# 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; KORTEWEG-DE 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}

}