Pierce instability and bifurcating equilibria
Technical Report
·
OSTI ID:6641303
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities.
- Research Organization:
- Mission Research Corp., Albuquerque, NM (USA)
- OSTI ID:
- 6641303
- Report Number(s):
- PB-87-143178/XAB; AMRC-R-282
- Country of Publication:
- United States
- Language:
- English
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