### Abstract

The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff's method of "secular regularization" is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the "eigenmode dominance" approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.

Original language | English (US) |
---|---|

Pages (from-to) | 110-115 |

Number of pages | 6 |

Journal | Physics of Fluids |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1985 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*28*(1), 110-115. https://doi.org/10.1063/1.865190

**Single-mode saturation of a linearly unstable plasma.** / Burnap, C.; Miklavčič, M.; Willis, B. L.; Zweifel, P. F.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 28, no. 1, pp. 110-115. https://doi.org/10.1063/1.865190

}

TY - JOUR

T1 - Single-mode saturation of a linearly unstable plasma

AU - Burnap, C.

AU - Miklavčič, M.

AU - Willis, B. L.

AU - Zweifel, P. F.

PY - 1985/1/1

Y1 - 1985/1/1

N2 - The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff's method of "secular regularization" is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the "eigenmode dominance" approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.

AB - The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff's method of "secular regularization" is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the "eigenmode dominance" approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.

UR - http://www.scopus.com/inward/record.url?scp=0021786766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021786766&partnerID=8YFLogxK

U2 - 10.1063/1.865190

DO - 10.1063/1.865190

M3 - Article

AN - SCOPUS:0021786766

VL - 28

SP - 110

EP - 115

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 1

ER -