Estimation Of Dusty Plasma Parameters From Measurements Of Characteristic Frequency Of Macroparticle Oscillation

X.G. Adamovich1, O.S. Vaulina2, K.B. Statsenko1,
Yu. Khrustalev1, I.A. Shakhova2, A.V. Gavrikov2, I.E. Dranzhevsky2
1Moscow Institute of Physics and Technology, 141700, Institutsky per., 9, Dolgoprudniy, Moscow region, Russia
2Institute for High Energy Densities, RAS, Izhorskaya 13/19, Moscow 127412, Russia
Abstract. A new method to obtain the characteristic frequency of macroparticle oscillation in dusty plasma is presented.
In this method we use experimentally received data (the mean-square displacement of dusty particles in the quasi- 2D
systems). During the experiment the following parameters were varied: the effective coupling parameter, the pressure of
the buffer gas, the concentration of grains. With the help of obtained values of the characteristic frequency the charge of
grains and electron temperature are estimated. The results show that the screening length in the interparticle interaction
potential is close to the electron Debye length.
Keywords: Dusty Plasma, Numerical Simulation, Experiment.
PACS: 52.25. Ub, 52.25. Zb, 82.70. Db
INTRODUCTION
The dusty plasma represents a good experimental model for studying strongly coupled systems (liquid or solid),
as the grains of dust are visible to the naked eye, and their motion can be recorded to a video camera. Laboratory
dusty plasma is an ionized gas containing small grains of solid matter (dust) that becomes electrically charged. Most
investigations of dusty plasma use the Yukawa (screened Coulomb) potential of interaction U = (eZр)2
exp(-r/λ)/r,
where e is the electron charge, eZр – the charge of one grain. The properties of such systems with a strong coupling are of
interest for the different fields of science (e.g. for molecular biology and polymer chemistry) [1,2].
Two dimensionless parameters responsible for the mass transfer and phase state in two dimensional (2d-) dissipative
systems were found [3-5] for κ = lp/λ < 6 where lp = n-1/3 is the mean inter-particle distance, and n is the particles’
concentration. These parameters are: the “screened” coupling parameter
Г*= 1.5 (Zрe)2 (1+κ+ κ2 /2) exp(-κ)/Tрlр, (1)
and the scaling factor ξ = vfr
–1 eZр [2 (1+κ+ κ2 /2) exp(-κ)/(πmplр
3)]1/2, associated with the characteristic frequency vfr of the
particle friction; here Tр is the temperature of particles with the mass mp. When Γ* reaches the value of Γ*
m ~ 106, the
two-dimensional system crystallizes into a structure, which has a hexagonal lattice.
In earlier works [6] the experimental and numerical analysis of mass transfer processes at the small observation
time was performed. In diffusion measurements the ratio of mean square displacement <x2> to the observation time
(mass-transfer evolution function D(t)= <x2>/(2t)) was calculated. For interacting particles at the small observation
times this D(t)- function reaches its maximum and then it tends to the constant value that is the diffusion coefficient.
Numerical simulations have shown that the behavior of D(t)- function in the liquid dust systems for the time less
than some critical value is similar to the D(t)- function for particles in solid. This function may be obtained from the
motion equation for one-dimensional harmonic oscillator with some characteristic frequency ω
and different Γ*: 2 – 27; 3 – 56; and with ξ= 0.93 and different Γ*: 4 – 12; 5 – 27; 6 – 56. The curves 6 and 7 are the
approximations of presented simulations by Eq. (9) with ω
с =ωh.
In this work we estimate ω
с based on experimental data and the above-stated approach. Then, with the help of the
obtained values of ω
с, we estimate such parameters of dusty plasma as the charge of grains and electron temperature.
DETERMINATION OF THE TYPICAL FREQUENCY
Based on the above-stated approach and the experimentally received information about the mean-square
displacement of the grains (about D(t)- function), we can find the characteristic frequency ω
с. The main problem is
that frame frequency of the usual video camera is less than ω
с, therefore it’s impossible to obtain necessary
information about the motion of grains. However, we avoid this difficulty by using the high-frequency highresolution
video camera.
The following parameters were varied during the experiment: the effective coupling parameter Г* (5-200),
pressure of the buffer gas (P ~ 5-30 Pa), the concentration of grains (100-250 grains/cm2). The radius of the grains
was rp = 6.37 mkm, density of the material – ρ = 1.5 g/cm3, the buffer gas – argon.
We should notice one of the advantages of the proposed method of estimating ω
с. It often happens that during the
experiment it is hard to measure the friction coefficient vfr. As is well known, the coefficient for the dust friction in
the free-molecular approach: vfr ~ P/(ρ rp ). The inaccuracy in finding rp and ρ may be caused by the imprecision
of production of grains. Also it is often difficult in experiment to keep the pressure at the same level. In our method
vfr is corrected automatically.
Figure 2 (a,b) shows the evolution of mass-transfer for theoretically and experimentally gained data, with Г*~ 40
(liquid-like dusty system) and Г* >150 (dusty crystal). Here we can clearly see that the solution of Eq. (2) is valid
for the liquids only on the small observation times, and in case of crystalline systems we can use this solution at all
time scales. We can write the effective coupling parameter Г* as [6]

The value of Г* is traditionally restored from the pair correlation functions of macroparticles. But this method has
essential disadvantages. First of all, during the process of filming of the grains some particles from the neighbouring
layer can come to a focus of video camera. As a result, the obtained from a correlation function mean interparticle
distance is undervalued, what influences the determination of Г*.
Figure 3 shows the comparison of the values of Г*, determined from the correlation functions, with those
obtained by the proposed method.с:

With information on plasma concentration (ne(i)), we can write the value of λ and the dust charge eZp (from the
measurements of ω
с) as function of Te, assuming Тi ~0.03 eV. Then we can find the electron’s temperature from a
balance equation Ii=Ie for both considered cases. The calculations were conducted for different values of the
coupling parameter and ion/electron concentrations (~ 108-1010 cm-3). The obtained results show, that if λ is
considered to be close to λ
i, the electron temperature must be above 100 eV; but the electron temperature in the nearelectrode
area of RF-discharge cannot exceed 4-7 eV. For the case of λ ~ λ
e we can obtain Te ~ 2-3 eV for both
approaches foe ion flow that are in good agreement with the experimental data on the electron temperature in RFdischarge.
CONCLUSION
We present a new method of estimation of the electron temperature and the charge of the grains in a dusty plasma
of RF-discharge. In this method we use experimentally received data (the mean-square displacement of dusty
particles in the quasi- 2D systems). During the experiment the following parameters were varied: the effective
coupling parameter, the pressure of the buffer gas, the concentration of grains. With the help of obtained values of
the characteristic frequency we estimate the electron temperature in RF-discharge. The results show that the
screening length in the interparticle interaction potential should be close to the electron Debye length, that is in
agreement with the earlier works [7].
ACKNOWLEDGMENTS
This work was partially supported by the Russian Foundation for Fundamental Research (No. 04-02-16362),
CRDF (No. RU-P2-2593-MO-04), the Program of the Presidium of RAS.
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