I've taken the liberty of making a copy of the patent drawing, and then removing a lot of the clutter
20. This is the cooler, a simple liquid-to-gas heat exchanger. The majority of the gas-cooling is performed here, rather than using only the classic annular water jacket around the "cold" cylinder. Due to the working gas being partially pressurized to increase the mass of the working gas...the gas portion is cylindrical tubing.
22. This is the regenerator, the classic Stirling "heat sponge" that gains and sheds heat in both directions.
34. This is a liquid jacket over the "cold" cylinder. Although it may in fact allow the working gas to shed some heat, the patent makes it clear that part #20 is the primary heat-shedding device. Notice that there is also a liquid jacket around the base of the "hot" cylinder, in order to keep the heat located at the hot cap from migrating through the crankcase. No specifics are given, but...I suspect both liquid jackets are connected to a common loop.
38. This is the tiny auxiliary piston that is fixed to the crown of the cold piston. It pulls gasses from the crankcase, presumably gasses that have leaked-by the piston sealing rings. It uses a one-way reed-style check-valve.
52. According the the documentation, this is a bleed valve that releases some of the working gas into the crankcase on purpose. They describe the way that they throttle the engine by two methods...first is they meter the fuel that is spraying into the external hot cap.
Secondly, by bleeding some of the working gas into the crankcase (using valve #52), the generator load will slow the engine. Increasing the working-gas mass will raise its power, leading to slightly faster RPMs, if the load remains constant. It is not described if this bleed valve is actuated electrically or by a magnetic signal, since it is inside the hermetically-sealed working-gas area.
One of the drawing items I removed is a recuperator, which is a sleeve-within-a-sleeve heat exchanger at the hot end. This allows the hot caps' exiting exhaust heat to warm-up the incoming air, and this fresh air is needed for the fuel combustion inside the hot cap. By adding this simple device, less fuel is needed to attain the desired temperature inside the hot cap.
Since the Alpha hot air engine cycle requires the hot piston to compress first (and the cold piston compresses 90 degrees later), the engine as drawn would rotate counter-clockwise.
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