Influences of Temperature and Average Interparticle Distance on the Properties

7/27/2019 Influences of Temperature and Average Interparticle Distance on the Properties

http://slidepdf.com/reader/full/influences-of-temperature-and-average-interparticle-distance-on-the-properties 1/4

Commun. Theor. Phys. (Beijing, China) 43 (2005) pp. 919–922c International Academic Publishers Vol. 43, No. 5, May 15, 2005

Influences of Temperature and Average Interparticle Distance on the Properties of

Two-Dimensional Dusty Plasma∗

LIU Song-Fen,1,† WANG Xin,1 LIU Yu-Bin,1 HU Bei-Lai,1 WANG Long,2 LIU Yan-Hong,2 and HUANG Feng2

1

Department of Physics, Nankai University, Tianjin 300071, China2Institute of Physics, the Chinese Academy of Sciences, Beijing 100080, China

(Received July 8, 2004; Revised September 10, 2004)

Abstract The structure and single-particle motion of a two-dimensional dusty plasma have been investigated. Pair

correlation function, mean square displacement, velocity autocorrelation function, and the corresponding spectrum func-

tion have been computed by molecular dynamical simulation. The results show that the coagulation of a two-dimensional

dusty plasma system is strongly affected by particle density and temperature, which are discussed in details.

PACS numbers: 52.27.-h, 52.27.Lw, 52.65.YyKey words: dusty plasma, molecular dynamics simulation, structure, single particle motion

1 Introduction

There is a great interest in the study of dusty plasmain the fields of astrophysics, solids, microelectronics, andbasic plasma physics both in experimental and theoreticalwork.[1,2] The research on dusty plasma is developed in as-trophysics, where people need to deal with a dusty plasmain space, such as planetary nebula and planetary magneticstratum and etc. With the development of industrial tech-nology, it is found that the existence of dusty plasma re-sults in serious problems of reducing the operating capa-bility of apparatus, even leading to the uselessness of theapparatus during the microelectronics manufacturing. Re-cently, the researches focus on the structure, phase transi-

tion, single dusty particle’s movement character, and wavedispersion of dusty plasma, which would provide the bet-ter understanding of behavior of dusty plasma.

Dusty plasma is a complex and strongly coupled sys-tem, being composed of a great deal of charged parti-cles, which are usually charged negatively as a resultof electrons and ions’ collecting motion. Many experi-ments have shown that dusty plasma could form a liquid-like, solid-like or gas-like structure in different laboratoryconditions.[3,4] And a two-dimensional dusty plasma lat-tice in an rf discharge was observed.[5] At the same time,molecular dynamical (MD) simulation turns out to be an-other important tool for investigating dusty plasma, which

could foretell some results of experiments.[6−9]

In this pa-per, based on the earlier work, we study the structuralcharacter and single-particle motion in a two-dimensionaldusty plasma at different temperatures as well as differentparticle densities.

2 Physical Model and Molecular DynamicalSimulation

We start our considerations with one of the most clas-sical dusty plasma systems, which has the identical par-ticles with the point charge Q and the mass M , inter-

acting exclusively through the Yukawa potential energyφ(r) = (Q2/4π0r)exp(−r/λD), and immersed in a neu-tral background, where r is the distance between two par-ticles, and λD denotes the Debye length of the backgroundplasma. There are three important parameters in this sys-tem: a = 1/

√ ndusty, κ = a/λD, Γ = Q2/(4π0akBT ),

where ndusty is the density of dusty plasma, a is the meaninterparticle distance, κ is the ratio of the mean interpar-ticle distance a to the Debye length λD, and the couplingparameter Γ is the ratio of the system’s Coulomb inter-action energy to their kinetic energies. T is the systemtemperature.

In this paper, we do some simulation in a 2D canonical

system. The constant temperature MD-Verlet arithmeticis used. We use the Nose–Hoover thermostat scheme[10]

to keep a constant temperature of the system. We put256 particles in a 2D square box with periodic boundaryconditions to study the structural properties and single-particle motion of an infinite system. In the calcula-tion, we defined the mean interparticle distance a as thelength unit; φ0 = Q2/4π0a as the unit of energy, t0 = Ma2/φ0 =

4π0Ma3/Q2 as time unit. We performed

0.03 ω−1pd as the time step, where ωpd =

Q2/0Ma3 is the

dusty plasma frequency, the initial run lasts 3 × 104 stepsfor equilibration, and the subsequent 3

×104 time steps

are measured by calculating the pair correlation function(PCF) g(r), the mean square displacement (MSD) and thevelocity autocorrelation function (VACF). These functionscould characterize the structural and single particle mo-tion properties of a 2D dusty plasma. We suppose κ = 1following with the experimental condition. Each charac-teristic function was calculated at different coupling pa-rameter and mean interparticle distances.

The pair correlation function g(r), the mean squaredisplacement r2(t), the velocity autocorrelation function

∗The project supported by National Natural Science Foundation of China under Grant Nos. 10175036 and 10205025†E-mail: [email protected]



920 LIU Song-Fen, WANG Xin, LIU Yu-Bin, et al . Vol. 43

Z (t) and its corresponding spectrum function are defined

by

g(r) = S

N

N (r,∆)

2πr∆ , (1)

r2(t)

= 1

N

N

i=1

(ri(t)−ri(0))2 , (2)

Z (t) = N

i=1 vi(t) · vi(0)N

i=1 vi(0) · vi(0), (3)

Z (ω) = 1

2π

∞−∞

Z (t) e−iωt dt , (4)

respectively, where N is the number of dust particles inthe simulation box, S is the area of the simulated region,N (r,∆) is the number of particles located between r−∆/2and r + ∆/2 (∆ = 0.1a), · · · · denotes the thermal av-erage, and ri(t) and vi(t) are the position and velocity of the i-th particle at time t, respectively.

3 Numerical Results and Discussions

The results of Liu[8,9] showed the structural and dy-namical properties in a 2D dusty plasma affected only bytemperature. In our simulation, we changed the interpar-ticle distance in order to represent the system propertiesfor different classical coupling parameters.

Fig. 1 (a) The pair correlation function g(r) varies withdifferent values of coupling parameter Γ and average in-terparticle distance a. (b) Its local amplification.

The static structural order of a condensed matter sys-tem is usually investigated by pair correlation function.Figure 1 shows g(r) varying with r/a at different valuesof coupling parameter Γ and the average interparticle dis-tance a. One can see from Fig. 1 that oscillation in peaksof g(r) is increasing with decreasing a for the same Γ, thevertex of the first peak increases and the peak width de-creases, which indicates that this system appears to have

a structural order. At certain a, the first peak splits. Forexample, at Γ = 50, the first peak splits at a = 0.5; atΓ = 100, 500, the split of the first peak enlarges withdecreasing a and at Γ = 500, the first peak splits intothree parts at a = 0.5. By integrating g(r), we got thateach particle has 6 nearest neighbors at all parameter. AtΓ = 25, there are 6 nearest neighbors, 12 next nearestneighbors and 18 next-next neighbors for any test parti-cle. This structure is similar to a liquid. At Γ = 500 anda = 0.577, there are 6-6-6-12-6-18 neighbors for any testparticle. This structure is close to a solid. All of theseresults show that the structural order of the 2D dustyplasma enhances with decreasing a for the same Γ.



No. 5 Influences of Temperature and Average Interparticle Distance on the Properties of · · · 921

Fig. 2 The mean square displacement varies with cou-pling parameter and average interparticle distance.

Studying the particles motion is the simplest method

to distinguishing a solid from a liquid. The mean square

displacement (MSD) of particles tends to a constant fora solid, and amplifies with the time of motion for a liq-

uid. Figure 2 shows the MSD varying with t/ω−1pd at dif-

ferent values of Γ and a. It is clear from Fig. 2 that the

MSD gradually increases or tends to be a constant rapidly

with decreasing the average interparticle distance a at the

same Γ. For example, at the condition of the Γ = 62.5,

r2(t) ∝ t1.0 at a = 1.0, r2(t) ∝ t0.417 at a = 0.577

and r2(t) ∝ t0.404 at a = 0.408 and t/ω−1pd ≤ 16.16,

corresponding to that of the diffusive and subdiffusive

regime,[11] which means that the dynamical process of

particles confined to their equilibrium positions gets more

quickly with increasing the number density.



922 LIU Song-Fen, WANG Xin, LIU Yu-Bin, et al . Vol. 43

Fig. 3 The velocity autocorrelation function with theircorresponding spectrum functions varies with differentcoupling parameter and average interparticle distance.

The velocity autocorrelation function (VACF) is thesimplest variable characterizing the dynamical informa-tion in the many-body system. Figure 3 shows the VACFand the corresponding spectrum function varying witht/ω−1

pd and ω/ωpd, respectively. From Fig. 3, one can see

that the oscillation of VACF strengthens with decreasinga for the same Γ. At the same time the oscillatory periodof Z (t) becomes shorter in time domain, accordingly, theoscillatory frequency becomes larger in frequency domain.At Γ = 100, the peak of low frequency oscillation appears,indicating a new oscillatory mode, and the frequency be-

comes higher at smaller a. Generally, at about Γ = 100,the 2D dusty plasma begins to coagulate, hence it is possi-ble to excite a transverse wave in a solid. So we can knowthat the system tends to a solid with increasing Γ anddecreasing a. At Γ = 10 no new oscillatory mode comesinto being with increasing interparticle distance. There-fore, we may conclude that the kinetic mode of a 2D dustyplasma system is only related with the temperature.

4 Conclusion

In summary, we have calculated the pair correlation,the mean square displacement and the velocity autocorre-lation function with its corresponding spectrum function

of a two-dimensional dusty plasma system by moleculardynamics simulation. Our results show that the dustyplasma could coagulate rapidly with increasing couplingparameter and decreasing average interparticle distance.Therefore, both the temperature and the number densityof the dusty plasm are important characteristic param-eters which affect the properties of the two-dimensionaldusty plasma system.

References

[1] D. Sansibiv and J. Goree, Phys. Rev. E59 (1999) 1047.[2] D.Y. Liu, D.Z. Wang, and J.Y. Liu, Acta. Phys. Sin. 49

(2000) 1094 (in Chinese).

[3] H. Thomas et al., Phys. Rev. Lett. 73 (1994) 652.

[4] A. Melzer, A. Homann, and A. Piel, Phys. Rev. E53

(1996) 2757.

[5] J.J. Hua, et al., Chin. Phys. Lett. 20 (2003) 155.

[6] P. Schmidt, et al., Phys. Rev. E56 (1997) 7310.

[7] G. Kalman and K.I. Golden, Phys. Rev. A41 (1990) 5516.

[8] B. Liu, et al., Chin. Phys. 12 (2003) 765.

[9] Y.H. Liu, et al., J. Phys. A: Math. Gen. 35 (2002) 9535.

[10] W.G. Hoover, Phys. Rev. A31 (1985) 1695.

[11] M.O. Robbins, K. Kremer, and G.S. Grest, J. Chem.Phys. 88 (1988) 3286.

Documents

Influences of Temperature and Average Interparticle Distance on the Properties