An experimental setup to demonstrate a recent scheme [Leopold et al., Phys. Plasmas 24, 073116 (2017)] to persistently over-inject a vacuum electron diode so that it self-oscillates in the GHz-frequency range and releases a periodic train of electron bunches is described. We present simulations in which we account for the finite rise time of the voltage accelerating electrons from a finite radius cylindrical thermionic cathode and finite grid electrode transparency, which make the experiment different from the original theoretical scheme. It was found that these experimental conditions do affect the expected results but a self-oscillating behavior is still possible. Our experimental results so far indicate the presence of the self-oscillatory behavior, but because the cathode used emits from a few hot-spots rather than uniformly, the beam current modulations are different from those obtained in the simulations.

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