Abstract
A model of a thermionic cathode in a planar diode in which the Poisson and Vlasov equations are solved in 3-D assuming an infinite magnetic field is presented. We explore how 2-D work function variations across the cathode surface may affect the transition between temperature-limited and space-charge-limited flow, commonly known as the “knee” of the Miram curve. We study a variety of work function distributions, both realistic and idealized, and demonstrate how emission from the lowest work function regions dominates the total anode current even when such regions make up a relatively small fraction of cathode area. Our model also illustrates the ability of cathodes to reach the full Child–Langmuir current despite the presence of a sizeable nonemitting region. We find that as the length scale of these work function variations decreases, the Miram knee grows sharper, indicating improved cathode performance.
Highlights
T HERMIONIC cathodes are commonly used to generate the electron beam that drives a wide variety of vacuum electronic devices, such as traveling wave tubes, klystrons, and magnetrons
To demonstrate the space charge shielding effect and resulting current compensation that low work function regions have on their high work function neighbors, we begin with simple arrangements of two work functions: φ1 = 2.0 eV and φ2 = 2.2 eV (Fig. 2)
In addition to being much more realistic in modeling a real cathode surface, it allows a much faster evaluation of various physical effects that could contribute to shape of the Miram curve
Summary
T HERMIONIC cathodes are commonly used to generate the electron beam that drives a wide variety of vacuum electronic devices, such as traveling wave tubes, klystrons, and magnetrons. If similar spatial variations of the discrete work function distributions were allowed in the x-direction on the cathode surface (Fig. 1), the 3-D MICHELLE code simulations did show a very smooth and rounded Miram curve, much like those experimentally observed, as we reported in [8]. It is, of substantial interest to extend the analytic 1-1/2-D model to 2-1/2-D, allowing the local work function φ(x, y) to vary in both x- and y-directions on the cathode surface.
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