. effect of needle radius and applied voltage on streamer velocity |
| author |
Manuilenko, O.V. Golota, V.I. |
| author_facet |
Manuilenko, O.V. Golota, V.I. |
| topic |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| publishDate |
2013 |
| language |
English |
| container_title |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Числове моделювання негативних стримерів у сильних неоднорідних електричних полях в азоті. Вплив радіуса голки і прикладеної напруги на швидкість стримера Численное моделирование отрицательных стримеров в сильных неоднородных электрических полях в азоте. Влияние радиуса иглы и приложенного напряжения на скорость стримера |
| description |
The results of numerical simulations of the propagation of a negative streamer in nitrogen in the uniform and strongly non-uniform electric fields are presented. It is shown that the propagation velocity of the streamer in a nonuniform electric field is always higher than its velocity in an uniform field at given voltages on electrodes. It is shown that as the needle radius decreases, the velocity of the streamer increases. The growth of streamer velocity, with decrease of the needle radius, is stopped when the needle curvature radius reaches a certain critical size. It is shown that in the region of the strong nonlinearity, when the streamer dynamics is determined by the charge of the streamer head, its velocity as a function of the longitudinal coordinate is independent of the needle radius. It is shown that the velocity of the streamer increases with growth of the applied voltage.
Наведено результати числового моделювання поширення негативного стримера в азоті в однорідних і сильно неоднорідних електричних полях. Показано, що швидкість поширення стримера в неоднорідному полі завжди більша його швидкості в однорідному полі при однакових потенціалах на електродах. Показано, що при зменшенні радіуса голки швидкість стримера збільшується при заданій напрузі на електродах. Зростання швидкості стримера, із зменшенням радіуса голки, припиняється, коли радіус кривизни голки досягає деякого критичного розміру. Показано, що в області сильної нелінійності, коли динаміка поширення стримера визначається його об'ємним зарядом, його швидкість, як функція поздовжньої координати не залежить від радіуса голки. Показано, що швидкість стримера зростає з ростом напруги, що прикладена до електродів.
Приведены результаты численного моделирования распространения отрицательного стримера в азоте в однородных и сильно неоднородных электрических полях. Показано, что скорость распространения стримера в неоднородном поле всегда больше его скорости в однородном поле при одинаковых потенциалах на электродах. Показано, что при уменьшении радиуса иглы скорость стримера увеличивается при заданном напряжении на электродах. Рост скорости стримера, с уменьшением радиуса иглы, прекращается, когда радиус кривизны иглы достигает некоторого критического размера. Показано, что в области сильной нелинейности, когда динамика распространения стримера определяется его объемным зарядом, его скорость, как функция продольной координаты не зависит от радиуса иглы. Показано, что скорость стримера возрастает с ростом напряжения, приложенного к электродам.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112169 |
| citation_txt |
Numerical simulation of negative streamers in strong non-uniform electric fields in nitrogen. Effect of needle radius and applied voltage on streamer velocity / O.V. Manuilenko, V.I. Golota // Вопросы атомной науки и техники. — 2013. — № 4. — С. 189-193. — Бібліогр.: 8 назв. — англ. |
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2025-11-26T02:58:33Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2013. №4(86) 189
NUMERICAL SIMULATION OF NEGATIVE STREAMERS IN STRONG
NON-UNIFORM ELECTRIC FIELDS IN NITROGEN.
EFFECT OF NEEDLE RADIUS AND APPLIED VOLTAGE
ON STREAMER VELOCITY
O.V. Manuilenko, V.I. Golota
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 negative streamer in nitrogen in the uniform and
strongly non-uniform electric fields are presented. It is shown that the propagation velocity of the streamer in a non-
uniform electric field is always higher than its velocity in an uniform field at given voltages on electrodes. It is
shown that as the needle radius decreases, the velocity of the streamer increases. The growth of streamer velocity,
with decrease of the needle radius, is stopped when the needle curvature radius reaches a certain critical size. It is
shown that in the region of the strong nonlinearity, when the streamer dynamics is determined by the charge of the
streamer head, its velocity as a function of the longitudinal coordinate is independent of the needle radius. It is
shown that the velocity of the streamer increases with growth of the applied voltage.
PACS: 52.80.Mg, 52.80.Tn
INTRODUCTION
Papers [1 - 5] are devoted to the numerical modeling
of the negative streamer in nitrogen within the drift -
diffusion approximation. In these works, with the ex-
ception of [5], the regular nonadaptive meshes to solve
the continuity and Poisson equations are used. Streamer
is a nonlinear structure with a sharp edge. Therefore, for
its correct resolution in numerical simulations the expo-
nential representation for the current density in the drift-
diffusion approximation - the Scharfetter-Gummel algo-
rithm [6], or numerical schemes with adaptation of a
regular grid [5] were used. Regular meshes, as opposed
to irregular grids, which are used in the finite element
method, can not accurately describe the arbitrary
boundaries of complex shape, such as the needle - to -
plane. Therefore, the finite element method was used in
our simulations.
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 [7, 8]. The effect of
the needle radius on the negative streamer speed has
been studied just for one electrode potential. It has been
shown that the velocity of the negative streamer in a
nonuniform electric field is higher than its velocity in a
uniform field. It has been shown that as the radius of the
needle decreases, the streamer velocity increases.
The results of numerical simulations of negative
streamer dynamics in nitrogen, using the finite element
method (SUPG, CWDPG), are presented below. The
computer simulations were performed for uniform and
non-uniform electric fields. The effect of applied volt-
ages at different radii of the needle on the streamer
speed is investigated.
1. MODEL
The set of equations describing the propagation of
the negative (anode - directed) streamer in nitrogen is:
( ) izeeee
e SnDEn
t
n
=∇−−⋅∇+
∂
∂ r
μ , (1)
( ) iziiii
i SnDEn
t
n
=∇−⋅∇+
∂
∂ r
μ (2)
( )ie
o
nneV −=∇
ε
2 , VE −∇=
r
, (3)
where en in are the number densities for electrons and
positive ions, eμ , iμ are the electron and ion mobili-
ties, eD , iD are the diffusion coefficients for electrons
and ions. V is the potential of electric field, e is the
electron charge, oε is the permittivity of free space. izS
is the rate of charged particle generation due to colli-
sional ionization:
( )EEEnS ooeeiz
rr
/exp|| −= αμ , (4)
where oα is the ionization coefficient, oE is the
threshold field for impact ionization. In the right hand
sides of equations (1) and (2) other sources and sinks of
charged particles, such as, photoionization and recom-
bination, were not included. These sources and sinks are
negligible, compared to the impact ionization, for pure
nitrogen on the simulation time (streamer propagation
time through the discharge gap).
Expression (4) allows the introduction of a set of natu-
ral scales: spatial scale ool α/1= , electric field scale oE ,
velocity scale oeo Ev μ= , time scale ooo vlt /= , diffusion
scale ooo tlD /2= , and density scale ( )oooo leEn ⋅⋅= /ε .
For nitrogen, under normal conditions,
oE = 197600 V/cm, oα =4332 cm-1, eμ =460 cm2V-1s-1.
Passing in (1) - (3) to dimensionless variables olrr /rr
= ,
ottt /= , oee nnn /= , oii nnn /= , the following equa-
tions can be obtained:
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=∇−−⋅∇+
∂
∂
||
1exp||
ε
εε r
rr
eee
e nnDn
t
n
,
(5)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
∂
∂
||
1exp||
ε
ε r
r
e
i n
t
n
,
(6)
ρ−≡−=∇ ie nnV2 , V−∇=ε
r
. (7)
ISSN 1562-6016. ВАНТ. 2013. №4(86) 190
Ions in (6) are further considered as immovable,
since their mobility is several orders of magnitude
smaller than the electron mobility, which allows ne-
glecting their displacement for the simulation time.
Fig. 1 shows the simulation domain, example of
mesh for solution of (5) - (7) and the boundary condi-
tions. Initially electrons and ions are located at the cath-
ode with number densities: ( )σδ /exp 2rnn ie
r
−⋅== ,
δ =10-4, σ =100. The potential of the anode changed in
simulations: 0V = {96, 128, 160, 192}, which corre-
sponds for the plane - to - plane geometry approxi-
mately to {74.1, 98.8, 123.5, 148.2} kVcm-1. Dimen-
sionless diffusion coefficient is D = 0.1, which corre-
sponds to 1800 cm2s-1. The other parameters are:
zL =256, rL = 128, H = 40, needle radius is one of
nR ={20, 40, 80, inf}. nR = inf means uniform electric
fields, or plane - to - plane simulation domain. For the
plane - to - plane computation domain nR + ndlH =0.
Fig. 1. Simulation domain and boundary conditions
2. SIMULATION RESULTS
Figs. 2, 3 show, for example, the computer simula-
tion results of the avalanche - to - streamer transition,
and the propagation of negative streamer through the
discharge gap with the uniform (left column) and non -
uniform (right column) electric fields. nR = 20.
V0 = 128. 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 );,( tzrε
r
at the same time points. The
time points are chosen so that the streamer in the uni-
form and non-uniform field advanced the same distance.
For the uniform field these time points are =t {115,
175, 200}, and for the non-uniform field these time
points are =t {50, 100, 125}.
As can be seen from Figs. 2 and 3, in the inhomoge-
neous field the streamer has a larger transverse dimen-
sion, higher speed and smaller forming time. In both
cases, the electric field is enhanced in front of the
streamer head, and weakened behind it.
Fig. 2. Space charge density );,( tzrρ .
Left column - uniform electric field.
Right column - non - uniform electric field
Fig. 3. Absolute value of the electric field );,( tzrε
r .
Left column - uniform electric field.
Right column - non - uniform electric field
ISSN 1562-6016. ВАНТ. 2013. №4(86) 191
Fig. 4 shows the absolute value of the electric field
|);,0(| tzr =ε
r
, and the space charge density
);,0( tzr =ρ on the axis depending on the longitudinal
coordinate z at different time points =t [0,130] with
the step =dt 5. nR = 20 and 0V = 128. As can be seen
from Fig. 4, the vacuum (Laplacian) electric field of the
needle is quickly screened by the streamer. The electric
field |);,0(| tzr =ε
r
, as well as the space charge density
);,0( tzr =ρ , changes weakly when the streamer
moves through the discharge gap. When the streamer
head approaches the anode, this increases the local elec-
tric field in front of the streamer head, and leads to the
growing collisional ionization rate. This increases the
densities of charged particles and the space charge den-
sity );,0( tzr =ρ . It can be seen that the head of the
negative streamer, as it moves towards the anode, is
compressed in the longitudinal direction.
Fig. 4. Electric field |);,0(| tzr =ε
r
and space charge
density );,0( tzr =ρ on the axis at different times
Fig. 5 (left column) shows the z-coordinates of the
maximum of the electric field max|);,0(| tzr =ε
r
on the
axis as the function of time for different values of the
needle radii nR = {20, 40, 80, inf}, and the anode po-
tentials 0V = {96, 128, 160, 192}. nR = inf means uni-
form electric fields, or plane - to - plane computational
domain. Fig. 5 (right column) shows the velocity of
max|);,0(| tzr =ε
r
versus time, which is the negative
streamer propagation velocity through the discharge gap
- sV . As seen from Fig. 5, the streamer velocity in-
creases as the needle radius decreases. This increase in
the velocity goes up to a certain radius ( nR ~ 40), after
which the growth of streamer speed is cut off. As can be
seen from Fig. 5, the behavior of streamer velocity sV
as a function of time has four characteristic regions: (1)
the sharp drop at the beginning of the movement, (2) the
motion with a nearly constant velocity, (3) the region of
the first (low) acceleration, and (4) the region of the
second (strong) acceleration.
Fig. 5. Negative streamer dynamics for different radii of
the needle nR ={20, 40,80, inf} and different applied
voltages 0V = {96, 128, 160, 192}. Left - z-coordinate
of the maximum of the electric field
max|);,0(| tzr =ε
r
on the axis versus time.
Right - streamer velocity )(tVs versus time
For a plane - to - plane geometry, (1) and (2) repre-
sent the initial stage of an electron avalanche develop-
ment, when the space charge is small, and the external
electric field is not distorted by the space charge. The
region (3) corresponds to the nonlinear stage of streamer
propagation, when the magnitude of the space charge is
significantly different from zero, and the external elec-
tric field is significantly distorted. The region (4) corre-
sponds to the approach of the streamer to the anode, and
to its exit through the anode from the simulation domain.
Solution of the linearized equations (5) - (7) in one di-
mension, for the velocity of the ionization wave can be
presented by:
( )000 /1exp2 εεε −+= DVa , (8)
where 0ε is the external electric field, D is the diffu-
sion coefficient. aV is shown in Fig. 5 by a straight line.
Fig. 5 shows that after a rather rapid transition process
(region (1)) the streamer velocity sV approaches the
asymptotic velocity aV (region (2)), which corresponds
to the linear stage of the avalanche development.
In the case of non - uniform fields, the region (2) can
not be identified as the linear stage of the avalanche
development, because the effect of space charge appears
much earlier. This follows directly from the analysis of
potential distribution on the axis, which differs signifi-
cantly from the vacuum potential distribution in the re-
gion (2) for each of the needle radii nR = {20, 40, 80}
and applied voltages 0V = {96, 128, 160, 192}. Assum-
ing that the speed of the streamer is determined by the
electric field in the front of its head, it follows from the
ISSN 1562-6016. ВАНТ. 2013. №4(86) 192
simulations that consttzr ≈= max|);,0(| ε
r
, and for
max|);,0(| tzr =ε
r
in the region (2):
0V R
nR
max||εr E
aV
96 R =20,40,80 0.78 1.074
128 R =20,40,80 1.2 1.657
160 R =20,40,80 1.53 2.094
192 R =20,40,80 1.88 2.545
In the table,
nR
max|| εr is the averaged over the
needle radii electric field in the region (2), where the
electric field max|);,0(| tzr =ε
r
and the speed of the
streamer are slightly changed with time,
nR
nn
eDV
RR
E
a
max
1
maxmax 2
ε
εε
r
rr
−
+= . (9)
The velocity E
aV is shown in Fig. 5. As can be seen
from Fig. 5, the negative streamer speed is well de-
scribed by the expression (9).
Fig. 6 shows the velocity of the negative streamer
sV versus longitudinal coordinate z. It is seen that in the
strong non-linearity regions (regions (3), and (4)) the
speed of the streamer sV as a function of longitudinal
coordinate z is independent from the needle radius nR .
This can be explained by the screening of electric field
of the needle by the space charge of the streamer.
Fig. 6. Velocity of the negative streamer sV versus
longitudinal coordinate z for different needle radii
nR ={20, 40, 80, inf}, and different applied voltages
0V = {96, 128}
Fig. 7 shows the streamer velocity sV , for different
applied voltages 0V = {96, 128, 160, 192} with the con-
stant needle radius nR = {20, 40, 80, inf}. It is seen that
as the applied voltage increases, the streamer velocity
also increases.
Fig. 8 shows the streamer mean velocity >< sV as
a function of the needle radius nR ={20, 40, 80} for
different applied voltages 0V = {96, 128, 160, 192}.
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. It can be seen that
the >< sV increases as nR decreases at 0V =const.
Fig. 7. Negative streamer dynamics for different applied
voltages 0V = {96, 128, 160, 192} and different radii
of the needle nR ={20, 40, 80, inf}. Streamer velocity
)(tVs versus time
Starting from some nR , the growth of streamer
speed stops. It is also seen that >< sV increases with
0V .
Fig. 8. The dependence of the negative streamer aver-
age speed >< sV on the radius of the needle nR for
different applied voltages 0V = {96, 128, 160, 192}.
nR = {20, 40, 80}
Fig. 9 shows the streamer mean velocity >< sV as a
function of the applied voltages 0V ={96, 128, 160, 192}
for different needle radii nR ={20, 40, 80, inf}. It can be
seen that the >< sV increases linearly with applied
voltage 0V . It is seen also that the mean streamer veloc-
ity >< sV starting from certain nR , does not depend
on the needle radius nR .
Fig. 9. The dependence of the negative streamer
average speed >< sV on the applied voltage
0V = {96, 128, 160, 192} for different radii
of the needle nR ={20, 40, 80}
ISSN 1562-6016. ВАНТ. 2013. №4(86) 193
CONCLUSIONS
The results of numerical simulations of the propaga-
tion of the negative streamer in nitrogen in the uniform
and strongly non-uniform electric fields were presented.
Computer simulations were performed by finite element
method, which allows to accurately describe the
boundaries of complicated shape. Simulations were
done for different voltages, and for different radii of the
needles.
It was shown that the velocity of streamer propaga-
tion in the non - uniform electric field is always higher
than the velocity of streamer propagation in the uniform
field at given voltages on the electrodes.
It was shown that the behavior of streamer velocity
versus time has four specific regions: (1) the sharp drop
at the beginning of the movement, (2) the propagation
with a constant velocity, (3) the region of the first (low)
acceleration, and (4) the area of the second (strong) ac-
celeration when the streamer head approaches the an-
ode.
It was shown that as the needle radius decreases, the
velocity of the streamer increases. The growth of
streamer velocity, with decreasing needle radius, is
stopped when the needle curvature radius reaches a cer-
tain critical size.
It was shown that in the region of strong nonlinear-
ity, namely, in the space charge dominated region, the
streamer velocity as the function of longitudinal coordi-
nate is independent from the needle radius. It was
shown that the streamer velocity increases with growth
of the applied voltage.
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Article received 29.04.2013.
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ОТРИЦАТЕЛЬНЫХ СТРИМЕРОВ В СИЛЬНЫХ
НЕОДНОРОДНЫХ ЭЛЕКТРИЧЕСКИХ ПОЛЯХ В АЗОТЕ. ВЛИЯНИЕ РАДИУСА ИГЛЫ
И ПРИЛОЖЕННОГО НАПРЯЖЕНИЯ НА СКОРОСТЬ СТРИМЕРА
О.В. Мануйленко, В.И. Голота
Приведены результаты численного моделирования распространения отрицательного стримера в азоте в
однородных и сильно неоднородных электрических полях. Показано, что скорость распространения стриме-
ра в неоднородном поле всегда больше его скорости в однородном поле при одинаковых потенциалах на
электродах. Показано, что при уменьшении радиуса иглы скорость стримера увеличивается при заданном
напряжении на электродах. Рост скорости стримера, с уменьшением радиуса иглы, прекращается, когда ра-
диус кривизны иглы достигает некоторого критического размера. Показано, что в области сильной нелиней-
ности, когда динамика распространения стримера определяется его объемным зарядом, его скорость, как
функция продольной координаты не зависит от радиуса иглы. Показано, что скорость стримера возрастает с
ростом напряжения, приложенного к электродам.
ЧИСЛОВЕ МОДЕЛЮВАННЯ НЕГАТИВНИХ СТРИМЕРІВ У СИЛЬНИХ НЕОДНОРІДНИХ
ЕЛЕКТРИЧНИХ ПОЛЯХ В АЗОТІ. ВПЛИВ РАДІУСА ГОЛКИ І ПРИКЛАДЕНОЇ НАПРУГИ
НА ШВИДКІСТЬ СТРИМЕРА
О.В. Мануйленко, В.І. Голота
Наведено результати числового моделювання поширення негативного стримера в азоті в однорідних і
сильно неоднорідних електричних полях. Показано, що швидкість поширення стримера в неоднорідному
полі завжди більша його швидкості в однорідному полі при однакових потенціалах на електродах. Показано,
що при зменшенні радіуса голки швидкість стримера збільшується при заданій напрузі на електродах. Зрос-
тання швидкості стримера, із зменшенням радіуса голки, припиняється, коли радіус кривизни голки досягає
деякого критичного розміру. Показано, що в області сильної нелінійності, коли динаміка поширення стри-
мера визначається його об'ємним зарядом, його швидкість, як функція поздовжньої координати не залежить
від радіуса голки. Показано, що швидкість стримера зростає з ростом напруги, що прикладена до електродів.
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