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 the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
 Authors:
 Saha Institute of Nuclear Physics, Calcutta (India)
 Serampore College, West Bengal (India)
 Publication Date:
 OSTI Identifier:
 22304080
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CORRECTIONS; ION ACOUSTIC WAVES; KORTEWEGDE VRIES EQUATION; LANDAU DAMPING; NONLINEAR PROBLEMS; SEMICLASSICAL APPROXIMATION
Citation Formats
Mukherjee, Abhik, Janaki, M. S., and Bose, Anirban. Quantum corrections to nonlinear ion acoustic wave with Landau damping. United States: N. p., 2014.
Web. doi:10.1063/1.4886153.
Mukherjee, Abhik, Janaki, M. S., & Bose, Anirban. Quantum corrections to nonlinear ion acoustic wave with Landau damping. United States. doi:10.1063/1.4886153.
Mukherjee, Abhik, Janaki, M. S., and Bose, Anirban. Tue .
"Quantum corrections to nonlinear ion acoustic wave with Landau damping". United States.
doi:10.1063/1.4886153.
@article{osti_22304080,
title = {Quantum corrections to nonlinear ion acoustic wave with Landau damping},
author = {Mukherjee, Abhik and Janaki, M. S. and Bose, Anirban},
abstractNote = {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 the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.},
doi = {10.1063/1.4886153},
journal = {Physics of Plasmas},
number = 7,
volume = 21,
place = {United States},
year = {Tue Jul 15 00:00:00 EDT 2014},
month = {Tue Jul 15 00:00:00 EDT 2014}
}

The Landau damping rates of ion acoustic wave are studied by using VlasovPoisson model for unmagnetized Lorentzian or kappa distributed plasma containing electrons, positively and negatively charged ions. It is found that the damping rate of ion acoustic wave is increased with the decrease of kappa (i.e., the spectral index of Lorentzian distribution) value. The damping rates of the electrostatic wave in multiion component plasmas are discussed in detail which depends on electron to ion temperature ratio and ions masses and density ratios. The numerical results are also shown by choosing some typical experimental parameters of multiion plasmas.

Nonlinear electron Landau damping of ionacoustic solitons
Several authors have treated kinetic effects associated with the ionacoustic soliton; e.g., Ott and Sudan investigated linear electron Landau damping and Karpman and Lotko have looked at damping due to ion reflection. Here an O'Neiltype frozen wave calculation that includes effects associated with electron orbits in a soliton is presented. This calculation differs from previous ones in that the usual three time scale argument is made: ..omega../sub p/e >>..omega../sub b/e >>..gamma../sub L/. The orbit effects included in this ordering become important at the modest amplitude ePhi/T/sub e/> or approx. =(m/sub e//m/sub i/)./sup 2/ Saturation at finite amplitude is predicted.