### Abstract

*only*when, the Langmuir wave damping rate γ is much larger than Ω. The threshold is then reduced by a factor of order Ω/Ω, the optimum value of t being Δ2Ω –Γ for equal pump amplitudes, where Γ is the ion-acoustic wave damping rate and Γ « Ω. The analysis presented in a recent paper is shown to be valid only for γ « Ω, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (T

_{e}/T

_{i}» 1).

Language | English |
---|---|

Pages | 315-340 |

Number of pages | 26 |

Journal | Journal of Plasma Physics |

Volume | 24 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 1980 |

### Fingerprint

### Keywords

- ion-acoustic waves
- frequency
- plasmas
- parametric excitation

### Cite this

*Journal of Plasma Physics*,

*24*(2), 315-340. https://doi.org/10.1017/S0022377800022856

}

*Journal of Plasma Physics*, vol. 24, no. 2, pp. 315-340. https://doi.org/10.1017/S0022377800022856

**Theory of double resonance parametric excitation in plasmas. Part 2.** / Fried, Burton D.; Adler, Allen; Bingham, R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Theory of double resonance parametric excitation in plasmas. Part 2

AU - Fried, Burton D.

AU - Adler, Allen

AU - Bingham, R

PY - 1980/10

Y1 - 1980/10

N2 - Using a simpler formalism than in the original paper on this subject, we verify the earlier result that, for a pump frequency separation Δ approximately equal to twice the ion acoustic frequency Ω, the use of two long-wavelength pumps can reduce the threshold for parametric excitation of ion-acoustic waves when, and only when, the Langmuir wave damping rate γ is much larger than Ω. The threshold is then reduced by a factor of order Ω/Ω, the optimum value of t being Δ2Ω –Γ for equal pump amplitudes, where Γ is the ion-acoustic wave damping rate and Γ « Ω. The analysis presented in a recent paper is shown to be valid only for γ « Ω, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (Te/Ti » 1).

AB - Using a simpler formalism than in the original paper on this subject, we verify the earlier result that, for a pump frequency separation Δ approximately equal to twice the ion acoustic frequency Ω, the use of two long-wavelength pumps can reduce the threshold for parametric excitation of ion-acoustic waves when, and only when, the Langmuir wave damping rate γ is much larger than Ω. The threshold is then reduced by a factor of order Ω/Ω, the optimum value of t being Δ2Ω –Γ for equal pump amplitudes, where Γ is the ion-acoustic wave damping rate and Γ « Ω. The analysis presented in a recent paper is shown to be valid only for γ « Ω, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (Te/Ti » 1).

KW - ion-acoustic waves

KW - frequency

KW - plasmas

KW - parametric excitation

UR - http://journals.cambridge.org/action/displayJournal?jid=PLA

U2 - 10.1017/S0022377800022856

DO - 10.1017/S0022377800022856

M3 - Article

VL - 24

SP - 315

EP - 340

JO - Journal of Plasma Physics

T2 - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

IS - 2

ER -