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By applying the Maxwell and quantum hydrodynamic equations, we have studied the parametric instabilities of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) in an unmagnetized electron-ion quantum plasma. In this context, we have derived the nonlinear dispersion relations of the large-amplitude electromagnetic (EM) waves, the electrostatic electron plasma waves, and the ion-acoustic waves. The nonlinear evolution equations are then solved by utilizing the Fourier transform to obtain expressions for the three-wave decay and modulational instabilities with quantum corrections. It is found that the growth rate of the instabilities is a strong function of large-amplitude EM waves, and quantum effects due to Fermi pressure and quantum correlations stabilize both SRS and SBS instabilities. Expressions for the maximum growth rates attributed to SRS and SBS instabilities are also derived by ignoring the nonlinear correction shift on the frequency of EM waves. The relevance of nonlinear interaction of EM waves with a quantum dense astrophysical plasma is highlighted in the perspective of electron Fermi pressure and exchange-correlation effects, where the plasma density is high enough. [ABSTRACT FROM AUTHOR]

The linear and nonlinear properties of low-frequency electrostatic excitations of charged dust particles (or defects) in a dense collisionless, unmagnetized Thomas-Fermi plasma are investigated. A fully ionized three-component model plasma consisting of electrons, ions, and negatively charged massive dust grains is considered. Electrons and ions are assumed to be in a degenerate quantum state, obeying the Thomas-Fermi density distribution, whereas the inertial dust component is described by a set of classical fluid equations. Considering large-amplitude stationary profile travelling-waves in a moving reference frame, the fluid evolution equations are reduced to a pseudo-energy-balance equation, involving a Sagdeev-type potential function. The analysis describes the dynamics of supersonic dust-acoustic solitary waves in Thomas-Fermi plasmas, and provides exact predictions for their dynamical characteristics, whose dependence on relevant parameters (namely, the ion-to-electron Fermi temperature ratio, and the dust concentration) is investigated. An alternative route is also adopted, by assuming weakly varying small-amplitude disturbances off equilibrium, and then adopting a multiscale perturbation technique to derive a Korteweg-de Vries equation for the electrostatic potential, and finally solving in terms for electric potential pulses (electrostatic solitons). A critical comparison between the two methods reveals that they agree exactly in the small-amplitude, weakly superacoustic limit. The dust concentration (Havnes) parameter h=Zd0nd0/ne0 affects the propagation characteristics by modifying the phase speed, as well as the electron/ion Fermi temperatures. Our results aim at elucidating the characteristics of electrostatic excitations in dust-contaminated dense plasmas, e.g., in metallic electronic devices, and also arguably in supernova environments, where charged dust defects may occur in the quantum plasma regime. [ABSTRACT FROM AUTHOR]

The quantum hydrodynamical model is employed to investigate the nonlinear properties of the quantum dust acoustic waves in a magnetized dusty plasma composed of inertialess electrons, ions, and mobile positive/negative charged dust particles. For this purpose, a quantum Zakharov–Kuznetsov equation is derived and the basic features of the electrostatic excitations are investigated by applying the direct method. It is found that positive and negative bell-shaped solitary pulses become explosive pulses depending mainly upon the angles of propagation and dust polarity. Furthermore, the effects due to nondimensional quantum parameter and the external magnetic field are examined on the width of the quantum dust acoustic solitary pulses. The relevance of the present results to semiconductor quantum wells is mentioned. [ABSTRACT FROM AUTHOR]

A highly accurate calculation of the magnetic field line Hamiltonian in DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)] is made from piecewise analytic equilibrium fit data for shot 115467 3000 ms. The safety factor calculated from this Hamiltonian has a logarithmic singularity at an ideal separatrix. The logarithmic region inside the ideal separatrix contains 2.5% of toroidal flux inside the separatrix. The logarithmic region is symmetric about the separatrix. An area-preserving map for the field line trajectories is obtained in magnetic coordinates from the Hamiltonian equations of motion for the lines and a canonical transformation. This map is used to calculate trajectories of magnetic field lines in DIII-D. The field line Hamiltonian in DIII-D is used as the generating function for the map and to calculate stochastic broadening from field-errors and spatial noise near the separatrix. A very negligible amount (0.03%) of magnetic flux is lost from inside the separatrix due to these nonaxisymmetric fields. It is quite easy to add magnetic perturbations to generating functions and calculate trajectories for maps in magnetic coordinates. However, it is not possible to integrate across the separatrix. It is also difficult to find the physical position corresponding to magnetic coordinates. For open field lines, periodicity in the poloidal angle is assumed, which is not satisfactory. The goal of this paper is to demonstrate the efficacy of the symplectic mapping approach rather than using realistic DIII-D parameters or modeling specific experimental results. [ABSTRACT FROM AUTHOR]

The low frequency electrostatic and electromagnetic linear modes in a nonuniform cold quantum electron-ion plasma are studied. The effect of stationary dust on an electrostatic mode is also investigated. The quantum corrections in the linear dispersion relations of a cold dense plasma are presented with possible applications. [ABSTRACT FROM AUTHOR]

The linear and nonlinear properties of the ion-acoustic waves (IAWs) are investigated by using the quantum hydrodynamic equations together with the Poisson equation in a three-component quantum electron-positron-ion plasma. For this purpose, a linear dispersion relation, a Korteweg-de Vries equation and an energy equation containing quantum corrections are derived. Computational investigations have been performed to examine the quantum mechanical effects on the linear and nonlinear waves. It is found that both the linear and nonlinear properties of the IAWs are significantly affected by the inclusion of the quantum corrections. The relevance of the present investigation to dense white dwarfs (where the electron-positron annihilation can be unimportant) is discussed. [ABSTRACT FROM AUTHOR]

By employing the quantum hydrodynamic model and the reductive perturbation technique, a quantum Zakharov-Kuznetsov (QZK) equation is derived for finite but small amplitude ion-acoustic waves in a quantum magnetoplasma. The extended Conte’s truncation method is used to obtain the solitary, explosive, and periodic solutions of the QZK equation. Furthermore, the stability of the solitary wave solution of the QZK equation is investigated by using the small-k perturbation expansion method. [ABSTRACT FROM AUTHOR]

A new dispersion relation for low-frequency compressional electromagnetic waves is derived by employing quantum magnetohydrodynamic model and Maxwell equations in cold quantum dusty magnetoplasmas. The latter is composed of inertialess electrons, mobile ions, and immobile charged dust particulates. The dispersion relation for the low-frequency compressional electromagnetic modes is further analyzed for the waves propagating parallel, perpendicular, and oblique to the external magnetic field direction. It is found theoretically and numerically that the quantum parameter αq=(ni0/ne0)h2/(4memi) affects the real angular frequencies and the phase speeds of the compressional electromagnetic modes. Here, ni0 (ne0) is the equilibrium number density of the ions (electrons), me (mi) is the electron (ion) mass, and h is the Plank constant divided by 2π. [ABSTRACT FROM AUTHOR]

By employing one-dimensional quantum hydrodynamic (QHD) model for a three species quantum plasma, nonlinear properties of dust acoustic solitary waves are studied. For this purpose a Korteweg-de Vries (KdV) equation is derived, incorporating quantum corrections. The quantum mechanical effects are also examined numerically both on the profiles of the amplitude and the width of dust acoustic solitary waves. It is found that the amplitude remains constant but the width shrinks for different values of a dimensionless electron quantum parameter He = √Zd0ℏ²ω²pd)/memdCd4, where Zd0 is the dust charge state, ℏ is the Planck constant divided by 2π, ωpd is the dust plasma frequency, me (md) is the electron (dust) mass, and Cd is the dust acoustic speed. [ABSTRACT FROM AUTHOR]

The quantum hydrodynamic model for plasmas is employed to derive a new dispersion relation for the dust acoustic wave. It is found that the dispersion property of the latter is significantly affected by quantum corrections. [ABSTRACT FROM AUTHOR]

The parametric decay instability of a dust ion acoustic wave into low-frequency electrostatic dust-lower-hybrid and electromagnetic shear Alfvén waves has been investigated in detail in an inhomogeneous cold quantum dusty plasma in the presence of external/ambient uniform magnetic field. The quantum magnetohydrodynamic model of plasmas with quantum effect arising through the Bohm potential and Fermi degenerate pressure has been employed in order to find the linear and nonlinear responses of the plasma particles for three-wave nonlinear coupling in a dusty magnetoplasma. A relatively high frequency electrostatic dust ion acoustic wave has been taken as the pump wave. It couples with two other low-frequency internal possible modes of the dusty magnetoplasma, viz., the dust-lower-hybrid and shear Alfvén waves. The nonlinear dispersion relation of the dust-lower-hybrid wave has been solved to obtain the growth rate of the parametric decay instability. The growth rate is at a maximum for a small value of the external magnetic field B0. It is noted that the growth rate is proportional to the unperturbed electron number density noe and is independent of inhomogeneity beyond Le=2 cm. An extraordinary growth rate is observed with the quantum effect. [ABSTRACT FROM AUTHOR]

The quantum dust-acoustic double layers (QDADLs) are studied in an unmagnetized, collisionless quantum dusty plasma whose constituents are the electrons, ions, and negatively/positively charged dust particles. By employing the quantum hydrodynamical equations and the reductive perturbation technique, a quantum extended Korteweg–de Vries equation is derived. A steady-state double-layer solution of the latter is presented by taking into account the quantum-mechanical effects. It is numerically found that both compressive and rarefactive QDADLs can exist only for positive charged dust particles under the condition ni0/ne0<1, where ni0(ne0) is the unperturbed number density of the ions (electrons). It is further noted that the formation of the compressive and the rarefactive double layers depends on the quantum plasma parameters. The relevance of the present investigation to the dust charge impurities in laser-solid interactions is discussed. In general, this study should be useful for the diagnostics of charged dust impurities in ultrasmall microelectronic and nanoelectronic components, as well as in astrophysical objects where charged dust particles are inherently present. [ABSTRACT FROM AUTHOR]

Quantum plasma oscillations are studied in a strongly magnetized, ultra-dense plasma with degenerate electrons and positrons. The dispersive role of electron and positron quantum effects on low frequency (in comparison to electron cyclotron frequency) shear electromagnetic wave is investigated by employing hydrodynamic formulation. In the presence of ions, the density balance changes, and the electromagnetic wave (with frequency lower than the ion cyclotron frequency) is shown to couple with electrostatic ion mode under certain conditions. For such low frequency waves, it is also seen that the contribution of electron and positron degeneracy pressure is dominant as compared to their diffraction effects. The results are analyzed numerically for illustrative purpose pointing out their relevance to the dense laboratory (e.g., super-intense laser-dense matter interactions) and astrophysical plasmas. [ABSTRACT FROM AUTHOR]