# How really transverse is the filamentation instability?

## Abstract

It is generally considered that the linear filamentation instability encountered when two counter streaming electron beams interpenetrate is purely transverse. Exact and approximated results are derived in the relativistic fluid approximation showing that within some parameter range, filamentation can be indeed almost longitudinal with cos(k,E) < or approx. 1-3.1/{gamma}{sub b}, where {gamma}{sub b} is the relativistic factor of the beam. Temperature effects are then evaluated through relativistic kinetic theory and yield even fewer transverse filamentation modes. In the cold case, the transverse approximation overestimates the growth rate by a factor {proportional_to}{radical}({gamma}{sub b})

- Authors:

- ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
- (France)
- (Spain)

- Publication Date:

- OSTI Identifier:
- 20974862

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 3; Other Information: DOI: 10.1063/1.2710810; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; BEAM-PLASMA SYSTEMS; ELECTRON BEAMS; ELECTRON TEMPERATURE; INSTABILITY; ION TEMPERATURE; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; TEMPERATURE DEPENDENCE

### Citation Formats

```
Bret, A., Gremillet, L., Bellido, J. C., Departement de Physique Theorique et Appliquee CEA/DAM-Ile de France, Boite Postale 12, 91680 Bruyeres-le-Chatel, and ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real.
```*How really transverse is the filamentation instability?*. United States: N. p., 2007.
Web. doi:10.1063/1.2710810.

```
Bret, A., Gremillet, L., Bellido, J. C., Departement de Physique Theorique et Appliquee CEA/DAM-Ile de France, Boite Postale 12, 91680 Bruyeres-le-Chatel, & ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real.
```*How really transverse is the filamentation instability?*. United States. doi:10.1063/1.2710810.

```
Bret, A., Gremillet, L., Bellido, J. C., Departement de Physique Theorique et Appliquee CEA/DAM-Ile de France, Boite Postale 12, 91680 Bruyeres-le-Chatel, and ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real. Thu .
"How really transverse is the filamentation instability?". United States.
doi:10.1063/1.2710810.
```

```
@article{osti_20974862,
```

title = {How really transverse is the filamentation instability?},

author = {Bret, A. and Gremillet, L. and Bellido, J. C. and Departement de Physique Theorique et Appliquee CEA/DAM-Ile de France, Boite Postale 12, 91680 Bruyeres-le-Chatel and ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real},

abstractNote = {It is generally considered that the linear filamentation instability encountered when two counter streaming electron beams interpenetrate is purely transverse. Exact and approximated results are derived in the relativistic fluid approximation showing that within some parameter range, filamentation can be indeed almost longitudinal with cos(k,E) < or approx. 1-3.1/{gamma}{sub b}, where {gamma}{sub b} is the relativistic factor of the beam. Temperature effects are then evaluated through relativistic kinetic theory and yield even fewer transverse filamentation modes. In the cold case, the transverse approximation overestimates the growth rate by a factor {proportional_to}{radical}({gamma}{sub b})},

doi = {10.1063/1.2710810},

journal = {Physics of Plasmas},

number = 3,

volume = 14,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2710810

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