Abstract
Uniform density electron beam flow in a one-dimensional Pierce diode is alternately stable and unstable as the diode width is increased. Each stability transition corresponds to an equilibrium bifurcation involving either a static nonuniform equilibrium or a steady oscillatory configuration. The static equilibria, although nonlinear, are evaluated analytically and their stability properties derived. Details of the oscillatory solutions are determined numerically from integral equations relating the transit time of electrons in the diode to the electric field at the entrance plane. As the diode width is reduced, each oscillatory solution undergoes a sequence of subharmonic bifurcations, culminating in a chaotic strange attractor. The chaotic attractor itself terminates in a crisis after a further reduction of the diode width. Unlike other electron beam nonlinear oscillations (e.g., virtual cathodes), no particle reflections are required. This behavior has intrinsic interest as a possible model for beam turbulence in more complex geometries. In addition, it may find application in microwave generation.
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