Exchange corrections in a low-temperature plasma

Kinetic studies of exchange-correlation effect on the collective excitations of warm dense plasmas

The exchange-correlation of electrons, as a fundamental effect in quantum mechanics, plays an important role in the collective motions of electrons in warm dense matter. We derive the quantum kinetic equations based on the time-dependent Kohn-Sham equation. By using a temperature-dependent functional for the exchange correlation, the excitations of electrostatic waves are analyzed under the adiabatic local density approximation (ALDA). We find that the influences of the exchange-correlation effect on the group velocity of electrostatic waves can be as high as 10% when both the density and temperature are low. Moreover, we also compare the results obtained by using ALDA-based kinetic theory, exchange kinetic theory, and quantum hydrodynamics, and discuss the differences among them.

Nonlinear excitations of magnetosonic solitary waves and their chaotic behavior in spin-polarized degenerate quantum magnetoplasma

The quantum hydrodynamic model is used to study the nonlinear propagation of small amplitude magnetosonic solitons and their chaotic motions in quantum plasma with degenerate inertialess spin-up electrons, spin-down electrons, and classical inertial ions. Spin effects are considered via spin pressure and macroscopic spin magnetization current, whereas the exchange effects are considered via adiabatic local density approximation. By applying the reductive perturbation method, the Korteweg-de Vries type equation is derived for small amplitude magnetosonic solitary waves. We present the numerical predictions about the conservative system's total energy in spin-polarized and usual electron-ion plasma and observed low energy in spin-polarized plasma. We also observe numerically that the soliton characteristics are significantly affected by different plasma parameters such as soliton phase velocity increases by increasing quantum statistics, magnetization energy, exchange effects, and spin polarization density ratio. Moreover, it is independent of the quantum diffraction effects. We have analyzed the dynamic system numerically and found that the magnetosonic solitary wave amplitude and width are getting larger as the quantum statistics and spin magnetization energy increase, whereas their amplitude and width decrease with increasing spin concentration. The wave width increases for high values of quantum statistic and exchange effects, while their amplitude remains constant. Most importantly, in the presence of external periodic perturbations, the periodic solitonic behavior is transformed to quasiperiodic and chaotic oscillations. It is found that a weakly chaotic system is transformed to heavy chaos by a small variation in plasma parameters of the perturbed spin magnetosonic solitary waves. The work presented is related to studying collective phenomena related to magnetosonic solitary waves, vital in dense astrophysical environments such as pulsar magnetosphere and neutron stars.

Effects of group velocity and multiplasmon resonances on the modulation of Langmuir waves in a degenerate plasma

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schrödinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multiplasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multiplasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where ℏk∼mv_{F} with ℏ denoting the reduced Planck's constant, m the electron mass, and v_{F} the Fermi velocity; however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multiplasmon effects are forbidden.

Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons

Nonlinear ion-acoustic waves are analyzed in a nonrelativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite-temperature quantum kinetic theory in the long-wavelength limit. The dispersion relation of the obliquely propagating electrostatic waves in magnetized quantum plasma with arbitrary degeneracy of electrons is obtained. Using the reductive perturbation method, the corresponding Zakharov-Kuznetsov equation is derived, describing obliquely propagating two-dimensional ion-acoustic solitons in a magnetized quantum plasma with degenerate electrons having an arbitrary electron temperature. It is found that in the dilute plasma case only electrostatic potential hump structures are possible, while in dense quantum plasma, in principle, both hump and dip soliton structures are obtainable, depending on the electron plasma density and its temperature. The results are validated by comparison with the quantum hydrodynamic model including electron inertia and magnetization effects. Suitable physical parameters for observations are identified.