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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Published in:Вопросы атомной науки и техники
Date:2013
Main Author: Manuilenko, O.V.
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Language:English
Published: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2013
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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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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.
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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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection 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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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 1. A.A. Kulikovsky. Two-dimensional simulation of the positive streamer in N2 between parallel-plate electrodes // J. Phys. D: Appl. Phys. 1995, v. 28, p. 2483-2493. 2. R. Morrow, J.J. Lowke. Streamer propagation in air // J. Phys. D: Appl. Phys. 1997, v. 30, p. 614-627. 3. N.Y. Babaeva, G.V. Naidis. Two-dimensional mod- elling of positive streamer dynamics in non - uni- form electric fields in air // J. Phys. D: Appl. Phys. 1996, v. 29, р. 2423-2431. 4. A.A. Kulikovsky. Positive streamer in a weak field in air: A moving avalanche-to-streamer transition // Phys. Rev. 1998, v. 57, p. 7066-7074. 5. A.A. Kulikovsky. The role of photoionization in positive streamer dynamics // J. Phys. D: Appl. Phys. 2000, v. 33, p. 1514-1524. 6. G.E. 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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.