Abstract: A Brayton cycle engine including an inner wall assembly defining a detonation combustion region upstream thereof extended from a longitudinal wall into a gas flowpath. An actuator adjusts a depth of the detonation combustion region into the gas flowpath. A method for operating the engine includes flowing an oxidizer through the gas flowpath; capturing a portion of the flow of oxidizer via the inner wall; flowing a first flow of fuel to the captured flow of oxidizer; producing a rotating detonation gases via a mixture of the first flow of fuel and the captured flow of oxidizer; flowing at least a portion of the detonation gases downstream to mix with the flow of oxidizer; flowing a second flow of fuel to the mixture of detonation gases and oxidizer; and burning the mixture of the second flow of fuel and the detonation gases/oxidizer mixture.