Note on the effects of finite ion mass and electron thermal velocity spread on the aperiodic instabilities of a space-charge-neutralized electron beam in a planar diode

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Abstract
A hydrodynamic analysis of the aperiodic instabilities of a neutralized drifting electron stream in a short‐circuited planar diode is given in this work. The results of this investigation indicate the following: (i) An electron stream can be aperiodically unstable only if the electron stream’s Mach number exceeds unity in the diode space. The change from a monoenergetic electron beam to a dispersive electron beam results in a modification of the instability condition, a reduction of the growth rate, and a smaller value of critical current flowing through the diode. (ii) The aperiodic instability imbedded in the immobile ion background, i.e., the Pierce instability, cannot be eliminated by the first‐order motion of ions. The effect of the finite ion mass is not only to reduce the maximum growth rate of the Pierce instability and to increase the diode critical current, but also to introduce new aperiodic instabilities with growth rates generally smaller than that of the Pierce instability.