Air has a strong absorption line near 1.3THz (230 µm). The idea is to superheat the air with a narrow-band, coherent beam that reflects off container surfaces.
I doubt heating air with x-ray can be done. x-rays are hard to focus,
though we’d want to carry away waste heat by convection, or radiation if possible.
The engine design is so simple that i’m not really seeing a minimum speed for this.
Hot air simply flows out from one end of a large tube, while cooler air gets sucked in the other end.