The dynamics of macroparticles in a direct current glow discharge plasma under micro-gravity conditions

The dynamics of large-sized (70–180 µm) spherical bronze particles in a direct current glow discharge plasma was studied experimentally under microgravitation conditions. The temperatures, velocities, pair correlation functions and self-diffusion coefficients of macroparticles were measured at various discharge currents. The charges of dust particles (on the order of 106 e) corresponded to high surface potentials of about 30–40 V.


Introduction
A dust plasma is a partially ionized gas containing charged substance particles (dust) of micron dimensions. The size of dust particles allows them to be recorded on a videotape, which significantly simplifies the use of direct contactless methods for their diagnostics. A dust plasma is therefore a convenient experimental model for studying various transport phenomena in systems of interacting particles, such as charging and mass transfer, the formation of dust structures and complex oscillatory modes, etc [1]- [10]. In recent years, considerable attention has been given to experimental studies of dust plasmas under microgravitation conditions [6]- [10]. Such experiments allow a wide range of phenomena that cannot be observed in laboratories on the earth to be studied [6]- [8]: photoemission charging of aerosols in the upper layers of the atmosphere, ambipolar diffusion, the dynamics of large-size (larger than 100 µm) dust particles in a plasma, etc. Recent experiments performed by the Russian-German team on the International Space Station revealed the occurrence of several new phenomena in an RF discharge plasma, such as 'dust beats', the formation of plasma crystal with lattices of different types, opposite charging of macroparticles, etc. No analogues of such processes are observed under usual laboratory conditions [10].
In this work, we describe some of the earliest experiments on the dynamics of macroparticles under microgravitation conditions performed aboard the Mir space station during the 28th orbital expedition. The experiments were performed for large-size (∼100 µm) bronze particles in a direct current glow (dc-) discharge plasma.

Experimental details
The experimental unit is schematically shown in figure 1. The main element of the working chamber was a gas discharge tube of radius R t = 1.6 cm filled with neon (Ne) to a pressure of P = 1 Torr. The distance between a plane anode and a cathode was 28 cm. An insulated electrode was mounted at 4.5 cm from the anode. The electrode was made as two steel grids (wire 60 µm in diameter) with 150 µm ×150 µm meshes, and the distance between the grids was 1 cm. During experiments, the electrode was under a floating potential and prevented negatively charged macroparticles from escaping to the anode. Bronze spherical particles (particles 70-180 µm in diameter, mean radius a = 62.5 µm, density of the material ρ = 8.2 g cm −3 ) were placed between the grid electrode and the cathode. The diagnostics of macroparticles was performed with the use of a plane laser beam ('laser knife' about 300 µm wide, wavelength 0.67 µm) and additional illumination of the dust cloud by an incandescent lamp. In the latter case, the number of detected particles was determined by the depth of field of the video system, which allowed us to keep track of particle positions for long enough to analyse their transport characteristics. The image was recorded on a video tape at a 50 s −1 frame frequency. The video data were processed using a special program for identifying the displacements of separate particles in the visual field of video recording.
Experiments were performed at discharge currents (I = 0.1-0.8 mA) varied by the current source. Bronze particles were initially situated on the tube walls. For this reason, the system was subjected to a dynamic action (pushed) after switching on a discharge to shake off particles from the tube walls. After the dynamic action, bronze particles moved toward the insulated grid electrodes, in the vicinity of which ordered structures were formed (figures 2(a), (b)). The discharge was then 'quenched', the particles relaxed to the initial state (returned to the tube walls), and the experiment was repeated at a new gas discharge current value. Plasma concentration n 0 ≈ n 0 e ≈ n 0 i (here n 0 e(i) is the concentration of electrons (ions) in the absence of dust particles) in the region of the positive discharge column can be estimated from discharge current density measurements, j = I /π R 2 t ≈ 12-96 µA cm −2 ; this value should remain constant over the whole tube length: where µ e is the mobility of electrons (for neon, µ e P ≈ 1.5 × 10 6 Torr cm 2 V −1 s −1 ). In tubes with radii of 1-2 cm and P = 1 Torr, field E of the positive column in a normal glow discharge in neon is E ∼ 1 V cm −1 , the normal current density is j n = 5-6 µA cm −2 , and the mean electron energy characterizing electron temperature T e is about 3-5 eV [11]. Under our experimental conditions, discharges occurred in an anomalous mode (which followed from both the recorded current densities and current-voltage characteristics), and the electric field strength obeyed the equation E ∝ j 1/2 [11]. At E = 1.5 V cm −1 and j = 12 µA cm −2 , the mean plasma concentration calculated by (1) was n 0 = (5-14) × 10 7 cm −3 ( j = 12-96 µA cm −2 ). Taking into account the Bessel radial profile, the plasma density along the tube axis, where the parameters of dust particles were measured, reached values on the order of 2.4n 0 [11]. The further estimates will therefore be based on the assumption that, in the absence of particles, the concentration of electrons (ions) varied in the range 10 8 cm −3 under current density variations from 12 to 96 µA cm −2 .
108.4 (a) (b) Figure 2. Video images of (a) gas-discharge tube and (b) particle trajectories from the discharge positive column toward the insulated grid electrodes.

Measurement results and their analysis
The determination of dust charges from the drift velocity of macroparticles The mean drift velocity V p of particles from the positive column (figure 2(b), field A) to the grid electrode is shown in figure 3 as a function of discharge current I . As the velocity of particle motions in the measurement volume remained virtually constant, their charges eZ p could be found from the equation of motion [8] where m p is the mass of the particle and ν fr is the friction coefficient of dust particles, which determines the frequency of their collisions with surrounding gas neutrals [12,13], Here, l g (µm/Torr) ≈ 125/P is the free path of neon neutrals and η ≈ 3.17 (2) and (3), we find that particle charge Z p ≈ 10 6 is virtually independent of discharge current (figure 4, curve 1) and corresponds to fairly high surface potentials ϕ s = eZ p /a p ≈ 35-37 V. The errors in the ϕ s values obtained by this method are determined by the availability of a priori information on the field and friction coefficient values in (2).

The formation of liquid dust structures
The characteristic dimensions of dust clouds formed in the vicinity of the grid electrode (figure 2(b), field B) were about 2 cm in the radial direction and 0.7-1.3 cm from the grid edge where l max is the position of the main g(l) maximum and l p is the mean interparticle distance. The mean interparticle distance l p was changed from ∼750 to ∼1000 µm. Because of a fairly small number of particles in the laser knife plane, a quantitative analysis of the experimental g(l) functions is virtually impossible. Nevertheless, the presence of fairly well-defined secondary g(l) maxima is evidence of strong interparticle interactions and weak screening of particles (screening parameter κ = l p /λ < 1, where λ is the screening length).
According to the Lindemann criterion, a solid phase melts if the ratio between the root of the mean-square displacement 0 of particles from their equilibrium positions and the mean interparticle distance l p reaches about 0.15 [14]. In experiments, particle displacements are usually measured from the centre of mass of the system, that is = √ 2 0 , and the Lindemann parameter at the melting curve is therefore is the displacement of a separate particle and N denotes averaging over the ensemble of N particles) for 16 particles (N p = 16), which remain in the visual field of the video system for about 4.5 s, is shown in figure 6(a). Note that, during some time intervals, the N (t)/l p ratio remains constant and corresponds to the Lindemann criterion. When the observation time was decreased to about 1 s, the number of identified trajectories increased to N p = 70-120 at the expense of particles that experienced transitions between 'settled' states from one cloud region to another. Averaging of particle displacements N (t) over the ensemble was then close to time averaging, t N = (l(t) − l(0)) 2 N t ( figure 6(a)). Here, N,t denotes averaging over the ensemble and time, respectively. A similar picture was observed in numerical simulations of the dynamics of macroparticles with the Yukawa interaction potential ϕ = eZ p exp(−l/λ)/l in a strongly nonideal dust liquid [15]. 'Jumps' observed in simulated systems are illustrated by figure 6(b), where the difference between the ensemble N /l p and time t N /l p averages close to the crystallization curve of the system, where the * normalized nonideality parameter tends to 102, is shown. This difference vanishes as * decreases, and the system under study becomes ergodic.
The * normalized parameter value determines the degree of ordering and the dynamics of particles in nonideal Yukawa systems [15,16] where κ = l p /λ, = (eZ p ) 2 n 1/3 p /T p . Here, T p is the temperature of macroparticles in energy units.

Diffusion of macroparticles
The self-diffusion coefficient of macroparticles D p can be found from measured mean-square displacements from The relation between the D p self-diffusion coefficient given by D p = lim t→∞ D(t) and the * value (4) in strongly correlated ( * > 30) Yukawa systems can be written as [16]  where c ≈ 102 is the * parameter value at the crystallization point and ω l = eZ p (n p /π m p ) 1/2 (1 + κ + κ 2 /2) 1/2 exp(−κ/2) ≡ ( * T p /πl 2 p m p ) 1/2 is the normalized dust frequency. The error involved in approximation (6) sharply decreases as * increases; it amounts to about 30% for * ≈ 30 and less than 3% at * > 50 [15]. Equation (6) allows * to be determined fairly easily from the results obtained in measurements of the mean interparticle distance l p , temperature T p , and the D p diffusion coefficient of macroparticles. In our experiments the l p ≈ 700-1000 µm, and D p ≈ 0.1-1.1 mm 2 s −1 values were increased by the discharge current I . The value of diffusion coefficient for noninteracting particles (D 0 = T p /m p ν fr ) was found to be more than an order of magnitude larger than the D p value calculated by (5). The dust temperature T p was about 10 5 eV. The temperature of macroparticles was established by finding the Maxwell distribution that best described the recorded spectrum of instantaneous velocities of particles obtained by analysing video records. A similar procedure for determining temperature was described in [2,7]. The mean velocities of chaotic movement of particles were about 1 mm s −1 (see figure 3). Note that this procedure could underestimate the mean chaotic energy of particles (kinetic temperature) if the frame frequency w (50 s −1 in our experiments) did not satisfy the condition w ν fr [2].

The nonideality parameter and macroparticle charges
The * normalized parameter values reproduced by (6) from diffusion coefficient measurements are shown in figure 7 for the mean (a = 62.5 µm) and minimal (a min = 35 µm) particle sizes. Note that * determinations are only based on measurement results. The ν fr friction coefficient value depends on the radius of particles, but it does not significantly influence the * value because ν fr < ω l under the experimental conditions. If the effects of screening macroparticles in a plasma-dust system are significant, an analysis of diffusion of macroparticles on the assumption of negligibly weak screening ( * = , κ < 1) gives a minimal estimate of the charge Z p of 108.8 dust macroparticles irrespective of the form of the interparticle interaction potential. Parameter * ≈ measurements for κ = 0 allow surface potentials at I ≤ 0.5 mA to be determined. This gives ϕ s ≈ 42 V for medium-sized particles a = 62.5 µm and ϕ s ≈ 30 V for particles of radius a min = 35 µm (see figure 4). For I = 0.8 mA, the recorded surface potential value is lower by approximately 30%. The error in determining the charge of macroparticles is then substantially larger, because at low * < 35 values, (6) is fairly inaccurate (see figure 7). The obtained macroparticle charge estimates are in agreement with the results of determining Z p from the equation of motion (2). We can therefore hope that the surface potentials ϕ s ≈ 30-42 V (I ≤ 0.5 mA) and ϕ s ≈ 22-30 V (I = 0.8 mA) correctly reproduce the real Z p charge values, and, accordingly, the assumption of weak screening (κ < 1) of macroparticles corresponds well with the conditions existing in the dust system under study. According to the orbit motion limited (OML) theory, the particle charge Z p = zaT e /e 2 , where z ≈ 2-4 for most of the experimental conditions in a direct current glow discharge [17,18]. Note that, in the presence of large-size particles with a > 10-20 µm, the mean free path l i of ions (Ar, Ne) at room temperature becomes comparable with or smaller than a [11] and typical buffer gas pressures P ≈ 1 Torr. This decreases flow of ions onto the surface of a dust particle and, therefore, increases ϕ s and z. A similar effect was observed experimentally. For instance, it was shown in [8] that the surface potential of a particle grew approximately from 9 to 30 V as the particle radius increased from 2 to 7 µm in neon at P ≈ 0.5-1.5 Torr. This corresponded to changes in z approximately from 3 to 10 at T e = 3 eV. Thus we can assume that the dust surface potentials ϕ s = zT e /e can attain ∼30-50 V under the conditions of our experiments (a ∼ 30-90 µm > l i ∼ 10-20 µm) because the electron temperature is T e ∼ 3-5 eV for direct current glow discharges in neon [11].
Note also that high macroparticle charges Z p ≈ 10 6 at their concentrations n p ≈ 10 3 cm −3 do not correspond with the suggestion of the electroneutrality of the system, Z p n p + n e = n i , if we assume that the presence of dust particles have no significant influence on discharge conditions and the concentration of ions in the dust cloud is comparable with their concentration in the absence of macroparticles, n 0 i ≈ 10 8 cm −3 . Such a discrepancy has already been observed in laboratory conditions on the earth. For instance, heavy glass particles hovered in weak fields (about 1-12 V cm −1 ) of glow discharge strata and positive columns in neon [19], which led the authors of [19] to suggest either the existence of higher charges Z p or a sharp increase in electric field E caused by a change in the discharge conditions in the dust cloud.

The influence of macroparticles on equilibrium ionization
The influence of macroparticles on kinetic processes in a glow discharge can be substantial, because a considerable decrease in the concentration n e of electrons as a consequence of their effective loss on dust cloud particles results in an increase in electric field strength ( j = constant → En e = constant). The mean electron energy then increases, which causes an increase in ionization frequency ν i , which in turn increases the concentration of electrons to its equilibrium value.
As glow discharges in rare gases are usually controlled by ambipolar diffusion (plasma recombination on gas-discharge tube walls), this sequence is only observed if the electron loss frequency ν ep on dust cloud particles is comparable with or much larger than the ν ab frequency of diffusion electron loss [11], where D a ∼ = µ i T e /e is the ambipolar diffusion coefficient at T e T i , and µ i ≈ 3200 cm 2 V −1 s −1 is the mobility of singly charged ions in neon at P = 1 Torr.
The ν ep electron loss frequency on dust cloud particles can be estimated as Substituting the conditions of our experiments (a = 62.5 µm and n p = (1-3) × 10 3 cm −3 ) into (8), we find that, at z = 3-4, the ν ep electron loss frequency on dust cloud particles far exceeds the ν ab diffusion loss frequency (ν ep /ν ab > 10 at T e < 15 eV). We can therefore assume that discharge conditions in our experiments are determined by plasma recombination on the surface of particles. Under steady state conditions, the rate of electron loss should be compensated by the rate of particle creation, and, accordingly, the ionization frequency ν i should coincide with the electron loss frequency. Note that, in a positive column free of particles, ionization equilibrium is attained by equalizing the rates of plasma ionization (n 0 e ν i ) and recombination on tube walls (β ab n 0 e n 0 i ):n 0 e ν i ≡ n 0 e ν ab = β ab n 0 e n 0 i , and the condition of ionization equilibrium in a dust cloud is n e ν i ≡ n e ν ep = β ep n e n i , where β ab and β ep are the corresponding recombination coefficients. Suppose that the plasma recombination coefficients on tube walls and on the surface of dust particles are approximately equal, β ab ≈ β ep . The ratio between the n i concentration of ions in a dust cloud and the n 0 i concentration of ions in a plasma without macroparticles is then given by where the n 0 i ≈ (1-3)×10 8 cm −3 value corresponds to the experimental current density. Using (9) and taking into account (7) and (8), we find that n i ≈ (5-7.5) × 10 9 cm −3 at various discharge currents already at z = 4. At z = 3, n i is approximately three times smaller. The condition Z p n p < n i necessary for the confinement of negatively charged particles is therefore quite attainable in the plasma-dust system under consideration. Note once more in conclusion that plasma parameter estimates considered in this section are used to analyse a qualitative picture of the influence of particles on ionization processes under the conditions of a dense dust cloud.

Conclusion
This work describes the results of experimental studies of the dynamics of bronze macroparticles in a dc-discharge plasma under microgravitation conditions. The temperatures, concentrations, pair correlation functions, self-diffusion coefficients, and charges of macroparticles were measured in various discharge currents. An analysis of the measurement results showed that the observed structures of macroparticles corresponded to a strongly nonideal dust liquid 108.11 ( * ∼ 60-75), and their dynamics was in close agreement with the results of simulating Yukawa systems characterized by weak screening (κ < 1).
Experimental estimates of macroparticle charges corresponded to surface potentials of the order of 30-40 V, which far exceeded values predicted by the OML theory. This discrepancy could be related to both a decrease in the effective flow of ions onto particles whose radii were larger than the free path of ions and an increase in the temperature of electrons in the dust cloud because of an influence of macroparticles on equilibrium ionization in dc-discharge.
Note once more in conclusion that experiments on studying interaction potentials and charging processes for large-size 100 µm particles in a dust plasma cannot be performed under earth gravitation conditions.