**1.3. Dusty plasma in atmosphere and laboratory**

There are many systems in the atmosphere where dust particles are established. Spaces between the stars are filled with a large amount of dust and gases. Dust particles in the interstellar region are metallic i.e. graphite, magnetite, and amorphous of carbon, dielectric material i.e. silicates and ices, etc. Comets, planetary space, planetary ring, and earth atmosphere are the region of our solar system. Gossamer ring, halo ring, and main rig are the three systems of Jupiter's ring. In the Saturn rings systems are mostly ices and its size vary from meter to micron. A Uranian rings system has major rings such as 6, 5, 4, 3, α, β, η, γ. In Neptune's ring systems appear in curios twisted materials and structure is dirty ice and composition such as iron, nickel, sulfur, earth atmosphere dusty ice, etc. [9]. A simple device for producing dusty plasmas is a dusty plasma device which is a single-ended *Q*-machine modified to allow the dispersal of dust grains. Dusty plasmas are produced by suspending micron-sized dust particles in a stratum of a dc neon glow discharge. Dusty plasma has been for the first time confined in cylindrical symmetric radio frequency plasma (RF) system also in the semiconductor industry.

### **1.4. Role of dust particles and applications**

Dust particles have charge and chemically active species, it is formed and growth in dusty plasma devices. Sometimes in the form of a mixture of gases such as SiH4, silane, oxygen, O2 , and Ar, etc. Secondly dust particles are formed in devices when atoms and molecules are spurted from walls and electrodes into the plasma by electron and ion bombardment. Moreover, the growth of dust particles in the plasma is coagulation, nucleation and surface growth. Thermal fluctuations and Coulomb interaction play the significant role for determination structure of SCCDPs. When the values of Г (>1) increase then system organized from nonideal gases phase to ordered condensed phase. Dust particles are suspended in the gaseous plasma phase with few electrons temperature and charge up to 104 ordered. Interestingly, the dust clouds in a dusty plasma formed into the structural form even at room temperature. Dust particle has large mass as compared to ion and an electron which gives the results slowly downtime scale and it can easily observed the macroscopic structure and its dynamical behavior directly study in space and real time [10]. Dusty plasma used for nanocrystalline silicon particles grow in the silane plasmas used to increase efficiency and lifetime of the silicon solar cells. It is used for thin film coating applied in plasmaenhanced chemical vapor deposition (PECVD) for the improvement of material surface properties. Carbon-based nanostructure growth in the hydrocarbon plasmas or fluorocarbons used to produce thin carbon films. It is used to improve material properties such as chemical inertness, high hardness and wear resistance. Self-lubrication coating and wear resistance using different compound as a dust particle (MoS<sup>2</sup> ). Ar/CH4 plasma used for making the nanocrystalline diamond films fabricated which as exceptional properties such as chemical inertness, high hardness, and extreme smoothness which used to improve the performance of cutting tools. Diamond whiskers fabricated by the etching in RF plasmas for the enhancement of electron field emission. The reactive ion etching (RIE) process are used to a precise efficiently sharpen micro-tips of diamond [11]. Complex (dusty) plasmas (CDPs) have various advantages in a different industries, technologies, and energy sector due to the existence of dust particles. CDPs are stable under the laboratory condition. The CDPs can also be used for the diagnostic purpose because dust particles are trapped at the room temperature and keep their desire dynamical state for hours. Dusty plasma frequency in the range several hertz and easily observed through CCD cameras. It is produced in the gas discharge tube with natural gas pressure range that varies from 1 to 100 pa, which is subject to moderate damping [8]. Moreover, magnetized dustyplasma device used to produce a number of the verity of magnetic fields configuration with the help of four independent superconducting coils [12]. Magnetized glow discharge dusty plasma device, RF plasma device, ISS experiment and DC glow discharge devices used for different applications in industries and diagnostic purpose of dusty plasma. Dust particles are found in a tokamak (fusion plasma) and dusty plasmas depositions techniques devices [11, 13].

matter physics, the pair correlation function usually cannot be determined directly. Rather, the structure factor is determined by scattering of x-rays or neutrons. In dusty plasmas, we are able to measure the pair correlation function directly and to calculate the structure factor in order to compare with condensed matter experiments. The *S*(*k*,*ω*) is just the Fourier transform of the pair correlation function. Fluctuation of the dynamical density of dusty plasma generates current correlation spectra such as longitudinal and transverse currents [17]. Dynamic ion structure factor of warm dense matter and dense plasma consist of the complete information of ions in strongly interacting systems and also influenced by the electrons property. It is closely associated with density fluctuation, thus determines transport properties and many relaxations such as electrons ion temperature equilibrium and stopping power and also the equation of state. It is also used for diagnostics of the extreme states of matter like a warm dense matter of x-ray Thomson scattering [18]. Dynamical scattering function is given through times correlation function, fluctuated density of liquid argon and light

In this section, we have implemented molecular dynamic (MD) simulation code with Ewald summation for forces and energies which makes it possible to account the long-range Coulomb interparticle interactions. We trace the motion of single charge species and integrated through leapfrog method and assume that the presence of neutralizing homogenous background. In this plasma environment, random fluctuating forces and friction forces are acting on a charged particle in addition to which forces initiating from the interaction of charged particle. Length

tion for the beginning of simulation [15, 20]. Fluctuation of microscopic density is observed for different plasma parameters approaching near the equilibrium state [21]. The presented study includes the solution of the equation of motion of a system and particle interacts with each other through Yukawa potential. Provided that an accurate potential can be established for the system of attention under study and equilibrium MD (EMD) can be used irrespective of the phase condition and thermodynamic of the system involved. Yukawa potential is most commonly used potential (screened Coulomb) for SCCDPs including many physical systems such as physics of chemical and polymer, medicine and biology systems, astrophysics, environmental, etc. Major advantage for using this potential is that it reduces the calculation time compared other potentials [22]. The interaction potential energy of a charged particle in

> \_\_\_\_ 4 *<sup>o</sup> e* \_\_\_ −*r <sup>λ</sup>* \_\_\_*<sup>D</sup>*

is permittivity of free space. The scaling (dimensionless) parameters, which fully

Here *Q* is the charge on dust particle, *r* is the distance between interacting particles, λD is Debye screening length that accounts for the screening of interaction of other plasma spe-

characterized the system, one is known as Coulomb coupling parameter [23],

<sup>3</sup> ) 1/3 and particles have a random spatial configura-

Numerical Approach to Dynamical Structure Factor of Dusty Plasmas

http://dx.doi.org/10.5772/intechopen.78334

135

<sup>|</sup>**r**<sup>|</sup> (1)

\_\_\_\_ 4*N*

scattering function [19].

Yukawa liquid is given

cies and ε<sup>o</sup>

of simulation cubic box is defined as (

<sup>ϕ</sup>(**r**) <sup>=</sup> *<sup>Q</sup>*<sup>2</sup>

**2. Numerical model and simulation techniques**

#### **1.5. Dynamical structure factor**

The dynamical structure factor *S*(*k*,ω)] gives the information about static and dynamic properties of the fluid in simple and complex systems. In hydrodynamic condition, the *S*(*k,*ω) provides experimental calculable quantities such as the thermal diffusivity, adiabatic sound velocity and the ratio of specific heats [8]. These properties of the fluids are measured through light scattering, x-ray and inelastic neutron experiments on a substance such as dense plasmas, liquids, and glasses. Sound waves are generated through *S*(*k,*ω) in strongly coupled CDPs (SCCDPs) and density is more strongly damped at liquid phase [14, 15]. The SCCDP is many body dynamical systems that show different collective excitations and their properties investigated through numerical simulation and theoretical approaches [16]. In condensed matter physics, the pair correlation function usually cannot be determined directly. Rather, the structure factor is determined by scattering of x-rays or neutrons. In dusty plasmas, we are able to measure the pair correlation function directly and to calculate the structure factor in order to compare with condensed matter experiments. The *S*(*k*,*ω*) is just the Fourier transform of the pair correlation function. Fluctuation of the dynamical density of dusty plasma generates current correlation spectra such as longitudinal and transverse currents [17]. Dynamic ion structure factor of warm dense matter and dense plasma consist of the complete information of ions in strongly interacting systems and also influenced by the electrons property. It is closely associated with density fluctuation, thus determines transport properties and many relaxations such as electrons ion temperature equilibrium and stopping power and also the equation of state. It is also used for diagnostics of the extreme states of matter like a warm dense matter of x-ray Thomson scattering [18]. Dynamical scattering function is given through times correlation function, fluctuated density of liquid argon and light scattering function [19].
