Modulational interactions in quantum plasmas

Abstract

A formalism for treating modulational interactions of electrostatic fields in collisionless quantum plasmas is developed, based on the kinetic Wigner-Poisson model of quantum plasma. This formalism can be used in a range of problems of nonlinear interaction between electrostatic fields in a quantum plasma, such as development of turbulence, self-organization, as well as transition from the weak turbulent state to strong turbulence. In particular, using this formalism, we obtain the kinetic quantum Zakharov equations, that describe nonlinear coupling of high frequency Langmuir waves to low frequency plasma density variations, for cases of non-degenerate and degenerate plasma electrons.

Exchange corrections in a low-temperature plasma

“…Thus we conclude that the DFT exchange potential Eq. (13) are in qualitative agreement with the results obtained here, but that the numerical accuracy is better for Langmuir waves than for ion-acoustic waves.…”

“…Refs. [11,19,20,22]) computed from DFT is V x = 0.985(3π 2 ) 2/3 4πh 2 ω 2 e m e v 2 F n n 0 1/3 (13) that has been used for low-frequency ion-acoustic phenomena (e.g. Refs.…”

Short-wavelength soliton in a fully degenerate quantum plasma

“…Based on the kinetic Wigner-Poisson model of quantum plasma, the kinetic quantum Zakharov equations that describe nonlinear coupling of Langmuir waves to low frequency plasma density variations for cases of non-degenerate and degenerate plasma electrons were obtained in Refs. [13,14]. On the other hand, it is the QHD model that is most often used to study nonlinear phenomena, in particular, nonlinear waves and solitons in quantum plasmas [8,15].…”

Modulational and filamentational instabilities of a monochromatic Langmuir pump wave in quantum plasmas

“…These equations are valid under the set of assumptions in Ref. 56, among them the assumption of the equilibrium particle distributions. For the cases with nonequilibrium particle distributions, or studying the influence of nonlinear Landau damping on the modulational process, etc., in quantum plasma, one has to use the general quantum-corrected nonlinear equation with quantum-corrected effective cubic nonlinearity.…”