Limit Cycle Behaviour of the Bump-on-Tail Instability

P. A. E. M. Janssen; Jens Juul Rasmussen

doi:10.1063/1.863355

Limit Cycle Behaviour of the Bump-on-Tail Instability

P. A. E. M. Janssen, Jens Juul Rasmussen

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Abstract

The nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment.

Original language	English
Journal	Physics of Fluids
Volume	24
Issue number	2
Pages (from-to)	268-273
ISSN	1070-6631
DOIs	https://doi.org/10.1063/1.863355
Publication status	Published - 1981

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title = "Limit Cycle Behaviour of the Bump-on-Tail Instability",

abstract = "The nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment.",

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AU - Janssen, P. A. E. M.

AU - Juul Rasmussen, Jens

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N2 - The nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment.

AB - The nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment.

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DO - 10.1063/1.863355

M3 - Journal article

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SP - 268

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JO - Physics of Fluids

JF - Physics of Fluids

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Limit Cycle Behaviour of the Bump-on-Tail Instability

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