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We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schrodinger-like equations. The coupled set of equations is then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multidimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, beta proportional to lambda(C)n(0)(1/3) (where lambda(C) is the reduced Compton wavelength and n(0) is the particle number density) associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at n(0) similar to 10(30)cm(-3) to unstable (stable) ones at higher densities, i.e., n(0) greater than or similar to 7 x 10(33). It is also found that the higher the values of n(0), the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multidimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs and/or pre-Supernova stars.

A theoretical model is presented to investigate the existence, formation, and possible realization of nonlinear envelope ion acoustic solitary waves which accompany collisionless electron-positron-ion plasmas with high-energy electrons and positrons (represented by kappa distribution). By employing the reductive perturbation method, the hydrodynamic model and the Poisson equation are reduced to nonlinear Schrodinger equation. The effects of the superthermal parameters, as well as ion-to-electron temperature ratio on the propagation and stability of the envelope solitary waves are examined. The superthermal parameters (ion-to-electron temperature ratio) give rise to instability (stability) of the solitary excitations, since the instability window is strongly modified. Finally, the present results should elucidate the excitation of the nonlinear ion-acoustic solitary wave packets in superthermal electron-positron-ion plasmas, particularly in interstellar medium.

The nonlinear propagation of two-dimensional (2D) quantum ion-acoustic waves (QIAWs) is studied in a quantum electron–ion plasma. By using a 2D quantum hydrodynamic model and the method of multiple scales, a new set of coupled nonlinear partial differential equations is derived which governs the slow modulation of the 2D QIAW packets. The oblique modulational instability (MI) is then studied by means of a corresponding nonlinear Schrödinger equation derived from the coupled nonlinear partial differential equations. It is shown that the quantum parameter H (ratio of the plasmon energy density to Fermi energy) shifts the MI domains around the kθ -plane, where k is the carrier wave number and θ is the angle of modulation. In particular, the ion-acoustic wave (IAW), previously known to be stable under parallel modulation in classical plasmas, is shown to be unstable in quantum plasmas. The growth rate of the MI is found to be quenched by the obliqueness of modulation. The modulation of 2D QIAW packets along the wave vector k is shown to be described by a set of Davey–Stewartson-like equations. The latter can be studied for the 2D wave collapse in dense plasmas. The predicted results, which could be important to look for stable wave propagation in laboratory experiments as well as in dense astrophysical plasmas, thus generalize the theory of MI of IAW propagations both in classical and quantum electron–ion plasmas.

The dispersion relation for the dust acoustic wave (DAW) in an unmagnetized dusty plasma cylindrical waveguide is derived, accounting for strong electrostatic interactions between charged dust grains. It is found that the boundary effect limits the radial extent of the DAW. The present result should be helpful for understanding the frequency spectrum of the DAW in a dusty plasma waveguide with strongly coupled charged dust grains.

This paper focuses on the progress in understanding the shielding around a test charge in the presence of ion-acoustic waves in multispecies plasmas, whose constituents are positive ions, two negative ions, and Boltzmann distributed electrons. By solving the linearized Vlasov equation with Poisson equation, the Debye-Huckel screening potential and wakefield (oscillatory) potential distribution around a test charge particle are derived. It is analytically found that both the Debye-Huckel potential and the wakefield potential are significantly modified due to the presence of two negative ions. The present results might be helpful to understand and to form new materials from plasmas containing two negative ions such as Xe(+) - F(-) - SF(6)(-) and Ar(+) - F(-) - SF(6)(-) plasmas, as well as to tackle extension of the test charge problem in multinegative ions' coagulation/agglomeration.

Three-dimensional ion-acoustic envelope soliton excitations in electron-positron-ion magnetoplasmas are interpreted. This is accomplished through the derivation of three-dimensional nonlinear Schrodinger equation, where the nonlinearity is balancing with the dispersive terms. The latter contains both an external magnetic field besides the usual plasma parameter effects. Based on the balance between the nonlinearity and the dispersion terms, the regions for possible envelope solitons are investigated indicating that new regimes for modulational instability of envelope ion-acoustic waves could be obtained, which cannot exist in the unmagnetized case. This will allow us to establish additional new regimes, different from the usual unmagnetized plasma, for envelope ion-acoustic waves to propagate in multicomponent plasma that may be observed in space or astrophysics.

The influence of the intrinsic spin of electrons on the propagation of circularly polarized waves in a magnetized plasma is considered. New eigenmodes are identified, one of which propagates below the electron cyclotron frequency, one above the spin-precession frequency, and another close to the spin-precession frequency. The latter corresponds to the spin modes in ferromagnets under certain conditions. In the non-relativistic motion of electrons, the spin effects become noticeable even when the external magnetic field B₀ is below the quantum critical magnetic field strength, i.e. B₀ < B_Q = 4.4138 × 10⁹T and the electron density satisfies n₀ ≫ n_c ≃ 10³²m⁻³. The importance of electron spin (paramagnetic) resonance (ESR) for plasma diagnostics is discussed.

A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin-1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin-1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.

The excitation of electrostatic wakefields in a magnetized spin quantum plasma by the classical and the spin-induced ponderomotive force (CPF and SPF, respectively) due to whistler waves is reported. The nonlinear dynamics of the whistlers and the wakefields is shown to be governed by a coupled set of nonlinear Schrodinger and driven Boussinesq-like equations. It is found that the quantum force associated with the Bohm potential introduces two characteristic length scales, which lead to the excitation of multiple wakefields in a strongly magnetized dense plasma (with a typical magnetic field strength B(0)greater than or similar to 10(9) T and particle density n(0)greater than or similar to 10(36) m(-3)), where the SPF strongly dominates over the CPF. In other regimes, namely, B(0)less than or similar to 10(8) T and n(0)less than or similar to 10(35) m(-3), where the SPF is comparable to the CPF, a plasma wakefield can also be excited self-consistently with one characteristic length scale. Numerical results reveal that the wakefield amplitude is enhanced by the quantum tunneling effect; however, it is lowered by the external magnetic field. Under appropriate conditions, the wakefields can maintain high coherence over multiple plasma wavelengths and thereby accelerate electrons to extremely high energies. The results could be useful for particle acceleration at short scales, i.e., at nanometer and micrometer scales, in magnetized dense plasmas where the driver is the whistler wave instead of a laser or a particle beam.

The nonlinear propagation of electromagnetic (EM) electron-cyclotron waves (whistlers) along an external magnetic field, and their modulation by electrostatic small but finite amplitude ion-acoustic density perturbations are investigated in a uniform quantum plasma with intrinsic spin of electrons. The effects of the quantum force associated with the Bohm potential and the combined effects of the classical as well as the spin-induced ponderomotive forces (CPF and SPF, respectively) are taken into consideration. The latter modify the local plasma density in a self-consistent manner. The coupled modes of wave propagation is shown to be governed by a modified set of nonlinear Schrödinger-Boussinesq-like equations which admit exact solutions in form of stationary localized envelopes. Numerical simulation reveals the existence of large-scale density fluctuations that are self-consistently created by the localized whistlers in a strongly magnetized high density plasma. The conditions for the modulational instability (MI) and the value of its growth rate are obtained. Possible applications of our results, e.g., in strongly magnetized dense plasmas and in the next generation laser-solid density plasma interaction experiments are discussed.