The engine (10) includes at least one firing tube (12) wherein an exhaust stream (32) from the firing tube (12) drives a turbine (30). A scroll ejector attenuator (40) is secured between and in fluid communication with an outlet end (28) of the firing tube (12) and an inlet (76) of the turbine (30). The attenuator (40) defines a turning, narrowing passageway (72) that extends a distance the exhaust stream (32) travels before entering the turbine (30) to attenuate shockwaves and mix the pulsed exhaust stream (32) into an even stream with minimal temperature differences to thereby enhance efficient operation of the turbine (30) without any significant pressure decline of exhaust stream (32) pressure and without any backpressure from the attenuator (40) on the firing tube (12).