Quantum Diffraction Parameter Research Articles

Nonlinear analysis of ion‐acoustic solitary waves in an unmagnetized highly relativistic quantum plasma

AbstractThe present paper explores the dynamics of ion‐acoustic solitary waves (IASWs) within an unmagnetized, highly relativistic quantum plasma containing positive and negative ions alongside electrons, employing the quantum hydrodynamic model. The treatment accounts for the inertial characteristics of negative and positive ions, considering electrons as inertialess. The nonlinear nature of quantum IASWs is investigated through the derivation of the Korteweg–de Vries equation using the reductive perturbation method. The investigation highlights how wave propagation characteristics, whether compressive or rarefactive, are substantially modulated by several parameters, such as the quantum diffraction parameter , relativistic effects , equilibrium density , and ion mass ratio . The analysis identifies the existence of both slow and fast wave modes, heavily influenced by the relativistic parameters involved. Our findings have significant implications for the understanding of both laboratory and space plasmas, especially in contexts where negative ions are present.

Modulational instability of ion-acoustic waves in a dense quantum plasma

Modulational instability of ion-acoustic (IA) waves is investigated in an unmagnetized quantum plasma by adopting an equation of state for Fermi electron gas. To this end, a basic set of one-dimensional quantum hydrodynamic equations is reduced to a nonlinear Schrödinger equation using the reductive perturbation method. Quantum corrections are described using a nondimensional quantum parameter H proportional to the quantum diffraction parameter. Based on normalized electron temperature and chemical potential, new quantum criteria of modulational instability for IA waves are obtained and analyzed. Moreover, formation of rogue waves due to the modulational instability of IA waves and propagation of modulated IA packets in the form of bright and dark envelope solitons are examined for two different types of astrophysical plasma regions: white dwarf stars and warm dense matter.

Study of lump soliton structures in quantum electron‐positron‐ion magnetoplasma

AbstractSoliton theory is a very efficient and competent way to describe nonlinear features. Using Hirota bilinear method, we have obtained a lump soliton solution of the Kadomstev‐Petviashvili equation which is the reduced canonical form of the collisionless quantum electron‐positron‐ion magnetoplasma system. Due to its wide range of applications, the study of lump soliton structures is very much attractive and important. The amplitude of lump solitons is varied for different system parameters. During the analysis of the features of the lump solitons, it is found that the quantum diffraction parameter (He), statistical temperature ratio (σ), positrons number density (μp), magnetic intensity parameter (Ω) have a considerable impact on the lump solitons structures. Compressive as well as rarefactive lump soliton has been found during the investigation.

Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetized electron–positron–ion plasma

Abstract Nonlinear stable oscillations, solitary, periodic and shock waves in electron–positron–ion (EPI) quantum plasma in the presence of an external static magnetic field are reported. The Korteweg-de Vries-Burgers (KdVB) equation is derived by the reductive perturbation technique (RPT). The wave solution gives shock waves depending on various parameters as quantum diffraction parameter (β), electron and positron Fermi temperatures, and densities of the system species. Amplitude, polarity, speed, and width of wave solutions are remarkably modified by species densities, kinematic viscosity, and the Bohm potential. Existence of stable oscillation of ion-acoustic waves (IAWs) is shown by using the concept of phase plane analysis. Stability of wave solution is analysed by examining the Bohm potential effect. In the absence of dissipation, phase plane of the considered plasma system is analysed to discuss the existence of periodic wave solution. The results of this study could be helpful for comprehension of the wave features in dense quantum plasmas, like white dwarfs, laboratory plasma as interaction experiments of intense laser-solid matter and microelectronic devices.

Multistability and dynamical properties of quantum ion-acoustic flow

Multistability and dynamical properties of ion-acoustic flow are studied in a quantum plasma containing positive beam ions, positive ions and electrons. A four dimensional conservative dynamical system has been proposed for the considered plasma system and is analyzed by considering effects of Mach number and quantum diffraction parameter. Coexistences of multiple chaotic trajectories, chaotic with quasiperiodic and multiperiodic trajectories and chaotic with quasi-periodic and periodic trajectories for ion-acoustic waves are established. The results are suitable for application in comprehending the beam-plasma interaction and studying dynamics of coexisting features in extreme astrophysical plasmas, such as, neutron stars.

Average conservative chaos in quantum dusty plasmas.

We consider a hydrodynamic model of a quantum dusty plasma. We prove mathematically that the resulting dust ion-acoustic plasma waves present the property of being conservative on average. Furthermore, we test this property numerically, confirming its validity. Using standard techniques from the study of dynamical systems, as, for example, the Lyapunov characteristic exponents, we investigate the chaotic dynamics of the plasma and show numerically its existence for a wide range of parameter values. Finally, we illustrate how chaotic dynamics organizes in the parameter space for fixed values of the initial conditions, as the Mach number and the quantum diffraction parameter are continuously varied.

Multi-dimensional Instability of Dust Acoustic Waves in Magnetized Quantum Plasmas with Positive or Negative Dust

A survey of dust acoustic waves (DAWs) in magnetized dusty plasmas composed of negatively or positively charged mobile dust and intertialess quantum electrons as well as ions is presented. The Zakharov-Kuznetsov (ZK) equation is derived via reductive perturbation technique. The solitary wave solution of ZK equation is given and the numerical analysis of the solution with parameters in dust crystals is performed to study the properties of the DAWs with positive or negative dust. The multi-dimensional instability of these solitary waves is investigated via small-k perturbation method. The instability criterion and growth rate relying on obliqueness, the density ratio between ions and dust, the dust cyclotron frequency, the Fermi temperature ratio between electrons and ions, and quantum diffraction parameter are discussed for both cases. The implications of these results to the interior of white dwarf stars and magnetars have been briefly discussed.

Bernstein-Greene-Kruskal approach for the quantum Vlasov equation

The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables, similarly as in the solution of the Vlasov-Poisson system by means of the Bernstein-Greene-Kruskal method. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed and shown to be immediately integrable up to a recursive chain of quadratures in position space only. As it stands, the treatment of the self-consistent, Wigner-Poisson system is beyond the scope of the method, which assumes a given smooth time-independent external potential. Accuracy tests for the series expansion are also provided. Examples of anharmonic potentials are worked out up to a high order on the quantum diffraction parameter.

Sagdeev Potential Approach for Quantum Dust Ion Acoustic Waves in an Electron-Positron-Ion-Dusty plasma

Using the one-dimensional quantum hydrodynamic (QHD) model including the Poisson equation, Sagdeev’s pseudopotential process is used to explore the propagation features of dust ion acoustic (DIA) solitary waves in an unmagnetized electron-positron-ion-dusty (e-p-i-d) quantum plasma. The asymptotic expansion is used to achieve the pseudopotential function for small values of the parameter H of quantum diffraction. QDIA solitary wave’s existence domain is explored in terms of real Mach number boundaries. The numerical modeling results demonstrate that the dust grains can affect not just the amplitude and width, but also the soliton’s domain of existence. The impacts of the quantum diffraction parameter on the soliton width are also addressed. It is also noted that the positron density may influence the propagation of the wave.

Dust-acoustic cnoidal waves in a magnetized quantum dusty plasma

ABSTRACT An investigation of nonlinear dust-acoustic cnoidal waves in a magnetized quantum dusty plasma consisting of inertial dust, inertialess electrons and ions is presented. The Korteweg–de Vries (KdV) equation is obtained by employing reductive perturbation technique and analytical solution of KdV equation is derived by employing the Sagdeev pseudopotential approach. Numerical analysis of the solution is performed to study the characteristics of the dust-acoustic cnoidal waves. In this study, positive (negative) potential dust-acoustic cnoidal waves are observed for the case of positive (negative) dust grains. The influence of various parameters such as quantum diffraction parameter of electrons and ions, magnetic field strength, obliqueness, concentration of ions and Fermi temperature (electrons and ions) has been studied. In the limiting case, dust-acoustic cnoidal wave solution is found to reduce to solitary wave solution.

Nonplanar ion acoustic waves in collisional quantum plasma

The dynamics of nonlinear ion acoustic waves (IAWs) is studied in homogeneous, unmagnetized, collisional quantum plasma consisting of electrons and ions in bounded nonplanar (cylindrical/spherical) geometries. By using the reductive perturbation method, the nonplanar Kakutani and Kawahara equation is derived to investigate the nonlinear quantum IAW profiles. The dissipation is introduced by taking into account the collision among the plasma constituents in presence of quantum diffraction effect. Numerically, the effects of various plasma parameters, such as, the collisional parameter (η), the quantum diffraction parameter H, have been examined on the propagation of nonplanar IAW structures in quantum plasma. It is shown that in nonplanar geometry, plasma parameters play a vital role on the basic features of nonlinear structures (viz. amplitude, width, speed, and so on). It is also found that the properties of IAW structures in nonplanar geometry significantly differ from those in planar geometry.

Magnetosonic solitons in dense astrophysical plasmas with exchange-correlation potential effects

Low frequency magnetosonic waves propagation in dense astrophysical electron-ion plasmas are studied in the presence of exchange-correlation potential effects of degenerate electrons. Two fluid quantum magnetohydrodynamic model (QMHD) is employed and quantum effects like temperature degeneracy, Bohm potential and exchange-correlation effects are taken into account the momentum equation of degenerate electrons fluid. The Korteweg-de Vries (KdV) equation for nonlinear magnetosonic waves is derived by employing reductive perturbation method. It is found that the phase velocity of the magnetosonic wave is enhanced in dense plasmas in the presence of exchange-correlation force in the model. The exchange-correlation force due to degenerate electrons also effects on the amplitude and width of the magnetosonic soliton in quantum plasmas, where both positive and negative polarity structures of magnetosonic waves are formed depending on the numerical value of quantum diffraction parameter (i.e., less than or greater than 6). These single pulse structures move with speed greater (for positive polarity structure) or less (for negative polarity structure) than the magnetosonic wave phase speed, respectively. The numerical plots are also illustrated by choosing the values of dense plasma parameters exist in compact stars already published in the literature.

Small amplitude waves and linear firehose and mirror instabilities in rotating polytropic quantum plasma

The small amplitude quantum magnetohydrodynamic (QMHD) waves and linear firehose and mirror instabilities in uniformly rotating dense quantum plasma have been investigated using generalized polytropic pressure laws. The QMHD model and Chew–Goldberger–Low (CGL) set of equations are used to formulate the basic equations of the problem. The general dispersion relation is derived using normal mode analysis which is discussed in parallel, transverse, and oblique wave propagations. The fast, slow, and intermediate QMHD wave modes and linear firehose and mirror instabilities are analyzed for isotropic MHD and CGL quantum fluid plasmas. The firehose instability remains unaffected while the mirror instability is modified by polytropic exponents and quantum diffraction parameter. The graphical illustrations show that quantum corrections have a stabilizing influence on the mirror instability. The presence of uniform rotation stabilizes while quantum corrections destabilize the growth rate of the system. It is also observed that the growth rate stabilizes much faster in parallel wave propagation in comparison to the transverse mode of propagation. The quantum corrections and polytropic exponents also modify the pseudo-MHD and reverse-MHD modes in dense quantum plasma. The phase speed (Friedrichs) diagrams of slow, fast, and intermediate wave modes are illustrated for isotropic MHD and double adiabatic MHD or CGL quantum plasmas, where the significant role of magnetic field and quantum diffraction parameters on the phase speed is observed.

Effect of doping on amplitude modulation of space-charge wave in semiconductor quantum plasma

To describe the modulational instability of space-charge waves in an n-type compensated semiconductor plasma, a nonlinear Schrodinger equation has been derived by using quantum hydrodynamical model and standard multiple scale perturbation technique. It has been shown that compensation factor (i.e. relative proportion of donor, acceptor and intrinsic carrier concentrations) and quantum diffraction parameter play important role in generating bright and dark envelope solitons within the semiconductor. Instability growth rate is also found to depend sensitively on the compensation factor and quantum diffraction parameter. From the linear dispersion relation it has been found that inclusion of quantum parameter gives rise to two new wave modes of purely quantum origin. Further the effect of compensation factor and quantum diffraction parameter on the linear dispersion characteristics has been analyzed. It has also been found that due to parabolicity of conduction band the group velocity of space-charge wave becomes dependent on compensation factor and quantum diffraction parameter.

Linear and nonlinear dust ion acoustic solitary waves in a quantum dusty electron-positron-ion plasma

The behavior of linear and nonlinear dust ion acoustic (DIA) solitary waves in an unmagnetized quantum dusty plasma, including inertialess electrons and positrons, ions, and mobile negative dust grains, are studied. Reductive perturbation and Sagdeev pseudopotential methods are employed for small and large amplitude DIA solitary waves, respectively. A minimum value of the Mach number obtained for the existence of solitary waves using the analytical expression of the Sagdeev potential. It is observed that the variation on the values of the plasma parameters such as different values of Mach number M, ion to electron Fermi temperature ratio σ, and quantum diffraction parameter H can lead to the creation of compressive solitary waves.

Arbitrary amplitude solitary waves in an unmagnetized quantum pair-ion plasma

Propagation of arbitrary amplitude solitary waves is investigated in an unmagnetized quantum pair-ion plasma through the usage of Sagdeev pseudopotential approach in the framework of quantum hydrodynamics model. Bohm potential is elucidated to have significant impact on the structure of solitary wave. We would like to demonstrate that the regions of stability for the solitary waves of this quantum plasma system are well determined by studying the phase portrait. Analytical calculations are employed to simplify the basic equations, which are then studied numerically. The numerical analysis of Sagdeev potential for small value of quantum diffraction parameter(H) shows that for such plasma, there exists only compressive solitons. The effect of different plasma parameters on the solitonic structure are traced .

Study of possible chaotic, quasi-periodic and periodic structures in quantum dusty plasma

Existence of chaotic, quasi-periodic, and periodic structures of dust-ion acoustic waves is studied in quantum dusty plasmas through dynamical system approach. A system of coupled differential equations is derived from the fluid model and subsequently, variational matrix is obtained. The characteristic equation is obtained at the equilibrium point, and the behavior of nonlinear waves is studied numerically using Runge-Kutta method. The behavior of the dynamical system changes significantly when any of plasma parameters, such as the dust concentration parameter, temperature ratio, or the quantum diffraction parameter, is varied. The change of the characteristic of solution of the system is extensively studied. It is found that the system changes its behavior from chaotic pattern to limit cycle behavior.

Low frequency waves and gravitational instability in homogeneous magnetized gyrotropic quantum plasma

In this work, the low frequency waves and gravitational (Jeans) instability of a homogeneous gyrotropic, magnetized, quantum plasma is investigated using the quantum magnetohydrodynamic and Chew-Goldberger-Low fluid models. An analytical dispersion relation for the considered system is obtained solving the linearized perturbations equations employing the Fourier transformation. The onset criterion of the “firehose” instability is retained in parallel propagation, which is unaffected due to the presence of quantum corrections. The gravitational mode modified by the quantum corrections is obtained separately along with the “firehose” mode. In perpendicular propagation, the quantum diffraction term is coupled with the Jeans and Alfven modes whereas in parallel propagation, the Alfven mode does not contribute to the dispersion characteristics as it leads to the “firehose” instability criterion in terms of quantum pressure anisotropy. The stabilizing influences of the quantum diffraction parameter and magnetic field on the growth rates of Jeans instability are examined. It is observed that the growth rate stabilizes much faster in transverse mode due to Alfven stabilization as compared to the longitudinal mode of propagation.

Head-on collisions of two types of dust-acoustic solitons in a magnetized quantum plasma

The head-on collisions of dust-acoustic waves (DAWs) in a dense magnetized quantum dusty plasma are investigated by using the extended version of the Poincare–Lighthill–Kuo (PLK) method. We discuss the theoretical predictions as regards the existence of compressive and rarefactive DAWs in the model. We also observe that, in the generic case, collisions are possible among the same polarity solitons, whereas in the special case, collisions are possible among the same or opposite polarity solitons. It is also observed that the phase shifts are significantly affected by the quantum diffraction parameter and the dust cyclotron frequency. The interesting observations of this manuscript are that the waves reach a maximum amplitude which is a superposition of the initial amplitude and they suffer a time delay during their collision. Our results may be useful in space and laboratory plasmas as well as in plasma applications.

Characteristic of ion acoustic shock waves in a dissipative quantum pair plasma with dust particulates

The behavior of quantum dust ion-acoustic (QDIA) shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied, using a quantum hydrodynamic model (QHD). The effect of dissipation due to the viscosity of ions is taken into account. The propagation of small but finite amplitude QDIA shocks is governed by the Kortoweg-de Vries-Burgers (KdVB) equation. The existence regions of oscillatory and monotonic shocks will depend on the quantum diffraction parameter (H) and dust density (d) as well as dissipation parameter (η0). The effect of plasma parameters (d,H,η0), on these structures is investigated. Results indicate that the thickness and height of monotonic shocks; oscillation amplitude of the oscillatory shock wave and it’s wavelength effectively are affected by these parameters. Additionally, the possibility of propagation of both compressive and rarefactive shocks is investigated. It is found that depending on some critical value of dust density (dc), which is a function of H, compressive and rarefactive shock waves can’t propagate in model plasma. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.