## Abstract

A set of equations describing the nonlinear multimode dynamics in the quasioptical gyrotron is derived. These equations, involving the slow amplitude and phase variation for each mode, result from an expansion of the nonlinear induced current up to fifth order in the wave amplitude. The interaction among various modes is mediated by coupling coefficients, of known analytic dependence on the normalized current I, the interaction length μ, and the frequency detunings Δ_{i} corresponding to the competing frequencies ω_{i}. The particular case when the modes form triads with frequencies ω_{1} + ω_{3} - 2ω _{2}≃0 is examined in more detail. The equations are quite general and can be used to study mode competition, the existence of a final steady state, its stability, as well as its accessibility from given initial conditions. It is shown that when μ/β_{⊥} ≫ 1, μ can be eliminated as an independent parameter. The control space is then reduced to a new normalized current Î and the desynchronism parameters ν_{i} = Δ_{i}μ for the interacting frequencies. Each coupling coefficient G_{ij} is written as G_{ij} = ÎS_{ij}Ĝ_{ij}(ν_{i},ν_{j}), where the nonlinear filling factor S_{ij}, carrying the information of the beam current spatial profile, can be computed independently. Therefore, it suffices to compute tables of Ĝ_{ij} as functions of ν_{1}, ν_{2}, and ν_{3} once to cover the parameter space. Results for a cold beam are presented here.

Original language | English (US) |
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Pages (from-to) | 3161-3174 |

Number of pages | 14 |

Journal | Physics of Fluids B |

Volume | 2 |

Issue number | 12 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |

## ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes