# Longitudinal sound waves in a collisionless, quasineutral plasma

## Abstract

The time evolution of slow sound waves in a homogeneous, collisionless and quasineutral plasma, in particular their Landau damping, is investigated using the kinetic-magnetohydrodynamics formulation of Ramos (J. Plasma Phys.vol. 81, 2015 p. 905810325; vol. 82, 2016 p. 905820607). In this approach, the electric field is eliminated from a closed, hybrid fluid-kinetic system that ensures automatically the fulfilment of the charge neutrality condition. Considering the time dependence of a spatial-Fourier-mode linear perturbation with wavevector parallel to the equilibrium magnetic field, this can be cast as a second-order self-adjoint problem with a continuum spectrum of real and positive squared frequencies. Therefore, a conventional resolution of the identity with a continuum basis of singular normal modes is guaranteed, which simplifies significantly a Van Kampen-like treatment of the Landau damping. The explicit form of such singular normal modes is obtained, along with their orthogonality relations. These are used to derive the damped time evolution of the fluid moments of solutions of initial-value problems, for the most general kinds of initial conditions. The non-zero parallel electric field is not used explicitly in this analysis, but it is calculated from any given solution after the later has been obtained.

- Authors:

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1538927

- DOE Contract Number:
- FG02-91ER54109

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Plasma Physics

- Additional Journal Information:
- Journal Volume: 83; Journal Issue: 6; Journal ID: ISSN 0022-3778

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
Ramos, J. J.
```*Longitudinal sound waves in a collisionless, quasineutral plasma*. United States: N. p., 2017.
Web. doi:10.1017/s0022377817000885.

```
Ramos, J. J.
```*Longitudinal sound waves in a collisionless, quasineutral plasma*. United States. doi:10.1017/s0022377817000885.

```
Ramos, J. J. Wed .
"Longitudinal sound waves in a collisionless, quasineutral plasma". United States. doi:10.1017/s0022377817000885.
```

```
@article{osti_1538927,
```

title = {Longitudinal sound waves in a collisionless, quasineutral plasma},

author = {Ramos, J. J.},

abstractNote = {The time evolution of slow sound waves in a homogeneous, collisionless and quasineutral plasma, in particular their Landau damping, is investigated using the kinetic-magnetohydrodynamics formulation of Ramos (J. Plasma Phys.vol. 81, 2015 p. 905810325; vol. 82, 2016 p. 905820607). In this approach, the electric field is eliminated from a closed, hybrid fluid-kinetic system that ensures automatically the fulfilment of the charge neutrality condition. Considering the time dependence of a spatial-Fourier-mode linear perturbation with wavevector parallel to the equilibrium magnetic field, this can be cast as a second-order self-adjoint problem with a continuum spectrum of real and positive squared frequencies. Therefore, a conventional resolution of the identity with a continuum basis of singular normal modes is guaranteed, which simplifies significantly a Van Kampen-like treatment of the Landau damping. The explicit form of such singular normal modes is obtained, along with their orthogonality relations. These are used to derive the damped time evolution of the fluid moments of solutions of initial-value problems, for the most general kinds of initial conditions. The non-zero parallel electric field is not used explicitly in this analysis, but it is calculated from any given solution after the later has been obtained.},

doi = {10.1017/s0022377817000885},

journal = {Journal of Plasma Physics},

issn = {0022-3778},

number = 6,

volume = 83,

place = {United States},

year = {2017},

month = {11}

}

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