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A near vacuum can produce a supersonic speed on an incoming stream which is only incidental to the outgoing exhaust, I think, due to a narrowing of the flow of the air coming through the leading part of the air inlet. The exhaust flow that educts the incoming air serves to set up the near vacuum on ...

No.. The reason for bringing the intake of the augmentor forward of the intake of the engine is that the incoming rush of air through the augmentor and out the exhaust is that a well placed inlet to the engine would benefit from that rush of air by way of a "shearing effect" similar to what happens ...

Why doesn't someone try extending the augmentor intake to a point forward of the ramjet intake so the incoming air would act like a high forward speed...? A ducted ramjet! Centrifugal flameholder? Static ramjet?