The capacitive component of double layer current in plasma

The features of nonstationary double layers in the high-current pulsed discharges have been theoretically and experimentally investigated in this paper. The expression for the capacity of strong double layer in quasi-MHD approximation has been obtained and the area of its applicability has been indi...

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Дата:	2017
Автори:	Hrechko, Ya.O., Azarenkov, N.A., Babenko, Ie.V., Ryabchikov, D.L., Sereda, I.N., Shovkun, M.A., Tseluyko, A.F.
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Мова:	English
Опубліковано:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2017
Назва видання:	Вопросы атомной науки и техники
Теми:	Низкотемпературная плазма и плазменные технологии
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/122155
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Цитувати:	The capacitive component of double layer current in plasma / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun, A.F. Tseluyko // Вопросы атомной науки и техники. — 2017. — № 1. — С. 219-222. — Бібліогр.: 3 назв. — англ.

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spelling	irk-123456789-1221552017-07-01T16:43:19Z The capacitive component of double layer current in plasma Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F. Низкотемпературная плазма и плазменные технологии The features of nonstationary double layers in the high-current pulsed discharges have been theoretically and experimentally investigated in this paper. The expression for the capacity of strong double layer in quasi-MHD approximation has been obtained and the area of its applicability has been indicated. The equation for the capacitive component of the double layer current has been derived in this paper. The dynamics of the double layer current capacitive component in the high-current pulsed discharge and the way to verify the calculations has been shown. Теоретически и экспериментально исследуются особенности нестационарных двойных слоёв в сильноточных импульсных разрядах. В квази-МГД-приближении получено выражение для ёмкости сильного двойного слоя и указана область его применимости. Получено уравнение для ёмкостной составляющей тока двойного слоя. Показана динамика ёмкостной составляющей тока двойного слоя в сильноточном импульсном разряде и приведен способ верификации расчётов. Теоретично та експериментально досліджуються особливості нестаціонарних подвійних шарів у си-льнострумових імпульсних розрядах. У квазі-МГД-наближенні отримано вираз для ємності сильного подвійного шару та вказана область його застосування. Отримано рівняння для ємнісної складової струму подвійного шару. Показана динаміка ємнісної складової струму подвійного шару в сильнострумовому імпульсному розряді та приведено спосіб верифікації розрахунків. 2017 Article The capacitive component of double layer current in plasma / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun, A.F. Tseluyko // Вопросы атомной науки и техники. — 2017. — № 1. — С. 219-222. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.40.Kh, 52.58.Lq, 52.59.Mv http://dspace.nbuv.gov.ua/handle/123456789/122155 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии
spellingShingle	Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F. The capacitive component of double layer current in plasma Вопросы атомной науки и техники
description	The features of nonstationary double layers in the high-current pulsed discharges have been theoretically and experimentally investigated in this paper. The expression for the capacity of strong double layer in quasi-MHD approximation has been obtained and the area of its applicability has been indicated. The equation for the capacitive component of the double layer current has been derived in this paper. The dynamics of the double layer current capacitive component in the high-current pulsed discharge and the way to verify the calculations has been shown.
format	Article
author	Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F.
author_facet	Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F.
author_sort	Hrechko, Ya.O.
title	The capacitive component of double layer current in plasma
title_short	The capacitive component of double layer current in plasma
title_full	The capacitive component of double layer current in plasma
title_fullStr	The capacitive component of double layer current in plasma
title_full_unstemmed	The capacitive component of double layer current in plasma
title_sort	capacitive component of double layer current in plasma
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2017
topic_facet	Низкотемпературная плазма и плазменные технологии
url	http://dspace.nbuv.gov.ua/handle/123456789/122155
citation_txt	The capacitive component of double layer current in plasma / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun, A.F. Tseluyko // Вопросы атомной науки и техники. — 2017. — № 1. — С. 219-222. — Бібліогр.: 3 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT hrechkoyao thecapacitivecomponentofdoublelayercurrentinplasma AT azarenkovna thecapacitivecomponentofdoublelayercurrentinplasma AT babenkoiev thecapacitivecomponentofdoublelayercurrentinplasma AT ryabchikovdl thecapacitivecomponentofdoublelayercurrentinplasma AT seredain thecapacitivecomponentofdoublelayercurrentinplasma AT shovkunma thecapacitivecomponentofdoublelayercurrentinplasma AT tseluykoaf thecapacitivecomponentofdoublelayercurrentinplasma AT hrechkoyao capacitivecomponentofdoublelayercurrentinplasma AT azarenkovna capacitivecomponentofdoublelayercurrentinplasma AT babenkoiev capacitivecomponentofdoublelayercurrentinplasma AT ryabchikovdl capacitivecomponentofdoublelayercurrentinplasma AT seredain capacitivecomponentofdoublelayercurrentinplasma AT shovkunma capacitivecomponentofdoublelayercurrentinplasma AT tseluykoaf capacitivecomponentofdoublelayercurrentinplasma
first_indexed	2025-07-08T21:15:37Z
last_indexed	2025-07-08T21:15:37Z
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fulltext	ISSN 1562-6016. ВАНТ. 2017. №1(107) PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 219-221. 219 THE CAPACITIVE COMPONENT OF DOUBLE LAYER CURRENT IN PLASMA Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun, A.F. Tseluyko V.N. Karazin Kharkiv National University, Kharkov, Ukraine E-mail: yarikgrechko18@gmail.com The features of nonstationary double layers in the high-current pulsed discharges have been theoretically and experimentally investigated in this paper. The expression for the capacity of strong double layer in quasi-MHD ap- proximation has been obtained and the area of its applicability has been indicated. The equation for the capacitive component of the double layer current has been derived in this paper. The dynamics of the double layer current ca- pacitive component in the high-current pulsed discharge and the way to verify the calculations has been shown. PACS: 52.40.Kh, 52.58.Lq, 52.59.Mv INTRODUCTION Recently, the interest in the study of space charge electric double layer in the plasma has renewed [1]. This is due to the ability of the double layer to input the pulse energy with a power density of 1…10 GW/cm2 locally into the plasma. Such power levels give the opportunity to obtain intensive neutron fluxes from the plasma, the super-powerful directional radiation and to provide high-gradient effect on the solids surface of different nature for modification of the structural-phase state on different scale levels. However, it should be noted that a double layer is a powerful dynamic system whose parameters are change at high speed. From electrical point of view double layer can be represented as an aggregate of a resistor and a capacitor (Fig. 1,b). When changing the voltage and current of the layer the capacitor charge also changes. This entails the appearance of the capacitive component in the discharge current, which must be taken into ac- count when calculating the input power into the dis- charge. CALCULATING The value of the current capacitive component  tiC is determined by the double layer charge changing  tQ :   ,DL DL C DL DL dV dC i t C V dt dt     (1) which depends both on the layer capacity DLC and its voltage DLV . Therefore, at first we define the layer ca- pacity. The double layer capacity Because the layer thickness is much smaller than its transverse dimensions, the double layer specific capaci- ty С1DL we find from the expression:   2 0 1 1 1 DLl DLDL DL dzz VV q C  . (2) The charge density distribution in the layer (z) de- pends on the charge distribution  znq  of 4th particles components [2] (see Fig. 1,а):          znqznqznqznqz ririreebibibee  , (3) where be – the accelerated electrons, bi – the accelerat- ed ions, re – the reflected electrons, ri – the reflected ions. Fig. 1. The qualitative potential distribution (a) and the charge density (c) in the double layer, the equivalent electrical circuit of the double layer (b) For accelerated electrons and ions the charge distri- bution is determined from the current continuity condi- tions:      z j e m zv j znq e be e be be bee    0 1 2 , (4) iDL jbe jbi e e i e iC CDL e i e RDL e b (z) z 0 lDL c е0 i0 VDL (z) z 0 lDL nbe nbi nre nri TeC TiC TeA TiA a miC ZiC miA ZiA 220 ISSN 1562-6016. ВАНТ. 2017. №1(107)      zVeZ m j zv j znq iDLiA iA bi bi bi bibi    0 1 2 , (5) where φе0,φi0 – potentials corresponding to the starting energy of the electrons evm eCee 22 00  and ions eZvm iAiAiAi 22 00  (ZiA – the effective ions charge). The volume charge density distribution of accelerat- ed ions using a Langmuir ratio [3] bebieiAiA jjmZm  , can be represented as:    zV j e m znq iDL be e bibi     02 . (6) The volume charge density distribution of reflected electrons  znq ree and ions  znq riri in case of the Maxwell velocity particle distribution function obey the Boltzmann law, and for strong double layer is given by:     eT zV eDLi be e ree eA DL e V j e m znq                  00 1 2 , (7)     0 0 1 . 2 ic iC ri ri z T Z ee be e DL i q n z m j e e V                  (8) (For strong double layer qαVDL >> Tα ). These expres- sions are obtained from the quasi-neutrality condition at the layer boundaries:       DLDLDL VzbiiaVzbeVzre nZnn    and       000   zbezbiiazriic nnZnZ  . After the substitution of equations (4,6,7,8) into the expression (3) using dimensionless quantities     DLVzz   , DLiCiCiC eVZT , DLeAeA eVT , DLee V00   , DLii V00   the charge density distri- bution in the strong double layer will look like:        1 1 2 1 1 1 1 1 . ic ea e be DL ai ce ce ai ai ce m j e V e e                                        (9) Thus, the specific capacity of the strong double layer (2) is given by:   3 2 1 2 , , , , ,DL e ai ce ic ea be DLC m e I j V       (10) where           ,11 11 11 ,,,, 1 5.0 0       de e I ea ic ceai aice ceai eaicceai        (11) whose solution has the form:               1 2 1 2 1 , , , , 2 0.5 1 2 0.5 1 1 1 1 1 . ic ea ea ic ea ai ce ai ai ce ce ic ce ai ea ai ce I e e e                                               (12) Integrating DLC1 on the layer surface, we obtain the double layer full capacity DLC :       1 3 2 3 2 3 2 , , , , 2 , , , 2 , , , . 2 DL DL DL DL DL S bee ic ea ai ce S DL ic ea ai cee be SDL bee ic ea ai ce DL C C ds jm I ds e V Im j ds e V im I e V                              (13) Here  DLS bebe dsji – the electron beam current in the layer can be associated with the total current through the layer DLi , which is the sum of electron bei and ion bii currents. Taking into account the Langmuir ratio  iAeiAbebibeDL mmZiiii  1 , (14) from which: iAeiA DLbe mmZ ii   1 1 . (15) Taking into account that 1iAeiA mmZ , then DLbe ii  , and finally, the double layer capacity is giv- en by:  ceaieaic DL DLe DL I V i e m C  ,,,, 2 23  . (16) Fig. 2 shows the dependence of the reduced double layer capacity DLDL iC on the layer voltage drop DLV at zero particles temperatures on the layer boundaries (ai = 0, ce = 0, ic = 0, ea = 0). It is seen that when the voltage increasing the double layer capacity decreases. When the voltage on the layer ~ 100 V and the current ~ 33 kA the layer capacity is ~ 0.5 µF! But when the voltage ~ 1 kV, and the current has same value, the layer capacity is reduced to 15 nF. Taking into account the particles temperature in the isothermal case reduced double layer capacity can be written as:   23 23 ,,,, 2 eaDL ceaieaice DL eaDL TeV I e m i TC    . (17) Fig. 3 shows the dependence of specific double layer capacity DLeaDL iTC 23 on the relative layer potential drop eaDL TeV at ceai   , eaic   . ISSN 1562-6016. ВАНТ. 2017. №1(107) 221 Nonmonotonic in the top left part of the graph asso- ciated with the violation of the expression applicability conditions (17), which is valid for the strong double layer ( eaDL TeV  ), when the penetration of reflected particles on the opposite side of the layer not taken into account. 10 1 10 2 10 3 10 4 10 5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 C D L /\| i D L \|, p F /A \|V DL \|, V Fig. 2. The dependence of the reduced double layer ca- pacity DLDL iC on the layer voltage drop DLV at 0 ai , 0 ce , 0ic , 0ea 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 С D L T 3 /2 /\| i D L \|, p F * eV 3 /2 /A \|eV DL /T ea \|, rel. u. Fig. 3. The dependence of the specific double layer ca- pacity DLeaDL iTC 23 on the relative layer potential drop eaDL TeV at ceai   , eaic   The capacitive component of the current The differential of the double layer capacity in (1) can be obtained by differentiating the expression (16) by DLi and DLV :           DL DLDL DL DL DL V Vdi id V A dC 2 3 23 , (18) where  ceaieaicIA  ,,,10687.1 8   , FV3/2/A. Substituting it in equation (1) we obtain the equation for current capacitive component  tiC :   3 2 3 . 2 C DL DL DL DL DL DL DL DL DL A i t dt i dV V d i V V i d V V              (19) Expressing the double layer current DLi through the discharge current i and the capacitive current Ci taking into account that iiC  we can write CCDL iiiii  . Substituting it in (19) and grouping terms, we can rewrite the expression for the current capacitive component in the form of: 3 2 1 1 2 1 . 2 C DL DL C C DL DL DL DL d i V dV i i dt A V V dt d i dV i dt V dt            . (20) Here are two cases when the capacitive current takes a positive value ( 0Ci ): 3 21 2 2 1 , 2 C DL DL C DL DL DL di dV V i dt V A dt d i dV i dt V dt                (21) and negative value ( 0Ci ): 3 21 2 2 1 . 2 C DL DL C DL DL DL di dV V i dt V A dt d i dV i dt V dt                 (22) Introducing the notation          dt dV V AV t DL DL DL 232 2 1  , (23)   i dt dV Vdt id tF DL DL  2 1 (24) and solving the differential equations (21) and (22) we find the expression for the capacitive component of the double layer current at 0Ci             t dd C deFeti t 0 00    , (25) 222 ISSN 1562-6016. ВАНТ. 2017. №1(107) and at 0Ci :             t dd C deFeti t 0 00    . (26) These equations are solved by numerical methods. Fig. 4 shows the dynamics of the double layer current capacitive component )(tiC (curve 1) and the active voltage )(tUa (curve 2) in the high-current pulsed dis- charge. 3.0µ 4.0µ 5.0µ 6.0µ -150 -100 -50 0 50 100 150 1 2 -15 -10 -5 0 5 10 i C (t ), A U a (t ), k V t, s 15 Fig. 4. The dynamics of the double layer current capaci- tive component )(tiC (1) and the active voltage )(tUa (2) of the high-current pulsed discharge It is seen that the current capacitive component has the form of bursts with positive and negative polarity. It means that charge-discharge of the double layer capaci- ty occurs constantly. When the voltage decreases the capacitive current value increases. This occurs due to the fact that the double layer capacity increases, that requires bigger current for its recharging. The accuracy of calculations was determined by the verification points, which were calculated from phase measurements by means of expression   DLDLDLC VViCi  , , where  – the cyclic fre- quency of the discharge current “fine structure” at the given point, VDL – the double layer potential drop which was assumed equal to the active discharge volt- age )(tUa , a layer capacity CDL is calculated for the discharge current values i and )(tUa . The figure shows that the verification points well agree with the calculat- ed curve of the current capacitive component. CONCLUSIONS The expression for the capacity of space charge elec- tric double layer in the plasma in quasi-MHD approxi- mation has been obtained in this paper. The applicabil- ity area of the found expression has been indicated. The estimates have shown that in pulsed discharges the ca- pacity double layer can reach considerable values com- parable to the capacity of the supply capacitor bank. It has been shown that when the layer voltage increases its capacity decreases. So by increasing the voltage drops from 102 to 105 V, the specific layer capacity decreases in 3·104 times. Taking into account the expression for the double layer capacity, the integral-differential equation for the capacitive component of the double layer current has been obtained in this paper. The numerical calculations have shown a good agreement between the calculated curve of the current capacitive component and the ex- perimentally obtained verification points. REFERENCES 1. Nagendra Singh. Current-free double layers: A re- view // Physics of Plasmas. 2011, v. 18, № 12, p. 122105-122105-24. 2. C. Charles. A review of recent laboratory double lay- er experiments // Plasma Sources Sci. Technol. 2007, v. 16, p. 1-25. 3. B. Ghosh et al. Electrostatic double layers in a multi- component drifting plasma having nonthermal electrons // Brazilian Journal of Physics. 2013, v. 43, № 1, p. 28-33. Article received 16.11.2016 ЁМКОСТНАЯ СОСТАВЛЯЮЩАЯ ТОКА ДВОЙНОГО СЛОЯ В ПЛАЗМЕ Я.О. Гречко, Н.А. Азаренков, Е.В. Бабенко, Д.Л. Рябчиков, И.Н. Середа, М.А. Шовкун, А.Ф. Целуйко Теоретически и экспериментально исследуются особенности нестационарных двойных слоёв в силь- ноточных импульсных разрядах. В квази-МГД-приближении получено выражение для ёмкости сильного двойного слоя и указана область его применимости. Получено уравнение для ёмкостной составляющей тока двойного слоя. Показана динамика ёмкостной составляющей тока двойного слоя в сильноточном импульс- ном разряде и приведен способ верификации расчётов. ЄМНІСНА СКЛАДОВА СТРУМУ ПОДВІЙНОГО ШАРУ В ПЛАЗМІ Я.О. Гречко, М.О. Азарєнков, Є.В. Бабенко, Д.Л. Рябчіков, І.М. Середа, М.О. Шовкун, О.Ф. Целуйко Теоретично та експериментально досліджуються особливості нестаціонарних подвійних шарів у си- льнострумових імпульсних розрядах. У квазі-МГД-наближенні отримано вираз для ємності сильного по- двійного шару та вказана область його застосування. Отримано рівняння для ємнісної складової струму по- двійного шару. Показана динаміка ємнісної складової струму подвійного шару в сильнострумовому імпуль- сному розряді та приведено спосіб верифікації розрахунків.

The capacitive component of double layer current in plasma

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