CC BY
13
Key words: plasma, numerical simulation, atmospheric discharges.
CO
to
SUBMICROSECOND ATMOSPHERIC ELECTRIC DISCHARGE FROM THE NON-UNIFORM ELECTRODE (TIP) TOWARDS THE PLANE ELECTRODE
Vasily Y. Kozhevnikova, Andrey V. Kozyrevb, Aleksandr O. Kokovinc, Vladislav S. Igumnovd
a Institute of High Current Electronics, Department of Theoretical Physics, Tomsk, Russian Federation, e-mail: Vasily.Y.Kozhevnikov@ieee.org, ORCID iD: http://orcid.org/0000-0001-7499-0578 b Institute of High Current Electronics, Department of Theoretical Physics, Tomsk, Russian Federation, e-mail: kozyrev@to.hcei.tsc.ru, ORCID iD: https://orcid.org/0000-0002-7078-7991 c Institute of High Current Electronics, Department of Theoretical £
Physics, Tomsk, Russian Federation, e-mail: alexander.kokovin.desch@gmail.com, ORCID iD: http://orcid.org/0000-0003-2068-7674 d National Research Tomsk Polytechnic University, Laboratory N 46,
<u
e-mail: vladislavigumnov@yahoo.com, |
Tomsk, Russian Federation e-mail: vladislavigumnov@> ORCID iD: http://orcid.org/0000-0002-3847-5322
DOI: 10.5937/vojtehg67-20796; https://doi.org/10.5937/vojtehg67-20796
FIELD: Plasma Physics ARTICLE TYPE: Original scientific paper ARTICLE LANGUAGE: English
Abstract: g
This paper deals with the results of a numerical simulation of the fast E atmospheric pressure discharge in a strongly non-uniform configuration of a tip-to-plane diode filled with a nitrogen and oxygen mixture. The simulation is based on the advanced hydrodynamic plasma discharge accounting also gas photoionization. It was shown that, in the absence of photoionization, discharge develops similarly to the case with photoionization, except the case of reversed voltage polarity. The theoretical results correspond to the existing experimental data for the spatial discharge structure and the current/voltage discharge characteristics.
2
CO <D
CD
"o >
CD
O CM
of
UJ
a.
Z) O
o <
o
X
o
LU
H ^
a. <
H
<
CD >o
X LU H O
O >
Introduction
Various gas-filled diodes are widely used in modern electro-technical devices. The tip-to-plane electrodes system represents probably the most common design of a gas diode unit with a strongly non-uniform configuration of an electric field. Namely, they are used as spark-gap high-voltage switches (Shaefer et al, 1990) as well as the main component of technological devices for the discharge plasma surface treatment (Akishev et al, 2001). Therefore, major theoretical problems of discharge development in such a system are intensively investigated by using various theoretical simulation approaches (Eichwald et al, 2011).
The discharges in gas-filled diodes are attractive due to the nontrivial switching characteristics and the low-temperature plasma parameters. Among the switching parameters, the breakdown formation time and the corresponding voltage amplitude are the most important. The plasma parameters, e.g. its spatial structure or its plasma-chemical composition are also of great importance, especially w.r.t. time-dependent studies. While the switching characteristics can be easily measured experimentally, the measurement of plasma parameters is much more complicated. That is the main reason to perform a theoretical simulation of gas discharge.
At present, we have a rather extensive base of experimental studies of this type of discharge, including those performed with picosecond and subnanosecond time resolutions, as well as with time synchronization of measured signals. As part of the series of experimental studies done by groups of Russian and Chinese researchers (Shao et al, 2013), a comparison can be made with the results of actual theoretical studies.
In this paper, we use a two-moment "liquid" discharge plasma model (Gogolides & Sawin, 1992) implemented in the Plasma module of COMSOL Multiphysics 5.2 software. It allows modeling the time-dependent discharge propagation from the metal non-uniform electrode (tip) towards the second electrode (plane) accounting for all necessary plasma-chemical reactions. The main aim here is to simulate nanosecond gas discharge and accurately obtain the spatial discharge structure evolution.The introduction is an introductory part of the article.
Experimental setup
The experimental setup is represented in Figure 1. The triggering pulse from 1 provides a signal that the voltage pulse generator 2 transforms into a negative polarity voltage pulse with the amplitude values in the range of U0 ~ 27-30 kV with the rise time tf ~ 200 ns. The
cathode here is a thin needle with a diameter of 0.4 mm having the tip curvature radius of 0.1 mm (medical syringe needle), while the anode is a simple plane electrode made of aluminum foil. The distance between the electrodes is equal to d = 9 mm. The nitrogen at 1 atm pressure with small (~2 %) oxygen admixture is used as the operating gas.
An ICCD camera was used to obtain a sequence of instant images of the discharge dynamics (depicted in Figure 2). The images from an ICCD camera are an integral picture of the glow of non-stationary discharge, which, to a certain extent, can be compared with the distribution of the discharge plasma at a given point in time. Based on this comparison of experimental and theoretical data can be done in the present work.
CO
55
£P Ш
Figure 1 - The experimental setup: 1 - triggering pulse generator, 2 - pulsed voltage source, 3 - capacitive voltage divider, 4 - current shunt resistor, 5 - storage oscilloscope, 6 - output window, 7 - ICCD camera, 8 - personal computer, 9 - metal tip cathode,
10 - plane anode electrode Рис. 1 - Схема эксперимента: 1 - запускающий генератор, 2 - импульсный источник напряжения, 3 - емкостный делитель напряжения, 4 - токовый шунт, 5 - цифровой запоминающий осциллограф, 6 - выходное окно, 7 - скоростная камера, 8 - компьютер, 9 - острийный катод, 10 - плоский анод Слика 1 - Поставка експеримента: 1 - генератор окидног импулса, 2 - пулсни извор напона, 3 - капацитивни разделник напона, 4 - шант отпорник, 5 -мемори^ски осцилоскоп, 6 - заштитни прозор, 7 - камера ИЦЦД, 8 - лични рачунар, 9 - катода - метални врх, 10 - анода - обична плочаста електрод
<и >
I
со ф
СО
"о
>
0
01
ОС LLJ
ОС ZD О
О _|
< с;
X О ш
н
>-
ОС <
(Л <
-J
О >о
X ш I-
о
о >
a) 71-74 ns
b) 74-77ns
c) 77-80 ns
Figure 2 - Instant photographs from the ICCD-camera (grey areas depict the electrodes) Рис. 2 - Мгновенные фотографии свечения, полученные скоростной камерой (области, отмеченные серым цветом обозначают электроды) Слика 2 - Инстант фотограф^е доб^'ене камером ИЦЦД (сиве зоне представ^а]'у електроде)
Theoretical model
For the simplicity reasons, a real three-dimensional diode in the model is substituted by a two-dimensional axisymmetric structure (Figure 3).
The gas discharge model is based on the two-moment "liquid" model where the movement of charged particles is covered by the drift-diffusion approximation (Gogolides & Sawin, 1992). Since the discharge characteristic time is short, the model implements only three important plasma-chemical reactions: electron impact ionization e + N2 ^ 2e + N2+, molecular nitrogen dissociation e + N 2 ^ e + 2N and photoionization hv + N2 ^ e + N2+.
The photoionization model we implement is based on the assumption (Kulikovsky, 1995) that the major contribution to the photoionization rate is produced by the radiation in the spectral range 980-1025 A, where the radiation absorption by nitrogen N2 can be omitted. The wavelength of 1025 A is the natural threshold for the molecular oxygen photoionization reaction. Below 980 A, the radiation is strongly absorbed by nitrogen providing insignificant contribution to the production of photoelectrons. Taking into account the fine structure of the oxygen absorption spectrum, in the integral over the wavelength range 980-1025 A in the general expression for the rate of photoionization was calculated and adopted for further computations.
со
55
£p <U
Figure 3 - The computational domain configuration (h = 1.6 mm, l = 4 mm, d = 9 mm)
Рис. 3 - Счётная область пространства (h = 1.6 мм, l = 4 мм, d = 9 мм) Слика 3 - Конфигураци]а области израчунаваъа (h = 1,6 mm, l = 4 mm, d = 9 mm)
We also draw the attention to the importance of taking into account the molecular nitrogen dissociation reaction as the main factor leading to electron energy losses (Cosby, 1993). Other plasma-chemical reactions typical to nitrogen, e.g. involving ions of atomic nitrogen, are omitted due to their smaller contribution to the fast discharge development. For the same reasons, we also exclude different kinds of neutral excited species. The electron component is described by the following equations system:
£
R
dnE dt
+ У-Г „ + E-Г _ = R„
(1)
where ne is the electron number density, ns is the electron energy density, t is the time variable, and E is the electric field strength. The source coefficients Re and Rs are defined by
Re = Kon И ПпПе + Sph ,
Rs= Kon (ЮПпПе + Kss fi)
ПпПе >
(2)
where k. (s) is the ionization rate as a function on the mean electron
ionv '
energy, s= ns / ne, nn is the total neutral number density, kdiss (s) is the dissociation rate coefficient, and Sph is the photoionization rate.
S
605
The ion component is described by
dn,
+ V-r; = R
dt 1 e (3) where nt is the N2 number density.
The electron, the electron energy and the ion density fluxes Te, r s and r; respectively, are given by the expressions
r = -n u E - DVn
e e *e e e
5 5
rs =- 3 nsUeE - 3 DeVns (4)
r i = - E - D Vn
where u and ¡m are the electron and ion mobilities, and De and D, are the electron and ion diffusivities.
The electric field is accounted self-consistently in the model by implementing the Poisson's equation:
s0V'E = -q (n, -ne)
(5)
where, q is the elementary charge, and s0 is the electrical constant.
The photoionization rate Sph is implemented in the "differential"
formulation i.e. based on the numerical solution of the Helmholtz equations set (Bourdon et al, 2007).
V2Sph - = -GphRe (Q)
Here, Aph is the effective photon path length, Gph is the coefficient of
the conversion of the ionization rate Re into photon radiation. The percent of oxygen admixture was set to 2 % (15 Torrs in the equivalent partial pressure units).
We use uniform plasma number density not exceeding 103 cm-3 and the zero electric field and the photoionization rate Sph as the initial conditions. The boundary conditions are given in terms of generalized expressions for the particle and the electron energy density fluxes on the solid electrode walls (Kozhevnikov et al, 2015)
^eaT)
1 _ " r e ■ n = 4 neVe ~r{ri * n ) + Mene (E ' U ) 5
r i ■n=4 nv(E ■n) (7)
rs n = 2 nsve -Z^r(ri ■ n). J.
where n is the normal vector to the wall surface, ve and vi are the
electron and ion thermal velocities, respectively, and y= 0.1 is the secondary electron emission coefficient of the ion-wall interaction in nitrogen.
The simulation also accounts the contribution of the field emission (autoelectronic emission) from the cathode surface due to the increase of an electrostatic field near the emission centers formed by the metallic surface roughness. This electron flux is given in terms of a convenient Fowler-Nordheim expression (Kozyrev et al, 1987).
The complete discharge plasma system of equations (1)-(4) is solved in the COMSOL Multiphysics software with Plasma Module implementing the above two-moment model DC-discharge physics. Prior e to this, the ionization rates and the electron mobility were calculated using the BOLSIG+ solver (Hagelaar & Pitchford, 2005) except the dissociation rate coefficient that was taken from another source (Cosby, 1993).
We compare the simulation results according to two discharge models. In the first one (I), photoionization was not included, while the second model (II) implements all enlisted elementary processes. The following simulation results of the calculations are the refinement of the preliminary computations of a similar discharge type presented in the conference paper (Kozhevnikov et al, 2018). The effects of oxygen molar fraction increasing in nitrogen (more than 2%) and gas diode parameters variations on the gas discharge dynamics have not been studied focusing on the configurations close to the experimental one. |
Results of the simulation
The comparison of the voltage - time profiles is shown in Figure 4 (switching characteristics) for both discharge models. We assume the breakdown formation to be a time point having the maximum voltage at the discharge gap.The breakdown occurs at tbreakdown ~ 92 ns e (Ubreakdown ~ 12 kV) for both simulation regimes (with photoionization and *
o
со ф
CD
15 >
О
см
ОС LLJ
ОС
о
о _|
< с;
X О ш
н
>-
ОС <
(Л <
-J
О >о
X ш н
о
о >
without it). The presence of photoionization just slightly reduces the breakdown voltage value by no more than 50 V. Such difference is negligibly small, so we can assume that the switching characteristics of two modes are practically identical.
-16
-20 -
- - -Source voltage front-edge *
— Gap voltage wio photoionization \ * Gap voltage with photoionization *
J_i_I_i_I_i_I_._L
0 20 40 60 80 100 120
Time, ns
Figure 4 - Discharge voltage- time profiles Рис. 4 - Коммутационные характеристики разряда Слика 4 - Профили пражъеъа напон-време
The discharge evolution is demonstrated in the sequence of the static images in Figure 5. In both cases, the discharge initiation occurs approximately at the time point of t = 50 ns. The movement of the plasma channel begins with the expansion of the initial cathode formation in both spatial directions. After that, approximately from the time point of t = 80 ns, the formation of a plasma tip on the spherical plasma cloud surface occurs. This tip is the main channel of the discharge which slightly expands in the radial direction during the motion. The formation of the initial spherical distribution is associated with the intense losses of the electron energy in the electron impact N2 dissociation reaction. After the electric field exceeds the Lozansky-Firsov criterion threshold value, the rapid ionization wave development starts from the 0.5-1.0 mm spherical layer surface. The process ends with the discharge gap switching stage at the time point of the gap intersection with the ionization wave channel (t = 90 ns). The gap voltage drop and the corresponding significant increase of the total discharge current accompanies this.
The comparison of calculations with photoionization and without it shows that the effect of the latter on the development of gas discharge is insignificant if the electron impact dissociation reaction of molecular
nitrogen is included in the model. Also, the quantitative characteristics of the plasma do not change. The significant increase of the oxygen partial pressure in the photoionization model, and hence the fraction of oxygen in gas mixture will probably lead to a visible change in the spatial discharge structure, but also the simulation will require a more accurate plasma-chemical reaction set. Nevertheless, one of this paper's aims is to investigate the influence of a minor electro-negative mixture to the discharge formation and evolution.
CO
55
Figure 5 - Spatial distribution of the electron number density (scale in cm-) for gas discharge a) without and b) with the photo-ionization process for the same time points Рис. 5 - Пространственные распределения концентрации электронов (в единицах в куб. см.) в газовом разряде a) без и b) с учётом процесса фотоионизации в одинаковые моменты времени Слика 5 - Просторна дистрибуци]а густине бро]а електрона (скала у cm-3) за пражшеше гаса: а) без процеса фоторнизаци^еза исте временске тачке и б) са процесом фоторнизаци^е за исте временске тачке
ГО
£Р Ш
2
CO <D
CD
"o >
CD
O CM
of
UJ
a.
Z) O
o <
o
X
o
LU
H ^
a. <
H
<
CD >o
X LU H O
O >
Additionally, the parameters of runaway electrons have been calculated in order to discover their influence on the discharge dynamics. The calculations were based on the "hybrid" theoretical approach, involving the principles of physical kinetics described earlier (Kozyrev et al, 2016). The results show that the runaway electron current passing through the anode is too small compared to the full discharge current, so the influence of the runaway electrons on the discharge is negligible. Such conclusions are connected with the long rise time (more than 100 ns) of the operating voltage pulse.
Conclusion
The simulation of the gas-filled diode breakdown in the tip-to-plane electrodes configuration shows good agreement with the existing experimental data. The current theoretical study shows that gas photoionization insignificantly affects the discharge spatial structure for the positive polarity of the anode voltage. It was also shown that, in gas mixtures containing a valuable amount of nitrogen, the electron impact dissociation plays an important role in the formation of the spatially-inhomogeneous discharge structure.
Our theoretical study of gas discharges of submicrosecond duration substantially complements the existing experimental base. The obtained information about the time-spatial discharge structure allows studying the generation of runaway electrons and X-rays under the atmospheric pressure. This opens up broad prospects for the creation of high voltage power supplies for UV and VUV excilamps as well as for the application in the fields of industrial X-ray radiography.
References
Akishev, Y., Goossens, O., Callebaut, T., Leys, C., Napartovich, A., & Trushkin, N. 2001. The influence of electrode geometry and gas flow on corona-to-glow and glow-to-spark threshold currents in air. Journal of Physics D: Applied Physics, 34(18), pp.2875-2882. Available at:
https://doi.org/10.1088/0022-3727/34/18/322.
Bourdon, A., Pasko, V.P., Celestin, S., Liu, N.Y., Segur, P., & Marode, E. 2007. Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations. Plasma Sources Science and Technology, 16(3), pp.656-678. Available at: https://doi.org/10.1088/0963-0252/16/3Z026.
CO
<u
Cosby, P.C. 1993. Electron-impact dissociation of nitrogen. The Journal of Chemical Physics, 98(12), pp.9544-9553. Available at: https://doi.org/10.1063/1.464385.
Eichwald, O., Yousfi, M., Ducasse, O., Merbahi, N., Sarrette, J.P., Meziane, M., & Benhenni, M. 2011. Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure. In H.E. Schulz Ed., Hydrodynamics - Advanced Topics.IntechOpen. Available at: https://doi.org/10.5772/28929.
Gogolides, E., & Sawin, H.H. 1992. Continuum modeling of radio-frequency glow discharges. I. Theory and results for electropositive and electronegative gases. Journal of Applied Physics, 72(9), pp.3971-3987. Available at: https://doi.org/10.1063/1.352250.
Hagelaar, G.J.M., & Pitchford, L.C. 2005. Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Science and Technology, 14(4), pp.722-733. Available at: https://doi.org/10.1088/0963-0252/14/4Z011.
Kozhevnikov, V.Y., Kozyrev, A.V., Batrakov, A.V., Semeniuk, N.S., & Karaban, V.M. 2015. Diagnostics of primary arcing in electronics of satellite telecommunication systems. In 2015 23rd Telecommunications Forum Telfor | (TELFOR).Institute of Electrical and Electronics Engineers (IEEE), pp.615-618. Available at: https://doi.org/10.1109/telfor.2015.7377542.
Kozhevnikov, V.Y., Kozyrev, A.V., Semeniuk, N.S., & Kokovin, A.O. 2018. Theoretical Simulation of Nanosecond High Pressure Gas Discharge in the Pinto-Plate Gap.In 2018 26th Telecommunications Forum (TELFOR).Institute of | Electrical and Electronics Engineers (IEEE), pp. 1-4. Available at: https://doi.org/10.1109/telfor.2018.8611902.
Kozyrev, A.V. et al. 1987. Autoemission processes and Transition from the glow-discharge to Arc-discharge. Zhurnal Tekhnicheskoi Fiziki, 51(1), pp.58-64.
Kozyrev, A., Kozhevnikov, V., Lomaev, M., Sorokin, D., Semeniuk, N., & Tarasenko, V. 2016. Theoretical simulation of the picosecond runaway-electron beam in coaxial diode filled with SF 6 at atmospheric pressure. EPL (Europhysics Letters), 114(4), p.45001. Available at:
https://doi.org/10.1209/0295-5075/114/45001. °
Kulikovsky, A.A. 1999. Two-dimensional simulation of the positive streamer in N 2 between parallel-plate electrodes. Journal of Physics D: Applied Physics, 28(12), pp.2483-2493. Available at: https://doi.org/10.1088/0022-3727/28/12/015.
Schaefer, G., Kristiansen, M., & Guenther, A. 1990. Gas Discharge Closing J Switches. Available at: https://doi.org/10.1007/978-1-4899-2130-7.
Shao, T., Tarasenko, V.F., Zhang, C., Baksht, E.K., Zhang, D., Erofeev, M.V., Ren, C., Shutko, Y.V., & Yan, P. 2013. Diffuse discharge produced by repetitive nanosecond pulses in open air, nitrogen, and helium. Journal of Applied Physics, 113(9), p.93301. Available at:
https://doi.org/10.1063/1.4794031.
in
СУБМИКРОСЕКУНДНЫИ РАЗРЯД АТМОСФЕРНОГО ДАВЛЕНИЯ С НЕОДНОРОДНОГО ЭЛЕКТРОДА (ОСТРИЯ) В НАПРАВЛЕНИИ ПЛОСКОГО ЭЛЕКТРОДА
14- а а
ю Василий Ю. Кожевников , Андрей В. Козырев ,
о Александр О. Коковина, Владислав С. Игумнов6
а Институт сильноточной электроники, Лаборатория теоретической о физики, г. Томск, Российская Федерация
™ 6 Томский политехнический университет, Лаборатория номер 46,
г. Томск, Российская Федерация
Е
=э РУБРИКА ГРНТИ: 29.27.00 Физика плазмы
о ВИД СТАТЬИ: оригинальная научная статья
ЯЗЫК СТАТЬИ: английский
<
Резюме:
х
и В данной работе рассматриваются результаты численного
моделирования быстрого разряда при атмосферном давлении в
оё сильно неоднородной конфигурации диода «острие-плоскость»,
¡5 заполненного смесью азота и кислорода. Моделирование
основано на современной гидродинамической модели разрядной
плазмы, учитывающей также фотоионизацию газа. Было
показано, что при отсутствии фотоионизации разряд
и развивается аналогично случаю с фотоионизацией (за
^ исключением случая обратной полярности приложенного
^ напряжения). Теоретические результаты соответствуют
существующим экспериментальным данным для структуры
пространственного разряда и для временных характеристик
ш тока / напряжения разряда.
н
о Ключевые слова: плазма, численное моделирование,
Ф атмосферные разряды.
>
ПРАЖ^Е^Е У НАНОСЕКУНДАМА ПРИ АТМОСФЕРСКОМ ПРИТИСКУ ОД НЕУНИФОРМНЕ ЕЛЕКТРОДЕ (ВРХ) ПРЕМА РАВНОJ ЕЛЕКТРОДИ
Васили ^ Кожевников3, Андре] В. Козирева, Александар О. Коковина, Владислав С. Игумнов6 а Институт високе стру]е, Ла6оратори]а за теорийку физику,
Томск, Руска Федераци]а 6 Политехнички универзитет у Томску, Ла6оратори]а 6р. 46, Томск, Руска Федераци]а
ОБЛАСТ: физика плазме
ВРСТА ЧЛАНКА: оригинални научни рад
иЕЗИК ЧЛАНКА: енглески
со
55
ГО
Ш
Сажетак:
У раду се pa3Mampajy резултати нумеричке симулацие брзог пражъеъа при атмосферском притиску у високо нехомогеноj конфигурации диоде типа врх-раван напуъене смешом азота и кисеоника. Симулациа се заснива на савременом хидродинамичком моделу пражъеъа плазме, ко\и тако^е узима у обзир фотоjонизациjу гаса. Показано jе да се, у одсуству фотоjонизуjуhег пражъеъа, он развиа слично као и код фоторнизац^е, са изузетком напона инверзне поларизацие. Теориски резултати су конзистентни са постоjеhим експерименталним подацима за просторну структуру пражъеъа и за карактеристике пражъеъа напона/струjе.
Къучне речи: плазма, нумеричка симулациа, атмосферска пражъеъа.
Paper received on / Дата получения работы / Датум приема чланка: 02.03.2019. Manuscript corrections submitted on / Дата получения исправленной версии работы / Датум достав^а^а исправки рукописа: 12.05.2019.
Paper accepted for publishing on / Дата окончательного согласования работы / Датум коначног прихвата^а чланка за об]ав^ива^е: 14.05.2019.
© 2019 The Authors. Published by Vojnotehnicki glasnik / Military Technical Courier
(www.vtg.mod.gov.rs, втг.мо.упр.срб). This article is an open access article distributed under the p
terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/rs/).
© 2019 Авторы. Опубликовано в «Военно-технический вестник / Vojnotehnicki glasnik / Military Technical Courier» (www.vtg.mod.gov.rs, втг.мо.упр.срб). Данная статья в открытом доступе и распространяется в соответствии с лицензией «Creative Commons» (http://creativecommons.org/licenses/by/3.0/rs/).
© 2019 Аутори. Обjавио Воjнотехнички гласник / Vojnotehnicki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). Ово jе чланак отвореног приступа и дистрибуира се у складу са Creative Commons лиценцом (http://creativecommons.org/licenses/by/3.0/rs/).
2
