External-circuit effects on Pierce-diode stability behavior

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Abstract
The effects of external-circuit resistance, inductance, and capacitance on the linear complex eigenfrequencies of the Pierce diode [J. Appl. Phys. 15, 721 (1944)] are separately investigated in the parameter range 0<α<3π, where α=ωpd/v̄. The results are compared to the ‘‘classical’’ (i.e., short-circuit) case. External-circuit resistance does not alter the stability behavior fundamentally for 0<π<2π, but can lead to complete stabilization in the domain 2π<α<3π, most of which is classically unstable. External-circuit inductance induces a new mode, which may go unstable even in the classically stable domain 0<α<π, thus providing a new possibility of generating HF oscillations in the Pierce diode. Finite external-circuit capacitance tends to stabilize the classically unstable parts of the domain π<α<3π, with the exception of a small, classically stable α domain near 3π, which is destabilized. Our results indicate that the effect of external-circuit elements on Pierce-diode stability behavior is significantly stronger than predicted by Raadu and Silevitch [J. Appl. Phys. 54, 7192 (1983)].