Voids in Dusty Plasma of a Stratified DC Glow Discharge in Noble Gases

Contrib. Plasma Phys. 56, No. 3-4, 234 239 (2016) / DOI 10.1002/ctpp.201500099 Voids in Dusty Plasma of a Stratified DC Glow Discharge in Noble Gases A. V. Fedoseev 1, G. I. Sukhinin 1,2, A. R. Abdirakhmanov 3, M. K. Dosbolayev 3, and T. S. Ramazanov 3 1 Institute of Thermophysics SB RAS, Ave. Lavrentyev, 1, Novosibirsk 630090, Russia 2 Novosibirsk State University, Pirogova Str., 2, Novosibirsk 630090, Russia 3 IETP, Al Farabi Kazakh National University - al Farabi Ave. 71, Almaty 050040, Kazakhstan Received 29 October 2015, revised 11 November 2015, accepted 16 November 2015 Published online 24 February 2016 Key words Dusty plasma, direct current glow discharge, ion drag force. Experimental investigations of dusty plasma parameters of a DC glow discharge were performed in helium and argon. In the discharge in helium, at high discharge current dust-free regions (voids) were formed in the center of the dust particles clouds that levitated in the strong electric field of a stratified positive column. In experiments with argon, the dust particles were moved from the center of the discharge tube to the periphery at high discharge current. The behavior of voids formation was investigated for different discharge conditions (sort of gas, discharge pressure and discharge current) and dust particles parameters (particles radii and particles total number). It was shown that it is the ion drag force radial component that leads to the formation of voids in helium and moves the particles to the tube periphery in argon discharge. 1 Introduction Dusty plasma is an ionized gas of electrons, ions, and micron-sized particles of condensed matter. It can be found in space, industrial devices and technological applications (see reviews [1, 2]). In laboratory conditions, dusty plasma is usually studied in RF [3, 4] and in DC glow discharges [5 7], as well as in a combined RF+DC discharge mode [8,9]. The formation of a great void in RF discharges in microgravity conditions is a well known phenomenon [10, 11]. Different theoretical models were developed to describe this phenomenon [12 14]. It was commonly accepted that an ion drag force is responsible for the void formation in the central part of RF discharges. The ion drag force is driven by an outflow of ions from an ionization source toward the surrounding dust cloud, which has a negative space charge [12]. Paper [15] presented new results on experimental observation of dust-voids formation of a DC glow discharge in helium. However, there is still lack of data concerning formation of the dust-free voids in a pure DC discharge in noble gases. The aim of the paper is to investigate the mechanism of dust-free voids formation in the clouds of dust particles in the positive column of a DC discharge in helium and argon. A previously developed model [15 17] for radial distributions of plasma parameters of a DC glow discharge was modified for different gases (helium and argon) to take into account properly the ion drag force. 2 Experiment The experiments were carried out in a DC glow discharge generated in a vertically oriented cylindrical glass tube with an inner diameter D in = 4.5 cm and an inter electrode distance of 50 cm (see Fig. 1). The experimental setup was described elsewhere [4,18]. The discharge was generated in He and Ar at pressures p =0.1 0.4 Torr and discharge currents I d = 1-20 ma. Particles were stored in a container with a grid positioned above the anode. When the container was shaken the particles fell downwards through the grid. We used monodisperse melamine Corresponding author. E-mail: fedoseev@itp.nsc.ru, Phone: +7 383 333 1095, Fax: +7 383 330 8480

Contrib. Plasma Phys. 56, No. 3-4 (2016) / 235 formaldehyde (MF) particles with a diameter 1 μm and a density of 1.51 g/cm 3 and polydisperse spherical hollow particles of glass with a diameter approximately 1-5 μm and a density of 0.3 g/cm 3. Fig. 1 Sketch of the experimental setup. In low-temperature discharge plasma, dust particles usually acquire a large negative charge of e 0 Z d 10 3 10 5 e 0 (where Z d is the charge number of a particle, e 0 is an elementary charge). The axial electric field E z (z) (z is the axial coordinate directed along the discharge tube axis) suspends a grain in the gravitational field in the striations of a glow discharge. The radial electric field E r (r) (r is the radial coordinate) traps negatively charged dust particles in the central region of the discharge tube, preventing them from escaping to the wall. Thus, the charged dust particles forme a dust cloud of about 3 cm in size within the striation region. In order to visualize dust particles in the discharge tube we illuminated the region where particles levitated with a diode laser beam (wavelength λ = 532 nm, power P = 220 mw). The horizontal cross section of the discharge tube with dust particles cloud was visualized by a thin laser sheet created by means of a cylindrical telescope. In Fig. 2 the photos of a stratum glow with clouds of dust particles in a DC discharge in helium are presented for different values of the gas discharge current I d. The green light regions are produced by a laser-knife horizontal cross section, i.e. the scattered laser light on the discharge tube wall and the cloud of dust particles. The outer lighting ring is a scattered light of the laser sheet on gas discharge tube wall (radius of the ring is equal to the tube inner diameter D in = 4.5 cm). The inner ring is a scattered light on dust particles. The cross sections were obtained for the central part of the dust clouds. For low values of the discharge current (I d < 4 ma) the clouds of dust particles have usual compact structures. In this case, there are no voids (dust-free regions) in the cloud and dust particles density distribution has a homogeneous decaying radial profile with a maximum in the center of the discharge tube. With an increase of the gas discharge current, the density of dust particles in the center of the cloud decreases. For high discharge currents (I d > 6 ma) the particles in the cloud are removed from the center of the discharge tube to its periphery. With a further increase of the discharge currents, the radius of the voids increases and green glowing circle of dust particles becomes more pronounced. In the case of high discharge currents (I d > 6 ma) in helium, the cloud of dust particles has a cup -like structure with no particles in the central and upper parts of the cloud. We can obtain different horizontal cross sections of the dust cloud starting from the bottom part of the cloud and to the upper part of the cloud. The circle-like structure of the horizontal cross section of the dust cloud (with the voids) were received only for central and upper parts of the cloud. In Fig. 3 the photos of a stratum glow with clouds of dust particles in a DC discharge in argon are presented for different values of the gas discharge current I d. The horizontal cross sections for the central part of the dust clouds were obtained by the top-view camera. As in helium, for low values of the discharge current (I d < 1 ma) the clouds of dust particles have usual compact structures. In this case, there are no voids (dust-free regions) in

236 A.V. Fedoseev: Voids in dusty plasma the cloud and dust particles density distribution has a homogeneous decaying radial profile with a maximum in the center of the discharge tube. With an increase of the gas discharge current, the density of dust particles in the center of the cloud decreases. The cylindrical symmetry starts to be broken. It should be noted that cylindrically symmetric dust-voids as in helium do not developed in argon discharge. For high discharge currents (I d > 1 ma) the cloud of dust particles removed from the center of the discharge tube to its periphery (Figs. 3b and 3c). The outer ring in Fig. 3c is a tube wall with diameter D in = 4.5 cm. Fig. 2 The photo of horizontal cross sections of a DC discharge in helium with dust particles clouds (angle view). Helium pressure p = 0.38 Torr. (a) I d = 4 ma. (b) I d = 8 ma. (c) I d = 13.4 ma. Polydisperse spherical hollow particles of glass, r d 1 5 μm. Fig. 3 The photo of horizontal cross sections of a DC discharge in argon with dust particles clouds (top view). Argon pressure p = 0.3 Torr. (a) I d = 0.83 ma. (b) I d = 5.72 ma. (c) I d = 9 ma. Monodisperse melamine formaldehyde particles, r d 1 μm. 3 Model To describe the formation of dust-free voids in the clouds of dust particles in DC discharge in noble gases we used previously developed self-consistent kinetic model for radial distributions of dusty plasma parameters [15]. The cloud of spherical dust particles with radii r d 0.5 μm was assumed to have some radial density distribution N d (r). The Boltzmann equation for electron energy distribution function (EEDF) was used in the conventional two-term approximation for isotropic f 0 and anisotropic (radial f r and axial f z ) components that are connected with the radial and axial components of the electric field, E z and E r (r) (for details, see [15 17]). The value of the axial electric field E z was determined by the balance of electrons and ions production in ionization S ion (f 0 )

Contrib. Plasma Phys. 56, No. 3-4 (2016) / 237 and their losses on the walls of the discharge tube and on the surface of dust particles. Obviously, these processes are non-local. From the Boltzmann equation we received the electron density n e (r) and radial j er and axial j ez current densities, the constants of ionization rate and electron and ion absorption rates on the dust particle surface. To calculate the ion density radial distribution n i (r), a drift-diffusion equation with the terms of ions production in electron-atom collisions and their losses in absorption on the dust particles surface was used. In pure noble gases without dust particles (i.e., outside the dust cloud), the coefficients of ion drift μ i and diffusion D i are determined mainly by charge exchange collisions and are connected with each other by the Einstein relation (μ i k B T i D i ). In a discharge with dust particles, the drift and diffusion coefficients depend on both gas density N g and dust particles density N d (r). The radial distribution of dust particles density N d (r) was calculated with the help of a drift-diffusion equation for negatively charged dust particles. It was assumed that the dust particles mobility μ d and diffusion D d coefficients obey the Einstein s relation, μ d k B T d D d. In this paper, we use the intermediate value T d =10eV because the choice of dust temperature was not very important for the obtained results. At the right boundary of numerical region, the dust particle density was assumed to be equal to zero due to a very high value of electric potential at the discharge tube wall. It should be noted that the dust particles can not overcome this potential, and are confined in the center of the tube, and form a dust cloud. Since there are no source and loss terms for dust particles, we do not need to take the actual values of mobility and diffusion coefficients only by taking into account the Einstein relation between them. In the process of numerical calculation, the radial profile of dust particles density evaluates, and in the final state the radial flux of dust particles becomes equal to zero, j dr (r) =0. The total force, F tot = F E + F id + F dd, acting on a dust particle in radial direction is the sum of electric force, F E = ez d (r)e r (r), ion drag force, F id j ir (r), and also the inter-particle repulsion force F dd. The dust-dust interaction repulsive force F dd was calculated as in [16]. The ion drag force, F id (r), has the opposite direction compared to the electrostatic force F E, and under certain conditions in the discharge tube can lead to the formation of a dust-free region in the central part of the discharge tube around its axis. There are many papers devoted to the evaluation of the ion drag force, and in this paper the ion drag force F id was taken in the form [19]. Equations for electrons, ions and dust particles were complemented by the Poisson equation for a selfconsistent electric field E r (r). Together they form a complete system of equations for determining four unknown plasma parameters n e (r), n i (r), N d (r) and E r (r) in a self-consistent way. A time-dependent problem for electrons, ions and dust particles based on the balance equations with the production and destruction terms obtained with the help of the Boltzmann equation for EEDF and the electric field obtained from the Poisson equation was solved. At each time step, the dust particle charge number Z d was found from the equality of electron and ion fluxes to the surface of the dust particles, I e + I i =0taking into account the electron and ion distribution functions (see for details [16]). The axial electric field strength was also recalculated at each time step with the help of the feedback between the discharge current I d and E z. The procedure was repeated until a complete convergence of all plasma and dust particles parameters was achieved. It should be noted that we are not interested in time evolution of plasma parameters and consider only the final converged solution for the given gas discharge and dust particles parameters. 4 Results The analysis [15] of the papers devoted to investigations of the voids formation in a dusty plasma shows that the void is formed in RF discharges when the ion drag force exceeds the electrostatic force (it is assumed that other forces, i.e. gravity and thermophoretic forces, are negligible). If the ion drift velocity u i = μ i E is proportional to the electric field strength E, the ratio of ion drag force F id and electric field force F E can be roughly presented in the form [10, 15, 17]: F id /F E μ i n i Z d, (1) i.e. the ratio is proportional to ion mobility μ i, ion density n i, and dust particles charge Z d. The evaluation of this expression [17] showed that the condition F id /F E 1 can be achieved more easily at low gas pressures (μ i 1/p He ), at high discharge currents (n i I d ), and for dust particles with larger radii (Z d r d ). In the case of a DC discharge with cylindrical symmetry, the voids are formed at the axis of the discharge tube. The radial component of the ion drag force F id (r) pushes dust particles out from the center of a dust cloud to the

238 A.V. Fedoseev: Voids in dusty plasma periphery in spite of the electrostatic force F E (r), which captures the particles at the axis of the discharge tube. The condition F id (r)/f E (r) 1 is fulfilled in the region of the void. To describe the obtained experimental results we calculate the radial dependencies of dusty plasma parameters for different discharge currents I d = 4-13.4 ma and constant gas pressures. In Fig. 4 the radial distributions of dust particles densities N d (r) are presented for I d = 8, 10.4, 13.4 ma at constant helium pressure p = 0.38 Torr. It is seen that at a low discharge current I d = 8 ma, the radial distribution of dust particles density N d (r) is a decaying function. The maximum density is at the axis of the discharge tube, r = 0 cm. At a discharge current I d = 10.4 ma, the maximum in the radial distribution of dust particles density shifts some distance from the tube axis, r 1 cm. The local non-zero minimum is formed at the tube axis. It is the ion drag force radial component exceeding the electrostatic force that moves the particles from the center (see below). At discharge current I d = 13.4 ma, the maximum of dust particles density is at r 1.3 cm. Thus, the higher discharge current, the wider the void. For the discharge in argon, the radial distributions of dust particles densities N d (r) are presented in Fig. 5 for I d = 6, 10, 14 ma at constant argon pressure p = 0.4 Torr. It should be noted that in calculations in the frame of the developed 1D model we can obtain only cylindrically symmetric solutions. In experiments, the cloud of dust particles moved as a whole object to the periphery of the discharge, i.e. to the discharge tube wall, due to some asymmetric instability. However, the model can be helpful for obtaining the conditions when the resulting force acting on dust particles will move them from the center of the discharge tube. The comparison of results for helium (Fig. 4) and argon (Fig. 5) shows that in argon more pronounced dust-void is formed at the same gas discharge and dust particles conditions. This fact means that expression (1) is larger for argon. Fig. 4 Dust particles density radial distributions. Helium pressure p = 0.38 Torr, N tot =2N 0, r d = 0.5 μm. Solid line for I d = 8 ma, dashed line for I d = 10.4 ma, dashed dotted line for I z = 13.4 ma. Fig. 5 Dust particles density radial distributions. Argon pressure p = 0.4 Torr, N tot =2N 0, r d = 0.5 μm. Solid line for I d = 6 ma, dashed line for I d = 10 ma, dashed dotted line for I z =14mA. It should be noted that in experiments in helium we used polydisperse spherical hollow particles of glass with radius r d 1 5 μm. In order to compare the behavior of dust-void formation and ion drag in helium and argon, the radial distributions of dust particles densities N d (r) are presented in Figs. 4 and 5 for the same dust particles radius r d = 0.5 μm. The calculations were also made for a bigger dust particles radius r d =2μm. The maximums of dust particles density radial distributions shift towards the discharge tube wall compared to the obtained results for r d = 0.5 μm. Taking into account that Z d r d and expression (1), the smaller the dust particles radius, the smaller the ion drag force. Thus, the formed voids are narrower. To describe the influence of gas pressure on the voids formation we have also performed the calculation [15] for lower gas pressure p = 0.3 Torr. The results have shown that the lower is gas pressure, the higher is the reduced mobility of ions and the wider voids are formed. One more parameter which influences the dusty plasma parameters is the total number of dust particles N tot. It should be noted that this parameter is not easy to control in experiments. The number of dust particles and its radial profile are formed self-consistently. In calculations, we can set up different values of a total number of dust particles per unit length (per 1 cm) of the positive column, which is equal to the integral of particle density over

Contrib. Plasma Phys. 56, No. 3-4 (2016) / 239 the discharge tube cross section. It was obtained that the absolute values of dust particles densities are almost in linear dependence on N tot, and the maximums of distributions N d (r) stay almost in the same radial positions. In a discharge with dust particles, the ion density n i (r) increases and the electron density n e (r) decreases in the region of a dust cloud. The calculations show that the condition of quasi-neutrality n i n e +N d Z d is fulfilled almost in the whole discharge gap. The positive values of volume charge outside the dust cloud determine the radial distribution of the electric potential (according to the Poisson equation). In a steady state, the total dust particles flux is equal to zero in the whole discharge cross section. The results show that in the present conditions the diffusion term of dust particles flux is negligible. The inter-particle repulsive force is almost ten times smaller than the other components. Thus, the radial distribution of dust particles is determined mainly by the ion drag force and by the electric force. It should be noted that the obtained conditions of the void formation (Eq. 1) is not trivial. We cannot simply increase the discharge current (or increase the particles radii or reduce the gas pressure) by the factor of two and receive a two times more pronounced void. These parameters strongly depend on each other self-consistently. If we increase the discharge current, then the axial and radial electric field strengths, the charge of particles and other parameters will change adjusting to each other. This is what occurs in the experiments and it is taken into account in our model. 5 Conclusion Experimental and theoretical investigations of the dusty plasma of a DC glow discharge in helium and argon were performed. In the discharge in helium, dust-free regions (voids) were formed in the center of dust particles clouds that levitated in the strong electric field of a stratified positive column. In experiments with argon, the cloud of dust particles moved as a whole object to the periphery of the discharge due to some asymmetric instability. The behavior of dust particles was investigated experimentally for different discharge gases (helium and argon), gas pressures and discharge currents and radius and total number of dust particles. To describe the obtained phenomenon, previously developed model [15] for the positive column of a DC glow discharge with dust particles was implemented. The model was modified to obtain solutions for different inert gases (helium and argon). Experimental and calculated results show that it is the ion drag force radial component that leads to the formation of the voids, and more pronounced voids are formed for higher discharge current, for dust particles with larger radii and under lower gas pressures. The comparison of calculated results for helium and argon was performed and showed a good agreement with experimental results. Acknowledgements Kazakhstan. The work was supported by grant 3112/GF4 of the Ministry of Education and Science of Republic of References [1] V.E. Fortov, A.G. Khrapak, S.A. Khrapak et al., Physics-Uspekhi 47, 447 (2004). [2] O. Ishihara, J. Phys. D 40, R121 (2007). [3] H. Thomas, G.E. Morfill, V. Demmel et al., Phys. Rev. Lett. 73, 652 (1994). [4] T.S. Ramazanov, K.N. Dzhumagulova, A.N. Jumabekov, M.K. Dosbolayev, Phys. Plasmas 15, 053704 (2008). [5] V.E. Fortov, A.P. Nefedov, V.M. Torchinskii et al., J. Exp. Theor. Phys. Lett. 64, 92 (1996). [6] G.I. Sukhinin, A.V. Fedoseev, T.S. Ramazanov et al., J. Phys. D. 41, 245207 (2008). [7] E. Thomas, Contrib. Plasma Phys. 49, 316 (2009). [8] V. Fortov, G. Morfill, O. Petrov et al., Plasma Phys. Control. Fusion 47, B537 (2005). [9] S. Mitic, B.A. Klumov, S.A. Khrapak, G.E. Morfill, Phys. Plasmas 20, 043701 (2013). [10] G.E. Morfill, H.M. Thomas, U. Konopka et al., Phys. Rev. Lett. 83, 1598-1601 (1999). [11] T. Bockwoldt, O. Arp, K.O. Menzel, A. Piel, Phys. Plasmas 21, 103703 (2014). [12] J. Goree, G.E. Morfill, V.N. Tsytovich, S.V. Vladimirov, Phys. Rev. E 59, 7055 (1999). [13] V.N. Tsytovich, S.V. Vladimirov, G.E. Morfill, J. Goree, Phys. Rev. E 63, 056609 (2001). [14] M.R. Akdim, W.J. Goedheer, Phys. Rev. E 65, 015401 (2001). [15] A.V. Fedoseev, G.I. Sukhinin, M.K. Dosbolayev, T.S. Ramazanov, Phys. Rev. E 92, 023106 (2015). [16] G.I. Sukhinin, A.V. Fedoseev, S.N. Antipov at al., Phys. Rev. E 87, 013101 (2013). [17] G.I. Sukhinin, A.V. Fedoseev, M.V. Salnikov et al., Europhys. Lett. 103, 35001 (2013). [18] T.S. Ramazanov, T.T. Daniyarov, S.A. Maiorov et al., Contrib. Plasma Phys. 51, 505 (2011). [19] S.A. Khrapak, S.V. Ratynskaia, A.V. Zobnin, et al., Phys. Rev. E 72, 016406 (2005).