Particle charging in beam-plasma systems

The particle charging in an electron beam-plasma discharge is studied by means of the classical orbit motion limited approximation and on the basis of a discrete charging model. The particle charge fluctuations due to the stochastic nature of charging process are considered. The Fokker-Planck descri...

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Datum:	2013
Hauptverfasser:	Bizyukov, А.А., Romashchenko, E.V., Sereda, K.N., Abolmasov, S.N.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2013
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Низкотемпературная плазма и плазменные технологии
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/109285
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:	Particle charging in beam-plasma systems / А.А. Bizyukov, E.V. Romashchenko, K.N. Sereda, S.N. Abolmasov // Вопросы атомной науки и техники. — 2013. — № 1. — С. 183-185. — Бібліогр.: 9 назв. — англ.

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spelling	irk-123456789-1092852016-11-23T03:02:20Z Particle charging in beam-plasma systems Bizyukov, А.А. Romashchenko, E.V. Sereda, K.N. Abolmasov, S.N. Низкотемпературная плазма и плазменные технологии The particle charging in an electron beam-plasma discharge is studied by means of the classical orbit motion limited approximation and on the basis of a discrete charging model. The particle charge fluctuations due to the stochastic nature of charging process are considered. The Fokker-Planck description of the particle charging has been presented. An analytical expression for the charge distribution function has been derived taking into account the processes of the collection of plasma electrons and ions by the dust grain and secondary electron emission from it. В рамках классического приближения ограниченного орбитального движения и на основе дискретной модели изучается зарядка частиц в пучково-плазменных разрядах. Рассматриваются флуктуации заряда частиц, связанных со случайностью процесса зарядки. Представлено описание Фоккера-Планка зарядки частиц. Выведено аналитическое выражение для функции распределения заряда с учетом процессов поглощения электронов и ионов плазмы пылевой частицей и с учетом вторичной электронной эмиссии. У рамках класичного наближення обмеженого орбітального руху та на підставі дискретної моделі вивчається зарядження частинок у пучково-плазмових системах. Розглянуто флуктуації зарядження частинок, пов’язаних з випадковістю процесу зарядження. Представлено опис Фоккера-Планка зарядження частинок. Отримано аналітичний вираз для функції розподілу заряду, з урахуванням процесів поглинання електронів та іонів плазми пиловою частинкою та з урахуванням вторинної електронної емісії. 2013 2013 Article Particle charging in beam-plasma systems / А.А. Bizyukov, E.V. Romashchenko, K.N. Sereda, S.N. Abolmasov // Вопросы атомной науки и техники. — 2013. — № 1. — С. 183-185. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.59.-f http://dspace.nbuv.gov.ua/handle/123456789/109285 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 Bizyukov, А.А. Romashchenko, E.V. Sereda, K.N. Abolmasov, S.N. Particle charging in beam-plasma systems Вопросы атомной науки и техники
description	The particle charging in an electron beam-plasma discharge is studied by means of the classical orbit motion limited approximation and on the basis of a discrete charging model. The particle charge fluctuations due to the stochastic nature of charging process are considered. The Fokker-Planck description of the particle charging has been presented. An analytical expression for the charge distribution function has been derived taking into account the processes of the collection of plasma electrons and ions by the dust grain and secondary electron emission from it.
format	Article
author	Bizyukov, А.А. Romashchenko, E.V. Sereda, K.N. Abolmasov, S.N.
author_facet	Bizyukov, А.А. Romashchenko, E.V. Sereda, K.N. Abolmasov, S.N.
author_sort	Bizyukov, А.А.
title	Particle charging in beam-plasma systems
title_short	Particle charging in beam-plasma systems
title_full	Particle charging in beam-plasma systems
title_fullStr	Particle charging in beam-plasma systems
title_full_unstemmed	Particle charging in beam-plasma systems
title_sort	particle charging in beam-plasma systems
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2013
topic_facet	Низкотемпературная плазма и плазменные технологии
url	http://dspace.nbuv.gov.ua/handle/123456789/109285
citation_txt	Particle charging in beam-plasma systems / А.А. Bizyukov, E.V. Romashchenko, K.N. Sereda, S.N. Abolmasov // Вопросы атомной науки и техники. — 2013. — № 1. — С. 183-185. — Бібліогр.: 9 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT bizyukovaa particlecharginginbeamplasmasystems AT romashchenkoev particlecharginginbeamplasmasystems AT seredakn particlecharginginbeamplasmasystems AT abolmasovsn particlecharginginbeamplasmasystems
first_indexed	2025-07-07T22:51:40Z
last_indexed	2025-07-07T22:51:40Z
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fulltext	ISSN 1562-6016. ВАНТ. 2013. №1(83) 183 PARTICLE CHARGING IN BEAM-PLASMA SYSTEMS А.А. Bizyukov1, E.V. Romashchenko2, K.N. Sereda1, S.N. Abolmasov3 1V.N. Karazin Kharkov National University, Kharkov, Ukraine; 2V. Dahl East Ukrainian National University, Lugansk, Ukraine; 3LPICM, CNRS, Ecole Polytechnique, Palaiseau, France The particle charging in an electron beam-plasma discharge is studied by means of the classical orbit motion limited approximation and on the basis of a discrete charging model. The particle charge fluctuations due to the sto- chastic nature of charging process are considered. The Fokker-Planck description of the particle charging has been presented. An analytical expression for the charge distribution function has been derived taking into account the processes of the collection of plasma electrons and ions by the dust grain and secondary electron emission from it. PACS: 52.59.-f INTRODUCTION The generation of particles ranging in the size from several microns to a few hundred microns has been ob- served in many technological vacuum-plasma processes such as vacuum arc methods for depositing decorative and hardening coatings [1]. The presence of particles in the plasma flow worsens the coating parameters. This is a serious detriment which must be avoided. We recently studied the behaviour of the floating electric potential of a macroparticle in an electron beam- plasma system in the framework of the orbit motion limited (OML) approach [2] with account of secondary electron emission [3]. We have used a “continuous charging model” which assumes that the steady-state potential to which a dust grain is charged has been de- termined by the balance of the currents that are col- lected by the grain surface and emitted from it [4]. This paper extends our previous work to include the effect of discreteness of the electrostatic charges that make these currents. 1. CONTINUOUS CHARGING MODEL Let us consider a beam-plasma discharge in which the number density of dust grains is low and the average intergrain distance l is much larger than the Debye length dλ in plasma. This allows us to consider the plasma with isolated dust grains [5]. Dust grain of ra- dius la d <<<< λ behaves like a spherical electric probe at floating potential fϕ [6]. The charge on a dust particle is the result of the net effect of all possible cur- rents to the particle surface. The charging of dust grain mainly occurs by the collection of electrons and ions from the plasma. In addition to this, dust grains are ex- posed to high-energy electron beam, which releases electrons by secondary electron emission process. The dust particle acquires instantaneous charge zeq = (with e the elementary charge and z an integer). The charging of a dust particle is governed by the following equation ∑= j jI dt dz , sbiej ,,,= , (1) where the sum is taken over all the fluxes jI of charged particles collected or emitted by the dust particle. Index j here represents the various species: e – indicates plasma electrons; −i plasma ions; −b beam electrons; −s secondary electrons. The ion, plasma-electron and beam-electron fluxes flowing onto the dust grain surface in the framework of OML model are ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ −= i si Tii kT ezvnaI ϕπ 18 0 2 , 0<sϕ , ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ −= i si Tii kT ezvnaI ϕπ exp8 0 2 , 0>sϕ , ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = e s Tee kT evnaI ϕπ exp8 0 2 , 0<sϕ , ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ += e s Tee kT evnaI ϕπ 18 0 2 , 0>sϕ , (2) ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ −= b s ebbb evnaI ε ϕπ 12 , 0<sϕ , ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ += b s ebbb evnaI ε ϕπ 12 , 0>sϕ , Where – e is the electronic charge, zie is the ionic charge, sϕ is the dust grain surface potential, a is the dust grain radius (for arc plasmas, this radius is usually from a few hundred nanometers to several tens of mi- crons) , 0n ( bn ) is the plasma (beam electron) density, eT ( iT ) is the electron (ion) temperature, e e Te m kTv = , ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = i i Ti m kTv is the electron (ion) thermal velocity, em ( im ) is the electron (ion) mass, k is the Boltzmann constant, e b eb m v ε2 = is the beam electron velocity , bε is the energy of beam electrons. For 0>sϕ and si ekT ϕ<< , the ion flux to the grain surface can be ignored. The flux sI of secondary electrons is connected to flux bI of beam electrons through the secondary emis- sion coefficient δ : 184 ISSN 1562-6016. ВАНТ. 2013. №1(83) bs II δ= . (3) The coefficient δ is described by the empirical de- pendence connected to the energy of primary electrons reaching the grain surface [3]: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −= bm sb bm b m e ε ϕε ε εδδ 2exp4.7 . (4) Here bmε is the primary electron energy at which the secondary electron emission coefficient reaches the val- ue mδ . The floating potential fϕ can be found from the bal- ance of the particle fluxes to/from its surface. 0=∑ j jI . (5) The charge on a grain q is related to the dust poten- tial by: sCq ϕ= , (6) in which an isolated dust grain is considered as a spheri- cal capacitor C of radius a . For a spherical dust grain satisfying da λ<< , in vacuum the capacitance is given by [7] aC 04πε= . (7) Hence, if one knows the potential of the dust grain and its radius, it is easy to determine its charge saq ϕπε04= . (8) Let define the charging time τ , which indicates how fast a grain can charge up in a plasma, as an RC time. RC=τ . (9) The resistor R is related to the slope of the charac- teristic of a spherical probe at floating potential fϕ . Therefore, f j j s I d d R ϕ ϕ ∑=− 1 . (10) Thus, we choose τ as the linear charge relaxation time required for the grain charge to approach its equi- librium value within one e-fold. For example, when bmse εϕ << , the dust particle acquires a positive charge during ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ++= b eb e kT n nanekT ε πδπετ 0 0 2 0 2 112 . (11) The fact that relaxation time τ is inversely propor- tional to both size of the dust grain and plasma density means that the fastest charge relaxation occurs for large grains and high plasma densities. Also the relaxation time depends on electron temperature and secondary electron emission coefficient δ . 2. DISCRETE CHARGING MODEL The currents collected by the grain surface and emit- ted from it actually consist of individual electrons and ions. Let assume that all the ions carry a single charge. Electrons and ions arrive at the particle’s surface at ran- dom times. Upon collision with plasma particles and with beam electrons, the particle charge undergoes a stepwise change 11 ±=− −ii zz . The charge losses are due to secondary electron emission and absorption of plasma ions, while the increase in charge of negatively charged particles is due to absorption of plasma elec- trons. The generation and loss of a unit elementary charge is a one-step Markov process for which transi- tion from state z can only go to either state 1−z or state 1+z . The probability for one charging event does not depend on the history previous events. This Mark- ovian property enables us to write a so-called Fokker- Planck equation for the distribution function Zf [8]: ( ) ( )[ ] ( ) ( )[ ]tzfzB z tzfzA zt f zz z , 2 1, 2 2 ∂ ∂ + ∂ ∂ −= ∂ ∂ (12) where ( ) 0→Δ Δ Δ = t t zzA (13) and ( ) 0 2 →Δ Δ Δ = t t zzB . (14) The distribution function Zf is interpreted as the fraction of the particles that carry the discrete elemen- tary charge z . It is normalized by 1=∫ ∞ ∞− dzf z . (15) Also, we have made use of the fact that Zf must be “slow” function of the charge. A Fokker-Planck equation is identical to the con- tinuous equation. The equation (12) can be rewritten as z j t f z ∂ ∂ −= ∂ ∂ . (16) Here “flux” is given by ( ) ( ) ( ) ( )[ ]tzfzB z tzfzAj zz , 2 1, ∂ ∂ −= . (17) For case 0=j , we have equilibrium distribution ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ∫ dz zB zA zB Czf )( )(2exp )( )( , (18) where C is the constant, calculated from condition (15). The first drift coefficient of the Fokker-Planck equa- tion is the definition of the particle flux. Then, this coef- ficient reads ∑= j jIzA )( (19) To determine the second diffusive coefficient )(zB , we also use the analogy to a capacitor charging through a resistor R following Einstein’s model for the thermal noise in an electric circuit [9]: R kT t q e t 2 0 2 = Δ Δ →Δ . (20) Therefore, an expression for the second drift coeffi- cient )(zB is Re kTzB e 2 2)( = . (21) Figs. 1 and 2 show the charge distribution function at small values of secondary electron emission coefficients for typical laboratory plasma conditions: hydrogen ISSN 1562-6016. ВАНТ. 2013. №1(83) 185 Fig. 1. Charge distribution function of dust particles with plasma density n0 = 109 cm-3and different beam electron energy: 1 – εb = 70 eV; 2 – εb = 50 eV; 3 – εb = 25 eV Fig. 2. Charge distribution function of dust particles with plasma density n0 = 1010 cm -3 and different beam electron energy: 1 – εb = 70 eV; 2 – εb = 50 eV; 3 – without electron beam plasma with a plasma density of, n0 = 109…1010 cm -3, an electron temperature of, Te = 10 eV an ion tempera- ture of Ti = 1 eV, grain radii of, a = 1 µ·m beam elec- tron energies of εb = 25…100 eV. As the plasma den- sity increases, the effects caused the electron beam be- come weaker. CONCLUSIONS It has been shown that injection of an electron beam into a dusty plasmas can significantly increase the nega- tive potential of a dust grain at small values of secon- dary electron emission coefficients. This allows to raise the efficiency of plasma purification methods, namely evaporation and Rayleigh decay of macroparticles. REFERENCES 1. A.A. Andreev, L.P. Sablev, et al. Vacuum Arc De- vices and Coatings. Kharkov: «NNTS KHFTI», 2005 (in Russian). 2. V.E. Fortov, A.G. Khrapak, etal. Dusty plasmas // Physics – Uspekhi. 2004, № 47(5), p. 447-492. 3. I.M. Bronshten and B.S. Framan. Secondary Electron Emission. Moscow: «Nauka», 1969. 4. A.A. Bizyukov, E.V. Romashchenko, K.N. Sereda, and A.D. Chibisov. Electric Potential of a Macroparticle in Beam-Plasma Systems // Plasma Physics Reports. 2009, v. 35, № 6, p. 499-501. 5. P.K. Shucla and A. Mamun. Introduction to Dusty Plasma Physics. Bristol: «IOP Publishing», 2002. 6. I. Langmuir.Collected Works of Irving Langmuir. Ed.by G. Suits. New York: «Pergamon», 1961. 7. A. Piel. Plasma Physics: An Introduction to Labora- tory, Space, and Fusion Plasmas. «Springer», 2010. 8. N.G.V. Kampen. Stochastic Processes in Physics and Chemistry. New York: «Elsevier», 1984. 9. I.A. Kvasnikov. Teorija neravnovesnyh system. M: «URSS», 2003 (in Russian). Article received 20.10.12 ЗАРЯДКА ЧАСТИЦЫ В ПУЧКОВО-ПЛАЗМЕННЫХ СИСТЕМАХ А.А. Бизюков, Е.В. Ромащенко, К.Н. Середа, С.Н. Аболмасов В рамках классического приближения ограниченного орбитального движения и на основе дискретной модели изучается зарядка частиц в пучково-плазменных разрядах. Рассматриваются флуктуации заряда час- тиц, связанных со случайностью процесса зарядки. Представлено описание Фоккера-Планка зарядки частиц. Выведено аналитическое выражение для функции распределения заряда с учетом процессов поглощения электронов и ионов плазмы пылевой частицей и с учетом вторичной электронной эмиссии. ЗАРЯДЖЕННЯ ЧАСТИНКИ В ПУЧКОВО-ПЛАЗМОВИХ СИСТЕМАХ О.А. Бізюков, О.В. Ромащенко, К.М. Середа, С.Н. Аболмасов У рамках класичного наближення обмеженого орбітального руху та на підставі дискретної моделі вивча- ється зарядження частинок у пучково-плазмових системах. Розглянуто флуктуації зарядження частинок, пов’язаних з випадковістю процесу зарядження. Представлено опис Фоккера-Планка зарядження частинок. Отримано аналітичний вираз для функції розподілу заряду, з урахуванням процесів поглинання електронів та іонів плазми пиловою частинкою та з урахуванням вторинної електронної емісії.

Particle charging in beam-plasma systems

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