3. Results and discussions

In this section, we describe the consequences of extensive MD simulations methodology work, carried out to explore the current correlation functions (compressional and share waves) of 3D Yukawa liquid via the EMD simulation technique. CL (k, t) (Eq. 7) and CT (k, t) (Eq. 8) is simulated at an extensive combinational range of parameters (Γ, κ, N and k). The CL(k, t) and CT(k, t) which are normalized by plasma frequency (ωp) has been extensively used for prior studies of SCDPs but while here we are investigating its correspondence with time (t). The information waves spectra for nuclear fusion device conditions is generated from simulation goes, that prediction which is true for frequency spectra, current correlation function [CL(k, t), CT(k, t)] simulation are executed for higher screening strength of spherical charged dust particles (κ = 4.5 and 5.5) and Coulomb coupling parameters (inverse of plasma temperature) parallel closely same experimental plasma state (κ, Γ). This was executed to facilitate comparison with presented simulation results and available data of recent and earlier.

In this section, we present our EMD simulation results and their discussion of wave spectra from the current correlation function in the longitudinal and transverse wave's modes. The specific attention in this chapter is given to CL(k, t) and CT(k, t) for a different combination of plasma parameters which are investigate the behavior of transverse and longitudinal waves in 3D SCDPs. Explanation qualitatively features of the longitudinal (compressional or sound) waves in 3D complex (dusty) plasma shown in Figures 2 and 3. Here our EMD outcomes we compute the CL(k, t) for κ = 4.5 and 5.5 for a number of particles (N = 500) and in the direction of wave vector numbers (k = 0, 1, 2 and 3). We determined properties of longitudinal waves in SCDPs at a different combination of plasma parameters (κ, Γ), the results have plotted the magnitude of CL(k, t) against simulation time (t). In our EMD simulations result, the effect about plasma temperature is observed on the magnitude, wavelength, frequency, and damping phenomena of waves in SCDPs. Figure 2 consists four panels which covering from non-ideal to the liquid and then liquefy state of dusty plasma. The panel (a) of both Figures 2 and 3 represent the results of longitudinal wave spectra in the non-ideal state of dusty plasma at κ = 4.5, 5.5 respectively. It is observed from first panel of these two figures that collective modes of wave spectra are highly damped due to high temperature of dust particles confirmed good agreement with earlier published worked by Nunomura due to

Wave Spectra in Dusty Plasmas of Nuclear Fusion Devices DOI: http://dx.doi.org/10.5772/intechopen.91371

Figure 2. EMD simulations results of wave spectra of the longitudinal mode against the simulations time (t) for κ = 4.5 covering from non-ideal to liquid states ((a) Γ = 1, (b) Γ = 5, (c) Γ = 20 (d) Γ = 100) of 3D SCDPs and N = 500 for higher wave number (k = 0, 1, 2 and 3).

collisions between particles [30] and Shahzad et al., for low screening strength [2]. The modes of these waves in amplitudes of longitudinal waves increased at higher wavenumber (k = 3) and also at lower wavenumber has low peak amplitude mode clearly seems from results plotted in Figures 2 and 3. The damping of waves at a higher temperature would attribute this to viscous/collision and Landau damping. The effects of Γ on the propagation of waves in SCDPs are observed from four panels of Figure 2. The frequency modes are increases and amplitude decreases of CL(k, t) with increasing Γ. With increasing Γ the thermal effect decreases in the magnitude and the correlation effect clearly seems. Figures 2 and 3 show the wave's spectra of longitudinal mode at different values of coupling which covering the non-ideal phase dusty plasma and also liquefy state. It is observed that the damping effect in wave's mode decrease with decreasing the plasma temperature. Here higher damping at Γ = 1 and at Γ = 5 comparatively low damped and then oscillate very at a low magnitude for Γ = 5. If we further increase the coupling values the damping decrease and longitudinal waves propagate in form of sinusoidal. At Γ = 20 and 100 waves in longitudinal modes properly propagate and with the passage of time, the magnitude of waves decreases we can observe Figures 2 and 3 (d) at Γ = 100 in the liquid liquefy phase.

There is a slight effect of screening strength (κ) on longitudinal wave's mode in plasma with respect to damping and propagation phenomena. The frequency and amplitude of waves in SCDPs are high at lower values of κ when we increase screening strength at the same N, k and Г amplitude and wavelength are gradual decreases with respect of κ. The magnitude of CL(k, t) 0.2332, 0.0379, 0.0057 and

#### Figure 3.

EMD simulations results of wave spectra of the longitudinal mode against the simulations time (t) for κ = 5.5 covering from non-ideal to liquid states ((a) Γ = 1, (b) Γ = 5, (c) Γ = 20 (d) Γ = 100) of 3D SCDPs and N = 500 for higher wave number (k = 0, 1, 2 and 3).

0.0014 for Γ = 1, 5, 20 and 100 respectively at κ = 4.5 and k = 0. When we increase value of screening κ = 4.5 to = 5.5 then the magnitude of CL(k, t) at k = 0 increase 0.2244, 0.0508, 0.0105 and 0.0016. In this chapter, we have simulated at an N = 500 for the same combination of parameters (N, κ, Г).

In this part, we have investigate CT(k, t) through EMD simulations for 3D SCDPs coulomb system in the classical ensemble (NVT) for N = 500 particles. The charged particles are interacting with each other via Yukawa pair potential. We have analyzed the behavior of the wave's spectra in the transverse (shear wave) direction in SCDPs, using Eq. (8), by EMD simulations technique. It is found that our results is calculated for CT(k, t) are in a good agreement using the EMD algorithm over an extensive range of plasma parameters and selecting a number of particles. We have ensured that the presented results of CT(k, t) are in satisfactory agreement with prior known simulation, theoretical and numerical results. In our MD simulation result, the effect of plasma temperature is observed on amplitude, wavelength, frequency, and propagation of waves in SCDPs.

Figures 4 and 5 demonstrate the Simulation results which are obtained for CT(k, t) of SCDPs plasma using EMD simulations at k = 0, 1, 2 and 3, Г = 1, 5, 20 and 50 for κ = 4.5 and 5.5. The given simulation results of CT(k, t) spectra are compared with increasing and decreasing sequences of κ, Г, and k. It is observed that the magnitude of transverse current waves has increases behavior with increasing wave Wave Spectra in Dusty Plasmas of Nuclear Fusion Devices DOI: http://dx.doi.org/10.5772/intechopen.91371

#### Figure 4.

EMD simulations results of wave spectra of the transverse mode against the simulations time (t) for κ = 4.5 covering from non-ideal to liquid states ((a) Γ = 1, (b) Γ = 5, (c) Γ = 20 (d) Γ = 100) of 3D SCDPs and N = 500 for higher wave number (k = 0, 1, 2 and 3).

numbers. We have observed from further EMD simulations calculation that magnitudes of this wave have decreasing behavior for a high number of particles. The absence of any structure of strongly coupled plasma in the liquid phase the shear waves are not propagated through it. Wave's in SCDPs are highly damped at high plasma temperature or low values of coulomb coupling. In Figure 4 plotted four penal of shear waves which covering from non-ideal to liquid state of dusty plasma.

The panel (a) of both Figures 4 and 5 represent the results of CT(k, t) spectra in the non-ideal state of dusty plasma. It is observed from these figures that collective modes of wave spectra are highly damped at higher plasma temperature and damping of transverse waves reduce with corresponding to decrease the plasma temperature. In the non-ideal state of dusty plasma, the transverse current wave's mode is highly damped as compare to longitudinal modes especially at higher wave's number in our case. CT(k, t) spectra having increasing behavior in the magnitude for wave vector. The damping of waves at a higher temperature would attribute this to viscous/ collision and Landau damping that confirmed from earlier published work of [2, 30]. The effects of Г on the propagation of waves in SCDPs are observed from four panels of Figure 2. The frequency modes are increases and amplitude decreases of CL(k, t) with increasing Г. With increasing Γ the thermal effect decreases in the magnitude and the correlation effect clearly seems. Values of CT(k, t) at different parameters as for k = 0(1), CT = 0.2558(0.9016), 0.0454(0.1749), 0.0141(0.0449), 0.0017(0.0071), and for the case k = 2(3) as CT = 2.3453(3.9837), 0.4218(0.7214), 0.0810(0.1260), 0.0144(0.0229), at Г = 1, 5, 20, 100 respectively for κ = 4.5. With the comparison of Figures 4 and 5, we have observed that there is a slight difference

#### Figure 5.

EMD simulations results of wave spectra of the transverse mode against the simulations time (t) for κ = 5.5 covering from non-ideal to liquid states ((a) Γ = 1, (b) Γ = 5, (c) Γ = 20 (d) Γ = 100) of 3D SCDPs and N = 500 for higher wave number (k = 0, 1, 2 and 3).

occurs when we increase the screening of dust charged particles. The propagation and damping behavior of waves in transverse direction remain nearly same with increasing screening. For particular wave's number (k), magnitudes of transverse waves have increasing behavior with increasing screening strength.
