### Abstract

The nonlinear dynamics of the bump-on-tail and current driven ion-acoustic instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density and the electron drift velocity respectively) above its neutral stable value by a small fractional amount A2, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behaviour is found. A short comparison with quasi-linear theory is given,

and the results are compared with experiment.

and the results are compared with experiment.

Original language | English |
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Place of Publication | Roskilde, Denmark |
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Publisher | Risø National Laboratory |

Number of pages | 35 |

ISBN (Print) | 87-550-0677-9 |

Publication status | Published - 1980 |

Series | Risø-M |
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Number | 2235 |

ISSN | 0418-6435 |

### Keywords

- Risø-M-2235

## Cite this

Janssen, P. A. E. M., & Juul Rasmussen, J. (1980).

*Limit cycle behaviour of the bump-on-tail and ion-acoustic instability*. Risø National Laboratory. Risø-M, No. 2235