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.
We have studied cloth fiber cold cathode emitters and have found them to be superior to many other types of cold cathode emitters. In this paper, the characteristics of this type of cathode are presented.
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