Dust Plasma Frequency Research Articles

Entanglement in a complex plasma

Quantum mechanical approach is extended to the interaction of dust particles in a complex plasma. Massive and highly charged dust particles interact each other through the exchange of quasi-particles (virtual waves) in a quantum mechanical viewpoint. The interaction is described by the Hamiltonian, which describes the two-particle system as uncoupled harmonic oscillators. When the pair of dust particles are embedded in the injected plasma wave, the Hamiltonian is found to show the presence of coupled harmonic oscillator indicating the emergence of the entanglement in semiclassical nature. The entanglement of a pair of dust particles is encapsulated in the Hamiltonian, which is formulated by the method of second quantization. The frequency of the wave to trigger the emergence of the entanglement is found to be one-half of the dust plasma frequency. The interaction between a pair of dust particles is formulated as a scattering process and is described by the transition probability. Measure of the semiclassical entanglement is shown by the entropy, and the resulting entropy is found to increase with time.

Effect of dusty plasma parameters on the low frequency Hall current instability

The effect of power-law dust size distribution and dust number density on the low frequency hall current instabilities have been studied in and above the equatorial electrojet altitudes using a linear fluid model consisting of electrons, ions and dust particles. The dispersion relation includes electron and ion drift perpendicular to the equilibrium uniform electric and magnetic field, mass and pressure of the charged species and collision between charged and neutral particles. The effect of dust size variation and dust number density on the instability have been investigated by varying the dust-plasma frequency in the dispersion relation. It has been found that in the region of the electrojet altitudes the variation of dust size for the case of broad dust size distribution and dust number density can substantially increase the growth rate and frequency of the instability. However, above the electrojet region where ions become weakly magnetized, the above two dust parameters have a negligible effect on the instability.The present analysis is applicable to the dusty meteor trail plasma of the ionospheric E-region.

Simulations of a low frequency beam-cyclotron instability in a dusty plasma

The nonlinear development of a low frequency beam-cyclotron instability in a collisional plasma composed of magnetized ions and electrons and unmagnetized, negatively charged dust is investigated using one-dimensional particle-in-cell simulations. Collisions of charged particles with neutrals are taken into account via a Langevin operator. The instability, which is driven by an ion $\boldsymbol{E}\times \boldsymbol{B}$ drift, excites a quasi-discrete wavenumber spectrum of waves that propagate perpendicular to the magnetic field with frequency of the order of the dust plasma frequency. In the linear regime, the unstable wavelengths are of the order of the ion gyroradius. As the wave energy density increases, the dominant modes shift to longer wavelengths, suggesting a transition to a Hall-current-type instability. Parameters are considered that reflect the ordering of plasma and dust quantities in laboratory dusty plasmas with high magnetic field. Comparison with the nonlinear development of this beam cyclotron instability in a collisionless dusty plasma is also briefly discussed.

Einstein Frequency Measurement for a Strongly Coupled Dusty Plasma

The Einstein frequency $\Omega _{E}$ was experimentally determined for a 2-D dusty plasma. We found $\Omega _{E}= 49.4 ~\text{s}^{-1}$ and 50.2 s−1 for the collection of microspheres in a crystalline and liquid-like state, respectively. Comparing to the nominal 2-D dust plasma frequency $\omega _{\mathrm {pd}}$ , we found the ratio $\Omega _{ E}$ / $\omega _{\mathrm {pd}}\approx 1$ / $\surd 3$ . This experimental ratio is consistent with previous predictions of Yukawa simulations. Our results were obtained by analyzing images of the microspheres to obtain their positions, charge, and the screening length; we used these measurements to calculate resonant frequencies of test particles.

Higher order structure in a complex plasma

The direct experimental determination of the 3-point static structure function S(3)(k1, k2, k0) of a 2-dimensional dusty plasma liquid is presented. The measurements are complemented by molecular dynamics simulations of the system, using parameters (dust charge, plasma frequency, coupling and screening coefficients), which are derived from the experimentally obtained 2-point static structure function S(2), as well as the dynamic structure function and current-current fluctuation spectra. The experimental results of S(3) are in good agreement with those of the simulations, including the (low wavenumber) domain, where S(3) acquires negative values. The “Convolution Approximation” (giving S(3) in a factorized form of S(2) functions) clearly breaks down in this domain; however, it is found to be a useful aid for explaining the main features of the S(3)(k1, k2, k0) functions, for which (experimental and simulation) maps are presented at selected values of one of its arguments.

Strongly correlated classical plasmas under external forcing and dissipation - an example using Molecular Dynamics

Systems with excess of average potential energy per particle than its kinetic energy develop strong correlations. It is well known that such systems are not amenable to standard procedures of BBGKY hierarchy. This results in failure of both kinetic and fluid models. Phenomenology is the normal way out. If such a strongly correlated system is further subjected to strong drive and/or dissipation, “near first principles” computational methods such as Molecular Dynamics become necessary. Formation of Rayleigh-Bénnard convection cells (RBCC), where a liquid is under the action of external gravity and external temperature gradient, is one such phenomena. We report here, the formation of RBCC in 2-dimensional strongly coupled Yukawa liquids, characterized by coupling strength Γ (ratio of average potential energy to kinetic energy per particle) and screening parameter κ (ratio of average inter particle distance to Debye length). We observe the existence of a critical external temperature difference, beyond which RBCC are seen to emerge. Beyond this critical external temperature difference, the strength of the maximum convective flow velocity is shown to exhibit a new, linear relationship with external temperature difference and with a slope independent of (Γ, κ). The time taken for the transients to settle down (ts) is found to be 10,000 to 20,000 ωpd-1, where ωpd is dust plasma frequency. At very high values of Γ and/or low values of κ, RBCC are seen to get suppressed.

Rogue waves for Kadomstev-Petviashvili solutions in a warm dusty plasma with opposite polarity

Kadomstev-Petviashvili (KP) equation is derived using reductive perturbation method. This equation transformed into a nonlinear Schrodinger equation (NLS) by using appropriate variable transformations. When the carrier wave frequency is much smaller than the dust plasma frequency, the DA waves generating modulated wave packets in the form of rogue waves. The dependence of rogue wave profile on system plasma parameters investigated numerically. The parameters in this model are within the ranges corresponding to upper mesosphere, cometary tails and Jupiter’s magnetosphere.

Observation of the Rayleigh-Bénard convection cells in strongly coupled Yukawa liquids

Using “first principles” molecular dynamics simulation, we report for the first time the formation of Rayleigh-Bénard convection cells (RBCC) in two-dimensional strongly coupled Yukawa liquids, characterized by coupling strength Γ (ratio of average potential energy to kinetic energy per particle) and screening parameter κ (ratio of average inter-particle distance to Debye length). For typical values of (Γ, κ), existence of a critical external temperature difference is demonstrated, beyond which RBCC are seen to set in. Beyond this critical external temperature difference, the strength of the maximum convective flow velocity is shown to exhibit a new, hitherto unsuspected linear relationship with external temperature difference and with a slope independent of (Γ, κ). The time taken for the transients to settle down (τs) to a steady state RBCC is found to be maximum close to the above said critical external temperature difference and is seen to reduce with increasing external temperature difference. For the range of values of (Γ, κ) considered here, τs ≈ 10 000–20 000 ωpd−1, where ωpd is dust plasma frequency. As Γ is increased to very high values, due to strong coupling effects, cells are seen to be in a transient state without attaining a steady state for as long as 100 000 ωpd−1, even for a very high external temperature difference. Role of system size, aspect ratio, and dust-neutral collisions has also been addressed.

Complex plasma in g×B configurations: Stability switching and stationary structure

In a low-pressure magneto-gravitated complex plasma, the stability state of dust gravitational drift wave is switched at a critical wavenumber and the propagating dust magneto-gravitational drift wave is transformed into an aperiodic stationary structure at a cut-off wavenumber. In this paper, two analytical formulas have been derived for the critical wavenumber of stability switching and the cut-off wavenumber of stationary structure. The critical wavenumber is equal to the ratio of ion plasma frequency to ion streaming velocity and the cut-off wavenumber is proportional to the ratio of dust plasma frequency to dust g×B drift velocity. These scaling formulas are in excellent agreement with exact numerical solutions of dispersion relations. These scenarios are expected to be observed in fully magnetized dusty plasma experiments as the next frontier for complex plasma research.

Resonant instability of the surface dust-acoustic wave in electron–positron–ion dusty plasmas including pair annihilation effects

Abstract The influence of electron–positron pair annihilations on the resonant instability of surface dust-acoustic wave is investigated in semi-bounded electron–positron–ion dusty plasmas. The dispersion relation and the temporal growth rate of the surface dust-acoustic wave including the pair annihilation effect are obtained by the specular reflection boundary condition. It is found that the electron–positron annihilation effect suppresses the temporal growth rate of the surface dust-acoustic instability and, however, increases the domain of the resonant instability. It is also shown that the pair annihilation effect on the growth rate decreases with increasing wave number and dust plasma frequency. The variation of the domain and magnitude of temporal growth rate is also discussed.

Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma

The formation and propagation of dust-acoustic (DA) solitary and rogue waves are studied in a non-relativistic degenerate Thomas-Fermi thermal dusty plasma incorporating transverse velocity perturbation effects. The electrons and ions are described by the Thomas-Fermi density distributions, whereas the dust grains are taken as dynamic and classical. By using the reductive perturbation technique, the cylindrical Kadomtsev-Petviashvili (CKP) equation is derived, which is then transformed into a Korteweg-deVries (KdV) equation by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. For the study of DA-rogue waves, the KdV equation is transformed into a self-focusing nonlinear Schrodinger equation. The variation of dust temperature and the electron density affects the nonlinearity and dispersion coefficients which suppress the amplitudes of the DA solitary and rogue waves. The present results aim to describe the nonlinear electrostatic excitations in astrophysical degenerate dense plasma.

Dust-acoustic solitary waves in a magnetized dusty plasma with nonthermal electrons and trapped ions

The nonlinear propagation of electrostatic dust-acoustic (DA) waves in a magnetized dusty plasma consisting of negatively charged mobile dusts, nonthermal fast electrons and trapped ions with vortex-like distribution is studied. Using the reductive perturbation technique, a Korteweg–de Vries (KdV)-like equation is derived which governs the dynamics of the small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is found that due to the dust thermal pressure, there exists a critical value (βc) of the nonthermal parameter β (>1), denoting the percentage of energetic electrons, below which the DA solitary waves cease to propagate. The soliton solution (traveling wave) of the KdV-like equation is obtained, and is shown to be only of the rarefactive type. The properties of the solitons are analyzed numerically with the system parameters. It is also seen that the effect of the static magnetic field (which only modifies the soliton width) becomes significant when the dust gyrofrequency is smaller than one-tenth of the dust plasma frequency. Furthermore, the amplitude of the soliton is found to increase (decrease) when the ratio of the free to trapped ion temperatures (σ) is positive (negative). The effects of the system parameters including the obliqueness of propagation (lz) and σ on the dynamics of the DA solitons are also discussed numerically, and it is found that the soliton structures can withstand perturbations and turbulence during a considerable time. The results should be useful for understanding the nonlinear propagation of DA solitary waves in laboratory and space plasmas (e.g., Earth’s magnetosphere, auroral region, heliospheric environments, etc.).

Beam cyclotron instability in a dusty plasma

A beam cyclotron instability in a plasma composed of magnetized ions and electrons and unmagnetized, negatively charged dust is investigated using linear kinetic theory. We consider the case where an ion E × E drift leads to the excitation of a discrete wavenumber spectrum of waves with frequency on the order of the dust plasma frequency for propagation perpendicular to the magnetic field. The unstable wavelengths are short, on the order of the ion gyroradius. Collisions of charged particles with neutrals are taken into account, as well as ion–dust and dust–dust collisions, which can be significant at the lower pressures considered. The behavior of the instability for oblique propagation is also considered. Application to possible laboratory dusty magnetoplasma parameters is discussed.

Effect of quantum corrections on the Jeans instability of self-gravitating viscoelastic dusty fluid

In this paper we investigate the effects of quantum correction on the Jeans instability of self-gravitating viscoelastic dusty electron-ion quantum fluids. The massive self-gravitating dust grains are assumed to be strongly coupled and non-degenerate having both viscous and elastic behavior while the inertialess electrons and ions are considered as weakly coupled and Fermi degenerate. The hydrodynamic model is modified and a linear dispersion relation is derived employing the plane wave solutions on the linearized perturbation equations for the considered system. It is observed that the dispersion properties are affected due to the presence of viscoelastic effects and quantum statistical corrections. The modified condition of Jeans instability and expression of critical Jeans wavenumber are obtained. Numerically it is shown that viscoelastic effects, dust plasma frequency and quantum statistical effects all have stabilizing influence on the growth rate of gravitationally Jeans mode. The growth rates are also compared in kinetic and hydrodynamic limits and it is found that decay in the growth of unstable Jeans mode is larger under the kinetic limits than the hydrodynamic limits. The results are discussed for the understanding of formation of dense degenerate dwarf star through gravitational collapsing which is assumed to be strongly coupled dusty quantum fluid where the strongly coupled dust provides inertia and Fermi degenerate electron and ions provide quantum statistical effects.

New low-frequency waves and negative mass instability in dusty plasmas

AbstractLow-frequency dusty plasma waves with frequencies much smaller than the frequency of charging collisions of plasma particles with dust particles are considered taking into account elastic and charging collisions of plasma particles with dust and neutrals. The usual dust sound waves with an upper frequency equal to the dust plasma frequency are found to be present only for wavelengths much smaller than the plasma particle effective mean free path due to the effective collision frequency. The effectice collision frequency is found to be inversely proportional to the square root of the product of the charging frequency and the frequency of particle momentum losses, involving processes due to elastic plasma particle–dust collisions and collisions with neutrals. It is shown that when the wavelength of the wave is much larger than the mean free path for effective collisions, the properties of the waves are different from those considered previously. A negative mass instability is found in this domain of frequencies when the effective mean free path of ions is larger than the effective mean free path of electrons. In the absence of neutrals, this appears to be possible only if the temperature of ions exceeds the electron temperature. This can occur in laboratory experiments and space plasmas but not in plasma-etching experiments. In the absence of instability, a new dust oscillation, a dust charging mode, is found, whose frequency is almost constant over a certain range of wave numbers. It is inversely proportional to the dust mass and charging frequency of the dust. A new dust electron sound wave is found for frequencies less than the frequency of the dust charging mode. The velocity of the dust electron sound wave is determined by the electron temperature but not the ion temperature, as for the usual dust sound waves, with the electron temperature substantially exceeding the ion temperature.

Rotating electric fields in complex (dusty) plasmas

The rotation of monolayer particle clusters suspended in the sheath of a rf discharge plasma was observed experimentally. The cluster rotation was driven by an electric field that rotated uniformly in the horizontal plane (“rotating wall” technique). No external magnetic field was applied. The cluster rotation velocity depended nonmonotonically on the manipulation field frequency that was much higher than the dust plasma frequency. Mechanisms of rotation are proposed based on the interplay between the electric and ion-drag forces. Possible applications of rotating electric fields in complex plasmas are discussed.

Complex plasma laboratory PK-3 Plus on the International Space Station

PK-3 Plus is the second-generation laboratory for the investigation of complex plasmas under microgravity conditions on the International Space Station (ISS). It has more advanced hardware, software and diagnostics than its precursor PKE-Nefedov (Nefedov et al 2003 New J. Phys. 5 33). The first experiments with PK-3 Plus show the perfect functioning of the apparatus and provide much better insights into the properties of complex plasmas. In particular, the ‘void’ in the center of the complex plasma cloud can now be easily closed, thus providing a much better homogeneity of the complex plasma—a feature which was hardly achievable before—but which is essential for many precision studies. Moreover, the use of the function generator at frequencies above the dust plasma frequency provides many possibilities for future experiments. Other interesting phenomena are related to high densities of the microparticles in the complex plasma. These so-called heartbeat and filamentary mode instabilities can be investigated in detail, by comparing particle motion with the discharge glow characteristics.

Landau damping of dust acoustic waves in a Lorentzian plasma

The Landau damping of dust acoustic waves propagating in a dusty plasma modeled by a Lorentzian (kappa) distribution for electrons and ions, and by a Maxwellian distribution for the dust grains is kinetically investigated. The dust acoustic waves are found in the range of kvd≪ω≪kvi≪kve, where vα is the thermal velocity of species α(=i,e,d). The damping rate is shown to be dependent on the spectral index κ as well as the ratio of ion density to electron. The maximum Landau damping rate is derived and found to be approximately 0.2σκωpd where ωpd is the dust plasma frequency and σκ is a κ-dependent factor, which has the maximum value of 1.33 (for the smallest κ) and reduces to unity as the nonthermal effect disappears.

Dust charge effects on the resonant instability of the dust-acoustic wave in a semibounded dusty plasma

The resonant instability of the surface dust-acoustic wave is investigated in a semibounded dusty plasma containing elongated and rotating dust grains. The temporal growth rate of the surface dust-acoustic instability is obtained by the plasma dielectric function with the specular reflection boundary condition. The results show that the domain of the instability increases with increase in the wave number, especially for the case of the negatively charged dust grains. It is also found that the growth rate of the instability with negatively charged dust grains is found to be smaller than that with positively charged dust grains. In addition, it is found that the growth rate decreases with increasing the ratio of the dust plasma frequency to the rotation frequency.

Relationship between dust acoustic waves in two and three dimensions

Low frequency electrostatic waves are investigated for a monolayer suspension of dust particles that are shielded by an ambient plasma of three-dimensional extension. The dispersion of the resulting dust acoustic surface waves is compared with dust acoustic waves in three dimensions and with lattice modes in two dimensions. It is found that the wave dispersion is determined by shielding of electric fields by electrons and ions on either side of the dust monolayer; this differs from previously studied cases of charged sheets in a vacuum. The phase velocity of these surface waves suggests the definition of a proper dust plasma frequency for monolayer systems.