Dust-acoustic shock waves due to strong correlation among arbitrarily charged dust

Cylindrical and Spherical Nucleus-Acoustic Solitary and Shock Waves in Degenerate Electron-Nucleus Plasmas

The basic characteristics of cylindrical as well as spherical solitary and shock waves in degenerate electron-nucleus plasmas are theoretically investigated. The electron species is assumed to be cold, ultra-relativistically degenerate, negatively charged gas, whereas the nucleus species is considered a cold, non-degenerate, positively charged, viscous fluid. The reductive perturbation technique is utilized in order to reduce the basic equations (governing the degenerate electron-nucleus plasmas under consideration) to the modified Korteweg-de Vries and Burgers equations. The latter are numerically solved and analyzed to detect the basic characteristics of solitary and shock waves in such electron-nucleus plasmas. The nonlinear nucleus-acoustic waves are found to be propagated in the form of solitary as well as shock waves in such degenerate electron-nucleus plasmas. Their basic properties as well as their time evolution are significantly modified by the effects of cylindrical as well as spherical geometries. The results of this study is expected to be applicable not only to astrophysical compact objects, but also to ultra-cold dense plasmas produced in laboratory.

Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form M_{shock}=1+sM_{exciter}, and to the prediction of a recent simulation.

Generalized hydrodynamics model for strongly coupled plasmas

Beginning with the exact equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we obtain the density, momentum, and stress tensor-moment equations. We close the moment equations with two closures, one that guarantees an equilibrium state given by density-functional theory and another that includes collisions in the relaxation of the stress tensor. The introduction of a density functional-theory closure ensures self-consistency in the equation-of-state properties of the plasma (ideal and excess pressure, electric fields, and correlations). The resulting generalized hydrodynamics thus includes all impacts of Coulomb coupling, viscous damping, and the high-frequency (viscoelastic) response. We compare our results with those of several known models, including generalized hydrodynamic theory and models obtained using the Singwi-Tosi-Land-Sjolander approximation and the quasilocalized charge approximation. We find that the viscoelastic response, including both the high-frequency elastic generalization and viscous wave damping, is important for correctly describing ion-acoustic waves. We illustrate this result by considering three very different systems: ultracold plasmas, dusty plasmas, and dense plasmas. The new model is validated by comparing its results with those of the current autocorrelation function obtained from molecular-dynamics simulations of Yukawa plasmas, and the agreement is excellent. Generalizations of this model to mixtures and quantum systems should be straightforward.

Nonlinear dynamics of large-amplitude dust acoustic shocks and solitary pulses in dusty plasmas

We present a fully nonlinear theory for dust acoustic (DA) shocks and DA solitary pulses in a strongly coupled dusty plasma, which have been recently observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002 (2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a generalized hydrodynamic model for the strongly coupled dust grains, accounting for arbitrary large-amplitude dust number density compressions and potential distributions associated with fully nonlinear nonstationary DA waves. Time-dependent numerical solutions of our nonlinear model compare favorably well with the recent experimental works (mentioned above) that have reported the formation of large-amplitude nonstationary DA shocks and DA solitary pulses in low-temperature dusty plasma discharges.

Nonplanar dust-acoustic Gardner solitons in a four-component dusty plasma

The nonlinear propagation of Gardner solitons (GSs) in a nonplanar (cylindrical and spherical) four-component dusty plasma (composed of inertial positively and negatively dust, Boltzmann electrons, and ions) is studied by the reductive perturbation method. The modified Gardner equation is derived and numerically solved. It has been found that the basic characteristics of the dust-acoustic (DA) GSs, which are shown to exist for μ around its critical value μ(c) [where μ=Z(dp)m(dn)/Z(dn)m(dp), Z(dn) (Z(dp)) is the number of electrons (protons) residing on a negative (positive) dust, m(dp) (m(dn)) is the mass of the positive (negative) dust, μ(c) is the value of μ corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (KdV) equation, e.g., μ(c)≃0.174 for μ(e)=n(e0)/Z(dn)n(dn0)=0.2, μ(i)=n(i0)/Z(d)}n(dn0)=0.4, and σ=T(i)/T(e)=0.1, n(e0), n(i0), and n(dn0) are, respectively, electron, ion, and dust number densities, and T(i) (T(e)) is the ion (electron) temperature], are different from those of the KdV solitons, which do not exist for μ around μ(c). It has been also found that the propagation characteristics of nonplanar DA GSs significantly differ from those of planar ones.

Effects of polarization force and effective dust temperature on dust-acoustic solitary and shock waves in a strongly coupled dusty plasma

A strongly coupled dusty plasma containing strongly correlated negatively charged dust grains and weakly correlated (Maxwellian) electrons and ions has been considered. The effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains) and effective dust temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure) on the dust-acoustic (DA) solitary and shock waves propagating in such a strongly coupled dusty plasma are taken into account. The DA solitary and shock waves are found to exist with negative potential only. It has been shown that the strong correlation among the charged dust grains is a source of dissipation and is responsible for the formation of the DA shock waves. It has also been shown that the effects of polarization force and effective dust-temperature significantly modify the basic features (e.g., amplitude, width, and speed) of the DA solitary and shock waves. It has been suggested that a laboratory experiment be performed to test the theory presented in this work.

Laboratory observations of self-excited dust acoustic shocks

Repeated, self-excited dust acoustic shock waves (DASWs) have been observed in a dc glow discharge dusty plasma using high-speed video imaging. Two major observations are reported: (1) The self-steepening of a nonlinear dust acoustic wave (DAW) into a saw-tooth wave with sharp gradient in dust density, very similar to those found in numerical solutions of the fully nonlinear fluid equations for a nondispersive DAW [B. Eliasson and P. K. Shukla, Phys. Rev. E 69, 067401 (2004)], and (2) the collision and confluence of two DASWs.