The possibility of creating an alternating current source based on a thermionic energy converter is because, under certain conditions, an electron instability can develop in such a diode in the collisionless mode, leading to a sharp current cut-off. To implement this effect, it is enough to short electrodes through inductance. To select the optimal operation mode of the generator, it is necessary to study external inductance influence on the development of the instability. This problem is theoretically studied in the proposed work, and both over-neutralized and under-neutralized modes are considered. Dispersion equations are obtained. It is shown that when external inductance is included an instability threshold can be moved below the Pierce one. Besides, this type of instability can develop only for inductance values from a limited range.