Thermal Fluctuations and Collective Modes in Strongly Coupled Dusty (SCD) Plasmas

Like every system, dusty plasma exhibits spontaneous molecular fluctuations at finite temperature. It also supports different types of collective modes excited externally. These fluctuations and excitations die due to different dissipation mechanisms in the medium such as diffusion, viscous flow, and thermal conduction. A study of them provides knowledge of transport phenomena at various wavelengths and frequencies, (κ, ω). Moreover, several recent theoretical investigations have predicted the existence of solitary structures, and have studied their propagation characteristics.

During the formation of a dusty plasma, grains accumulate high electric charges 10 ³ - 10 ⁵е and usually negative) due to the collection of electrons and ions in different proportions. The charging process modifies the electrical properties of the grains and surrounding plasma; and therefore, a study thereof is important for understanding the Debye shielding and potential distribution around the grains. Moreover, the fluctuation in the grain charge introduces a new time scale and influences the particle dynamics and collective phenomena at finite (κ, ω).

Due to high electric charge and low temperature (because of dust inertia, and high neutral pressure, a typical condition in most laboratory experiments), the coulomb coupling parameter, Γ, for the dust component (≡ Z_de / r₀T_d, where Z_d e is the charge on each dust grain, r₀ is the intergrain distance and T_d is the dust temperature) usually becomes greater than unity, and the system becomes a strongly coupled one. Various recent (laboratory and numerical) experiments have shown that the system has different phases (fluid, liquid, supercooled liquid, and crystal) depending on different values of parameters like Γ and κ (≡ r₀ / λ_D, where λ_D, is the Debye length of the plasma.

During the charging process, plasma particles are continually dissipated on the dust surface; and so, dust acts as a sink in the dusty plasma system. If it were only the case, quasi-neutrality condition would severely be affected in the neighbourhood of the dust grain. Therefore, to maintain a natural system, one needs to have more ionisation simultaneously or to pump plasma particles to the system from an external source (as it naturally happens when solar wind-rich with plasma matter flows into the rings of the outer planets in our solar system). So, a quasi-neutral dusty plasma is an excellent example of an open system. In this context, it may be noted that the study of thermodynamics and self-organisation in open systems has attracted wide attention and has become a subject of intense research at present.

The above discussion leads to a natural requirement of a unified description of various collective phenomena in dusty plasma existing in different phases. In the following two paragraphs, several theoretical models have been discussed in this direction:

• The usual hydrodynamic model of fluid assumes a continuum and introduces various densities, such as mass, momentum, and energy, densities to obtain a closed set of equations with them. One also includes schemes to calculate thermodynamic derivatives and transport coefficients in the model. But this model of matter does not take the interactions among individual particles into account; and so, is not suitable to study phenomena due to strong correlation effects and various modes at finite (κ, ω), comparable to molecular scales. To explain the physical behaviour of a system at the scale these properties and dynamics of individual particles become important, one adopts the methods of molecular dynamics. This method requires knowledge of interactions potential among the individual particles; and computer simulation is performed to obtain the time evolution of the system (typically with several hundreds of particles). One then calculates thermodynamic quantities and transport coefficients using methods which relies heavily on ergodic hypothesis.
• Generalised hydrodynamics extends the usual hydrodynamic picture of fluid to the regime of finite (κ, ω) where one basically retains the standard equations for densities but includes memory functions to account for correlation effects. The transport coefficients and thermodynamic derivatives are included in the momentum equation and are usually determined by molecular simulation or analytical schemes. Thus one obtains a unified description of liquid to address various problems in a wide region of κ – ω plane. This model is valid for 1 < Γ < Γ_c where Γ_c is the critical value of crystallisation; and it may even be applied to study systems beyond Γ_c as long as the systems retain their fluid characteristics. For still larger Γ molecular dynamics seems to be the only option at present.

With these results and trends one may now speculate that the Generalised Hydrodynamic (GH) model is the likely candidate to study SCD plasmas on the whole κ – ω plane (except in the limit κ → ∞ and ω → ∞, where individual grains behave as free particles). One needs to pursue molecular simulation to assist GH model and to investigate self-organisation and critical phenomena. The effect of charge fluctuations and thermal fluctuations on particle dynamics and collective modes must be included to provide a complete picture.