Nonlinear dynamics of ion acoustic waves in quantum pair-ion plasmas

Abstract: Abstract Multistability and chaotic scenario of arbitrary amplitude ion-acoustic waves in a quantum plasma consisting of negative ions, positive ions and electrons are investigated. The normalized basic equations are transformed to a four dimensional conservative dynamical system by introducing a travelling wave variable. Stability of the fixed points for the corresponding linearized system is briefly examined. Chaotic and quasi-periodic features of the arbitrary amplitude ion-acoustic waves are discussed using effective tools, viz. phase orientations, time series graph and graphs of Lyapunov exponents. Multistability phenomena is established with the help of phase spaces, largest Lyapunov exponents and cross-section of basins of attraction. The chaotic phenomena is further verified by 0−1 test. Results of this study can be applied in understanding dynamical phenomena of arbitrary amplitude ion-acoustic waves in quantum pair-ion plasmas.

Abstract: Abstract The propagation characteristics of solitary wave in a degenerate plasma in the presence of Landau-quantised magnetic field and heavy negative ion are studied. The nature of solitary wave in such plasma under the influence of magnetic quantisation and the concentration of both electrons and negative ions, as well as in the presence of degenerate temperature, are studied with the help of a time-independent analytical scheme of the solution of Zakharov–Kuznetsov equation. The electron density, as well as the magnetic quantisation parameter, has an outstanding effect on the features of solitary wave proliferation in such plasma. Interestingly, for any fixed electron density, the magnetic quantisation parameter has an equal control on the maximum height and dispersive properties of the solitary wave. Toward higher temperatures and higher magnetic fields, the width of the solitary wave decreases. For a lower magnetic field, the maximum amplitude of the solitary wave decreases rapidly at higher values of degenerate temperature and negative ion concentration; however, at a lower value of degenerate temperature, the maximum amplitude increases with increasing negative ion concentration.

Abstract: Lane formation dynamics in externally driven pair-ion plasma (PIP) particles is studied in the presence of external magnetic field using Langevin dynamics (LD) simulation. The phase diagram obtained distinguishing the no-lane and lane states is systematically determined from a study of various Coulomb coupling parameter values. A peculiar lane formation-disintegration parameter space is identified; lane formation area extended to a wide range of Coulomb coupling parameter values is observed before disappearing to a mixed phase. The different phases are identified by calculating the order parameter. This and the critical parameters are calculated directly from LD simulation. The critical electric field strength value above which the lanes are formed distinctly is obtained, and it is observed that in the presence of the external magnetic field, the PIP system requires a higher value of the electric field strength to enter into the lane formation state than that in the absence of the magnetic field. We further find out the critical value of electric field frequency beyond which the system exhibits a transition back to the disordered state and this critical frequency is found as an increasing function of the electric field strength in the presence of an external magnetic field. The movement of the lanes is also observed in a direction perpendicular to that of the applied electric and magnetic field directions, which reveals the existence of the electric field drift in the system under study. We also use an oblique force field as the external driving force, both in the presence and absence of the external magnetic field. The application of this oblique force changes the orientation of the lane structures for different applied oblique angle values.

Abstract: One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.

Abstract: The behavior of the electrons in a dense electron gas is analyzed quantum-mechanically by a series of canonical transformations. The usual Hamiltonian corresponding to a system of individual electrons with Coulomb interactions is first re-expressed in such a way that the long-range part of the Coulomb interactions between the electrons is described in terms of collective fields, representing organized "plasma" oscillation of the system as a whole. The Hamiltonian then describes these collective fields plus a set of individual electrons which interact with the collective fields and with one another via short-range screened Coulomb interactions. There is, in addition, a set of subsidiary conditions on the system wave function which relate the field and particle variables. The field-particle interaction is eliminated to a high degree of approximation by a further canonical transformation to a new representation in which the Hamiltonian describes independent collective fields, with ${n}^{\ensuremath{'}}$ degrees of freedom, plus the system of electrons interacting via screened Coulomb forces with a range of the order of the inter electronic distance. The new subsidiary conditions act only on the electronic wave functions; they strongly inhibit long wavelength electronic density fluctuations and act to reduce the number of individual electronic degrees of freedom by ${n}^{\ensuremath{'}}$. The general properties of this system are discussed, and the methods and results obtained are related to the classical density fluctuation approach and Tomonaga's one-dimensional treatment of the degenerate Fermi gas.

Abstract: It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schroedinger-Poisson system, in which the Schroedinger equation contains a new nonlinearity. For the case of a zero-temperature one-dimensional electron gas, this additional nonlinearity is of the form vertical bar {Psi} vertical bar{sup 4}. In the long-wavelength limit, the results obtained from the effective Schroedinger-Poisson system are in agreement with those of the Wigner-Poisson system. The reduced model is further used to describe the stationary states of a quantum electron gas and the two-stream instability.

Abstract: Accurate x-ray scattering techniques to measure the physical properties of dense plasmas have been developed for applications in high energy density physics. This class of experiments produces short-lived hot dense states of matter with electron densities in the range of solid density and higher where powerful penetrating x-ray sources have become available for probing. Experiments have employed laser-based x-ray sources that provide sufficient photon numbers in narrow bandwidth spectral lines, allowing spectrally resolved x-ray scattering measurements from these plasmas. The backscattering spectrum accesses the noncollective Compton scattering regime which provides accurate diagnostic information on the temperature, density, and ionization state. The forward scattering spectrum has been shown to measure the collective plasmon oscillations. Besides extracting the standard plasma parameters, density and temperature, forward scattering yields new observables such as a direct measure of collisions and quantum effects. Dense matter theory relates scattering spectra with the dielectric function and structure factors that determine the physical properties of matter. Applications to radiation-heated and shock-compressed matter have demonstrated accurate measurements of compression and heating with up to picosecond temporal resolution. The ongoing development of suitable x-ray sources and facilities will enable experiments in a wide range of research areas including inertial confinement fusion,more » radiation hydrodynamics, material science, or laboratory astrophysics.« less