Quantum corrections to nonlinear ion acoustic wave with Landau damping

Abstract

Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to presence of Landau damping terms has been calculated assuming the Landau damping parameter α1 = me/mi to be of the same order of the quantum parameter Q = 2 /(24m 2 c 2 s L 2 ). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.

Nonlinear Landau damping of wave envelopes in a quantum plasma

“…In what follows, we consider the harmonic modes with n = 3 and l = 0 from Eqs. (7) and (8). Then using the relations (15) and (16) we obtain a set of reduced equations, which after use of the Fourier-Laplace transforms with respect to η and σ and the initial condition (10), yieldf…”

“…Finally, considering the terms for n = 3 and l = 1 from Eqs. (7) and (8), and adopting the same procedure as in Ref. 4 we obtain (after rescaling with ζ = λτ ) the following quantum modified NLS equation for the small but finite amplitude perturbation φ(ξ, τ ) ≡ φ…”

Landau damping of Gardner solitons in a dusty bi-ion plasma

“…However, in the case of R 1 ∼ o( ) or R 1 ≈ 0, one has to deal with mKdV or Gardner equations which involve higher-order (of ) perturbations for the evolution of dust-acoustic solitary waves in the plasma. Figure 1 shows the contour plot of R 1 = 0 (the thin or black curve) in the σ − µ plane in which the nonlinear co-efficients b and b 1 , respectively, of the KdV and Gardner (obtained later) equations (20) and (87) vanish. The plot of R 2 = 0 (The thick or red curve) represents the same, however, for the vanishing of the nonlinear coefficient b 2 of the mKdV equation (90) (shown later).…”

“…On the other hand, in absence of the Landau damping effects (i.e., when a = 0), the KdV and mKdV equations [Eqs. (20) and (90)] have the following traveling wave solutions Following the same procedure as above and assuming that is a small parameter and 1 ∼ b, b 2 ∼ c a , analytic solutions of Eqs. (20) and (90) can also be obtained.…”

“…Recently, a number of attempts have been made to study the effects of Landau damping on nonlinear solitary waves owing to its importance in different plasma environments. To mention few, Mukherjee et al [20] studied the effects of linear Landau damping on the nonlinear ion-acoustic solitons in a quantum plasma with the description of KdV equation. The similar investigation was made by Barman et al [21] for nonlinear dust-acoustic solitary waves in a dusty pair-ion plasma.…”