Abstract
Wave’s spectra are investigated through an equilibrium molecular dynamic (EMD) simulation of three-dimensional (3D) strongly-coupled complex-dusty plasmas (SCCDPs). In this chapter, we have analyzed the correlation functions over a wide range of plasma parameters of Γ (≡1, 100) and of κ (≡4.5, 5.5) along with a higher wave’s numbers of k (≡1, 4). In EMD simulations, we have examined the propagation modes of wave in the longitudinal CL(k, t) and transverse CT(k, t) current direction at higher screening (κ). We have also analyzed the wave’s spectra in different regimes of plasma states of SCCDPs. A new simulation shows that the longitudinal (CL) and transverse (CT) waves in SCCDPs are damped for low values of Γ. However, these damping affects decrease comparatively with an increasing Γ. Outcomes show that amplitude and frequency modes of the CL and CT depend on κ, Γ, k and probably on a number of particles (N). The results obtained from EMD are in reasonable agreement with earlier known theoretical and experimental data. It has been shown that the present EMD method is the best tool for computing CL and CT in the SCCDPs over a suitable range of plasma parameters.
Keywords
- wave properties
- plasma parameters
- longitudinal current correlation
- transverse current correlation
- strongly coupled dusty plasmas
- equilibrium molecular dynamic
1. Introduction
A partially or fully ionized gas containing neutral atoms, electrons, ions and with the addition of dust particles is known as dusty plasma (DPs). This additional component (dust particle) increases the complexity in the behavior of the system, and thus refers to this system as “dusty” or complex plasma [1]. Nowadays the term “complex plasma” is commonly used in literature to differentiate the dusty plasma. Due to embedded dust particles in the plasma, these dust particles create changes in the charge composition. The new physical processes were introduced in the system such as the recombination of plasma on the particle surface and effects associated with the degeneracy, fluctuations of particle charges which also change the energy and transport phenomena. That’s the way the DPs became a new type of non-Hamiltonian systems. The presence of dust particles in the complex plasma is vital for the collective processes. These micro size dust particles create very low-frequency wave mode, which represents charge particle oscillations against the quasi-equilibrium background of ions and electrons. Generally, a dynamical time scale related to the dust component is in the range of 10–100 Hz. Recently the dusty plasma becomes an interesting field for researchers, technologist and scientists [2, 3]. The initial challenge of fusion in nuclear devices is to confine ionized isotopes of hydrogen atom known as plasma, increase the plasma pressure to initiate and sustain the fusion reaction [4].
Dusty plasma is classified on the basis of density, temperature, potential, and thermal energy. For classification of dusty plasma first, we define Coulomb coupling parameters. Coulomb coupling defines as “the ratio of average potential energy to the average thermal energy of neighboring charged particles” and mathematically written as
1.1 Weakly coupled dusty plasmas (WCDPs)
Weakly coupled dusty plasmas have higher average thermal energy than average potential energy due to neighboring charged particles. WCDPs have a high temperature, low density and value of Coulomb coupling parameter less than 1
1.2 Strongly coupled complex dusty plasmas (SCCDPs)
In strongly coupled dusty plasma (SCDP), the average potential energy of neighboring charged particles is dominated on the average thermal energy of the same charged particles. This type of dusty plasma has high charged particles density and low temperature. The SCDPs speedily become emerging fields from last three decades. Due to the presence of dust particles in the atmosphere, the dusty plasma becomes a very significant research field of astrophysical plasma and also in nuclear fusion devices [7, 8, 9]. At higher density and low temperature, the SCDPs undergo in crystallization phase. In Coulomb coupling systems, the SCDPs change phase from liquid to crystal phase at specific values of the Coulomb coupling parameters. SCDPs known as a warm liquid at
1.3 Properties of dust particles
Dust is present everywhere in the space and environment. Dust particles are much larger than electrons, ions, and neutral particles. Their sizes of dust particles vary from hundreds of millimeters to 10 nm and the mass of dust particle is approximately 7.53 × 10−10 kg. Their dynamic behaviors are easily observed through a CCD camera because of temporal and spatial scale. These dust particles are mostly negatively charged; however, sometimes they have positive charged also, that depends upon the charging phenomena. The large shielding clouds are created for balance the ion thermal current and electron thermal current. Charging phenomena of dust particles are photoionization, electron bombardment, sputtering, etc. The amount of charge at dust particles depends upon shape and size. Most often, they have spherical shape; however, sometimes they are of the form of rod type and or irregular shape [12, 15]. Dust particles are exposed to ion and electron currents from discharge plasma that’s why reached quickly in dynamical equilibrium. The electric charge on the dust particle depends upon their radius (size) and shape, and the charge amount is in the order of 103–104 electrons. Increasing the charge on the particles increases the electrostatic repulsion between them in a confined system and may lead to crystallization [16]. The dust particles are strongly coupled due to high electric charges and unable to move easily so that they look like a solid and liquid phase in the DPs. The phonon spectra in the DPs are easily calculated due to the thermal motion of dust particles [17]. The motion of dust particles generates the longitudinal and transverse waves in the dusty plasma. Due to the complex behavior of a dust particle in DPs, it becomes an independent field for researchers whose study dusty plasma with strong correlation. The charged dust particles are highly susceptible to the different forces in the plasma such as the electric field, neutral and ion drag and can serve as sensitive diagnostic tools [18].
1.4 The existence of DPs in nature and laboratory
DPs are found in the ionosphere, that’s a lower part of the earth. Noctilucent clouds (NLs) are composed of ice and dust from manmade pollution and heavy clusters. In the space environment, the examples of dusty (complex) plasma are Jupiter rings, were first observed in 1779, comets, planetary rings and spokes, Saturn’s rings and Neptune. The size of dust particles in Saturn ring varies from micron to sub-micron. The radial spokes also consist of micron and submicron sized dust charged particles that are electrostatically levitated. The presence of dust particles in the atmosphere at the altitudes in the range of 80 and 90 km was observed during polar summer mesopause [19]. The presence of dust particles was observed in the nuclear fusion devices, both Tokamaks and stellarators. Due to the presence of dust particles in these devices may disturb the performance and stop working on it. Nowadays, study of dust particles in fusion devices becomes very important. The charging mechanisms of dust particles in these devices are also investigated by Liu et al. [20]. It becomes very necessary for operational Tokamak or other fusion devices to study and found waves and transport properties of dusty plasma. Thermal conductivity, diffusion coefficient, shear viscosity in dusty plasma and charging mechanisms of dust particles in nuclear fusion devices are also needed to investigate [21]. The dust particles are also observed in radio frequency (RF) device and direct current (DC) glow discharge tube and Z-Pinch device etc. Under the laboratory condition, the plasma crystals are observed in different devices such as in RF, DC, thermal plasma, nuclear-induced dusty plasma over wide range of plasma parameters [22].
1.5 Nuclear fusion devices
Fusion energy is a source of energy for a future generation which is almost inexhaustible. Currently, it is an undefeatable challenge for engineering and thermophysical researchers. The basic challenge to achieve the fusion energy is “to achieve a rate of heat emitted by fusion plasma that exceeds the rate of energy injected into the plasma”. The central expectations are focused on two fusion reactor devices, one is Tokamak and the other is stellarator. Today the whole world community is working for nuclear fusion device, which is known as Tokamak. Fusion energy is investigated and comes closest to the explosion. These devices consist of a ring-type magnetic field used to confine the plasma. Tokamak plasma is confined by an electric current flowing in plasma, and in the stellarators, a magnetic field of very complicated shape used to confine plasma stationary. The Tokamak work only in the pulsed mode without auxiliary facilities and stellarators is suitable for continuous operation. The most effective magnetic field configuration is toroidal in the shape of the doughnut. The Tokamaks, stellarators and the reversed field pinch (RFP) are commonly under developing fusion nuclear devices based on toroidal confinement configuration. The Z-pinch is also nuclear fusion device in which is a strong electrical current in plasma to generate X-rays. The magnetized target fusion, referred to as a MIF (magneto-inertial fusion) system, is also currently in progress. In these nuclear devices, a magnetic field is applied to confine the plasma with the help of electromagnetic or mechanical linear implosion. A compression heating is provided with laser hot dense magnetized plasma which is created in the plasma focus (PF) devices. The PF devices belong to the family of dynamic noncylindrical Z-pinch. If in this device deuterium is used as gases then DD fusion reaction takes place [23, 24, 25, 26, 27].
1.6 Dusty plasma in fusion devices
The working conditions of nuclear fusion devices are such that the fuel of these devices must be heated up to heat fuel in nuclear fusion devices heat in the range of 100 × 108 K temperature, at this temperature the fuel is in the plasma state. The temperature of the plasma is very high, and materials are vaporized that contact with it, that’s why plasma must be confined kept in the magnetic fields. In the Tokamak reactor fuel is use in the range of grams (g), so it is a very safe device. The solid impurities are known as “dust” were also found and investigate Scrape-Off Layer transport that is a key element of edge physics research program. For safety precautions against the dust particles, it is very significant for engineers to predict where the quantity of dust particles increases. To resolve the dust transport problem in fusion devices it is necessary for physicists to develop a fully accurate dust transport code (DTC) [28]. It is also required to calculate the plasma parameters from geometrical relations and engineering constraints of nuclear fusion Tokamak device. Plasma density (
1.7 Waves spectra in dusty plasma
To understand dynamical information and basic properties of gas, liquids, and solids, it is compulsory to study the basic two phenomena such as phase transition and waves [31]. Dust particles in SCDPs support longitudinal (compressional) waves, also known as dust acoustic waves (DAWs) and transverse waves (shear) [12]. The propagations of longitudinal modes are faster than the transverse mode in the crystalline phase of dusty plasma. The WCDPs does not sustain the transverse wave and only sustain longitudinal waves. The compressional electrostatic waves and DAWs have low-frequency modes due to a larger mass of dust particles. In order to study the thermal motion of dust particles through MD simulation and it was found that cut off wave number is calculated for transverse mode near the solidification phase of dusty plasma [32]. The generalized hydrodynamics (GHD) model of the equation is predicted by the existence of transverse wave mode in the liquid and strong coupling regimes and dispersion properties of longitudinal modes [18]. Investigation of dusty longitudinal waves (DLWs—dust lattice waves) in two-dimensional bi-crystal in an arbitrary direction and it was found that hybrid modes have both components along with transverse and longitudinal directions. The hybrid modes become purely transverse to longitudinal waves for the angle of propagation is 0 or π/2 [33]. Background of the colloidal suspension liquid exerts large friction on the motion of charged particles than the background of dusty plasma gases. Due to low friction between charged particles in the gas phase of dusty plasma waves damped slowly. The complex (dusty) plasma the current correlation functions of complex (dusty) plasma are classified into the longitudinal current and transverse current, also known as longitudinal and transverse (shear) wave’s mode. In the classical fluids, when
The uniform liquid phase does not support transverse modes of waves. The reason for this is to ignore the migration of diffusion damping. For isotropy liquid, the transverse mode approaches the same Einstein frequency
1.8 MD simulation and types
An MD simulation is a tool that studies the microscopic model in a macroscopic system, and this model is quantified in terms of intermolecular interaction and the molecular structure. The results are obtained with accuracy through different simulation techniques (algorithm) and compared with theoretical and experimental results. Simulations are also used to study the wave properties of complex models at the microscopic level which cannot be investigated by experiments [36]. There are several computational techniques that have advantages and also disadvantages with their respective fields. Monte Carlo (MC) and molecular dynamics (MD) simulations are influential tools for the study of transport properties of dusty plasma. Transport properties can also be calculated by Langevin dynamics (LD), MC, path integral MC (PIMC) and MD methods. The disadvantage of the MC technique is that it cannot evaluate the transport properties of dynamical systems and cannot solve and apply the equations of motion [37].
2. Mathematical model and numerical method
In this chapter the EMD Simulations are performed for a selected system, having the number of particle
2.1 Current correlation functions
The SCDPs support both longitudinal and transverse waves. The experimental importance of time-dependent correlation function is that the spectroscopic technique an example of this technique is neutron scattering. Investigate microscopic dynamical quantities through the MD approach and then comparison by Fourier analysis of the simulation result. The local density gives information about the atom’s distribution. There is also possible to analyze the motion of atoms. The Fourier component of Particle current or momentum current for a single atomic particle in MD unit is given as.
where
The correlation function of the current vector component is defined as
For the isotropic fluid under consideration of symmetry above equation can be expressed in term of longitudinal current correlation and transverse current correlation in the relative direction of
Here
By putting
Where
The longitudinal current correlation also related to the dynamical structure factor.
In Eq. (9), the dynamical structure factor and longitudinal current correlation contain the same physical information of the systems. Transverse current and longitudinal current also explain the wave spectra in 3D SCDPs. In our EMD simulation model, the current correlation function is the only function of wavenumber and time (
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.
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
There is a slight effect of screening strength (
In this part, we have investigate
Figures 4 and 5 demonstrate the Simulation results which are obtained for
The panel (a) of both Figures 4 and 5 represent the results of
4. Summary
The EMD simulations are used to investigate the
Acknowledgments
The authors thank the National Advanced Computing Centre of National Centre for Physics (NCP), Pakistan and National High-Performance Computing Center (NHPCC) of Xian Jiaotong University, P.R. China for allocating computer time to test and run our MD code.
Abbreviation and symbol
equilibrium molecular dynamic
screening strength
Coulomb coupling
wavenumber (wave vector)
number of particles
dusty plasma
strongly coupled dusty plasmas
three dimensional
longitudinal current wave
transverse current wave
complex dusty plasmas
weakly coupled dusty plasmas
noctilucent clouds
reverse field pinch
magnetized target fusion
plasma focus
magneto-inertial fusion
Boltzmann constant
plasma density
plasma pressure
plasma temperature
normalized plasma pressure
the minor radius of the plasma
plasma toroidal current
dust acoustic wave
periodic boundary condition
radiofrequency
discharge current
dust transport code
molecular dynamic
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