Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

3-1-1984

Abstract

The method of characteristics and multiple-scaling perturbation techniques are used to study the space-charge instability of electron beams. It is found that the stable oscillating state (virtual cathode) created when the space-charge limit is exceeded is similar to a collisionless shock wave. The oscillatory solution originates at the bifurcation point of two unstable steady states. Complementary behavior (virtual anode) results when an ion beam exceeds its space-charge limit. The virtual cathode can also exist in the presence of a neutralizing heavy-ion background. The Pierce instability, where the electron and ion charge densities are equal, is a special case of this broader class. Estimates of the nonlinear growth rate of the instability at the space-charge limit are given.

Publisher

American Physical Society

Publication Title

Physical Review A

ISSN

1050-2947

Volume

27

Issue

3

First Page

1535

Last Page

1543

Language (ISO)

English

Sponsorship

American Physical Society

Comments

Article author is part of the Main Campus Math Department.

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Mathematics Commons

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