# Vlasov multi-dimensional model dispersion relation

## Abstract

A hybrid model of the Vlasov equation in multiple spatial dimension D > 1 [H. A. Rose and W. Daughton, Phys. Plasmas 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the z direction, and N flows. At each z, these flows are in the plane perpendicular to the z axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show approximate convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as N increases. Departure from strict rotational invariance about the z axis for small perpendicular wavenumber Langmuir fluctuations in 3D goes to zero like θ{sup N}, where θ is the polar angle and flows are arranged uniformly over the azimuthal angle.

- Authors:

- Department on Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131 (United States)
- Theoretical Division, Los Alamos National Laboratory, MS-B213, Los Alamos, New Mexico 87545 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22304071

- 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; APPROXIMATIONS; BOLTZMANN-VLASOV EQUATION; DISPERSION RELATIONS; EXACT SOLUTIONS; FLUCTUATIONS; MAGNETIC FIELDS; PLASMA; ROTATIONAL INVARIANCE

### Citation Formats

```
Lushnikov, Pavel M., E-mail: plushnik@math.unm.edu, Rose, Harvey A., New Mexico Consortium, Los Alamos, New Mexico 87544, Silantyev, Denis A., Vladimirova, Natalia, and New Mexico Consortium, Los Alamos, New Mexico 87544.
```*Vlasov multi-dimensional model dispersion relation*. United States: N. p., 2014.
Web. doi:10.1063/1.4886122.

```
Lushnikov, Pavel M., E-mail: plushnik@math.unm.edu, Rose, Harvey A., New Mexico Consortium, Los Alamos, New Mexico 87544, Silantyev, Denis A., Vladimirova, Natalia, & New Mexico Consortium, Los Alamos, New Mexico 87544.
```*Vlasov multi-dimensional model dispersion relation*. United States. doi:10.1063/1.4886122.

```
Lushnikov, Pavel M., E-mail: plushnik@math.unm.edu, Rose, Harvey A., New Mexico Consortium, Los Alamos, New Mexico 87544, Silantyev, Denis A., Vladimirova, Natalia, and New Mexico Consortium, Los Alamos, New Mexico 87544. Tue .
"Vlasov multi-dimensional model dispersion relation". United States.
doi:10.1063/1.4886122.
```

```
@article{osti_22304071,
```

title = {Vlasov multi-dimensional model dispersion relation},

author = {Lushnikov, Pavel M., E-mail: plushnik@math.unm.edu and Rose, Harvey A. and New Mexico Consortium, Los Alamos, New Mexico 87544 and Silantyev, Denis A. and Vladimirova, Natalia and New Mexico Consortium, Los Alamos, New Mexico 87544},

abstractNote = {A hybrid model of the Vlasov equation in multiple spatial dimension D > 1 [H. A. Rose and W. Daughton, Phys. Plasmas 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the z direction, and N flows. At each z, these flows are in the plane perpendicular to the z axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show approximate convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as N increases. Departure from strict rotational invariance about the z axis for small perpendicular wavenumber Langmuir fluctuations in 3D goes to zero like θ{sup N}, where θ is the polar angle and flows are arranged uniformly over the azimuthal angle.},

doi = {10.1063/1.4886122},

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}

}