Classical and quantum plasmas

Instability analysis of spin-electron-acoustic waves and the appearance of separated spin electron cyclotron mode in spin-polarized magnetized quantum plasma

Linear and nonlinear characteristics of electrostatic waves are studied in a magnetized plasma consisting of spin-up (n_{↑}) and spin-down (n_{↓}) state populations with uniformly distributed static ions in the background. The linear analysis shows the existence of four modes. One of these modes, termed the separated spin electron cyclotron wave, is found to be due to the separated spin populations. The Zakharov-Kuznetsov equation is derived by the reductive perturbation technique. The instability growth rate γ is obtained from the same equation. It is observed that the magnetized spin quantum plasma admits rarefactive soliton with constant amplitude but increasing width with the increasing strength of the applied magnetic field. It has also been observed that the amplitude of soliton decreases and its width increases with the increasing values of polarization ratio κ. The unstable region expands with the increase in polarization ratio and contracts with the increased plasma number density and magnetic-field strength. The (growth rate) γ of instability reduces by increasing the κ and is increasing when the density of the plasma and the strength of the magnetic field increasing. The model developed in this work finds its scope in studying degenerate electron gas and astrophysical systems such as pulsar magnetosphere and neutron stars.

Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma

A theoretical investigation has been carried out to examine the ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system containing inertialess ultra-relativistically degenerate electrons, and inertial non-relativistic positively charged heavy and light ions. The Burgers equation is derived by employing the reductive perturbation method. It can be seen that under the consideration of non-relativistic positively charged heavy and light ions, the plasma model only supports the positive electrostatic shock structure. It is also observed that the charge state and number density of the non-relativistic heavy and light ions enhance the amplitude of IASHWs, and the steepness of the shock profile is decreased with ion kinematic viscosity. The findings of our present investigation will be helpful in understanding the nonlinear propagation of IASHWs in white dwarfs and neutron stars.

Binding energy levels of a slowly moving ion in quantum plasmas

Electrostatic potential of a slowly moving ion in quantum plasmas is studied. This potential is composed of the Debye-Hückel potential and the wake potential. The near-field-wake potential is found. The binding energy levels of one-electron bound states of the ion are calculated by use of the Ritz variation method. The trial wave function contains three variational parameters. The presence of the wake field splits the binding energy levels. This effect is analogous to the Zeeman effect. The removal of the degeneracy of binding energy levels is influenced by the speed of ion and the number density of electrons. Compared with binding energy levels of a free ion, some binding energy levels of a moving ion in quantum plasmas are "pushed up."

Vortical dynamics of spinning quantum plasmas: helicity conservation

It is shown that a vorticity, constructed from the spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that obeys the standard vortex dynamics. Expressions for the quantum or spin vorticity and for the resulting generalized helicity invariant are derived. Reduction of the rather complex spinning quantum system to a well known and highly investigated classical form opens familiar channels for the delineation of physics peculiar to dense plasmas spanning solid state to astrophysical objects. A simple example is worked out to show that the magnetics of a spinning plasma can be much richer than that of the corresponding classical system.

Dispersion in a thermal plasma including arbitrary degeneracy and quantum recoil

The longitudinal response function for a thermal electron gas is calculated including two quantum effects exactly, degeneracy, and the quantum recoil. The Fermi-Dirac distribution is expanded in powers of a parameter that is small in the nondegenerate limit and the response function is evaluated in terms of the conventional plasma dispersion function to arbitrary order in this parameter. The infinite sum is performed in terms of polylogarithms in the long-wavelength and quasistatic limits, giving results that apply for arbitrary degeneracy. The results are applied to the dispersion relations for Langmuir waves and to screening, reproducing known results in the nondegenerate and completely degenerate limits, and generalizing them to arbitrary degeneracy.

Macroscopic description for the quantum Weibel instability

The Weibel instability in the quantum plasma case is treated by means of a fluidlike (moments) approach. Quantum modifications to the macroscopic equations are then identified as effects of the first or second kind. Quantum effects of the first kind correspond to a dispersive term, similar to the Bohm potential in the quantum hydrodynamic equations for plasmas. Effects of the second kind are due to the Fermi statistics of the charge carriers and can become the dominant influence for strong degeneracy. The macroscopic dispersion relations are of higher order than those for the classical Weibel instability. This corresponds to the presence of a cutoff wave number even for the strong temperature anisotropy case.

Ferromagnetic behavior in magnetized plasmas

We consider a low-temperature plasma within a newly developed magnetohydrodynamic fluid model. In addition to the standard terms, the electron spin, quantum particle dispersion, and degeneracy effects are included. It turns out that the electron spin properties can give rise to ferromagnetic behavior in certain regimes. If additional conditions are satisfied, a homogeneous magnetized plasma can even be unstable. This happens in the low-temperature high-density regime, when the magnetic properties associated with the spin can overcome the stabilizing effects of the thermal and Fermi pressure, to cause a Jeans-like instability.

Fluid turbulence in quantum plasmas

Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.