Nonlinear Landau damping of wave envelopes in a quantum plasma

Abstract

The nonlinear theory of Landau damping of electrostatic wave envelopes (WEs) is revisited in a quantum electron-positron (EP) pair plasma. Starting from a Wigner-Moyal equation coupled to the Poisson equation and applying the multiple scale technique, we derive a nonlinear Schrödinger (NLS) equation which governs the evolution of electrostatic WEs. It is shown that the coefficients of the NLS equation, including the nonlocal nonlinear term, which appears due to the resonant particles having group velocity of the WEs, are significantly modified by the particle dispersion. The effects of the quantum parameter H (the ratio of the plasmon energy to the thermal energy densities), associated with the particle dispersion, are examined on the Landau damping rate of carrier waves, as well as on the modulational instability of WEs. It is found that the Landau damping rate and the decay rate of the solitary wave amplitude are greatly reduced compared to their classical values (H = 0).

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

“…In this case, the quantum contributions are only due to the background distribution of electrons being a Fermi-Dirac distribution at zero temperature rather than a Maxwellian one. Though, the coefficients of the NLS equation will be somewhat modified, however, the results will be similar to some previous works [10], because the resonance velocity is only the group velocity. The regimes of k can be sort of 0 < k 0.59 for H ∼ 1.…”

“…Starting from the Wigner-Moyal equation coupled to the Poisson equation and using the multiple scale expansion technique we have derived a modified NLS equation with a nonlocal nonlinearity. It is shown that in contrast to classical and semiclassical results [9,10], both the local and nonlocal terms of the NLS equation get modified due to the multi-plasmon processes if the dimensionless quantum parameter H = ω p /mv 2 F or the dimensionless wave number k/mv F is not too small. In the regime of short wavelengths such that multi-plasmon processes are allowed, but still k < k cr such that one-plasmon resonances are forbidden, it is found that the three-plasmon processes play the dominant role for wave damping due to wave-particle interaction.…”

“…In what follows, we numerically analyze the properties of Ω r and Γ for different values of the carrier wave number k which correspond to, especially the modest and strong quantum regimes as discussed before (Since the semi-classical results are similar to the previous works [10], we skip those discussion in the present work). The results are displayed in Figs.…”

“…The latter, in some sense, corresponds to a weak quantum regime. In this situation, only the group velocity resonance becomes significant as in classical or semiclassical plasmas [9,10]. Thus, from the consequences of Fig.…”

“…Generalizing this setup to the more realistic case of propagating wave packet, the effects of group velocity resonances enter the picture [8][9][10]. In this context, the nonlinear theory of Landau damping due to group velocity resonance of wave envelopes has been developed in both classical [9] and semiclassical plasmas [10]. However, it has also been shown that going beyond the linear theory, wave damping can also take place due to multi-plasmon resonances [11,12], which can be present even for an infinite plane wave.…”