Well the first question should be if you are going for Constant Pressure Combustion or Constant Volume Combustion.
Constant pressure combustion is the current method of propulsion used.
Constant volume combustion is currently under research and is often called pulse detonation engine and its theoretically able to give better performance, the current problems are powering the detonation, and constructing a tube that can survive the detonation for any length of time.
one way for Constant pressure combustion would be to use carbon nano tubes to ionize the air and then use a MHD drive, it would work at subsonic for supersonic you would need something more to ionize more air faster.
the REB and direct alpha could both be used for either propulsion method based on the engine design.
