A longitudinally and transversely coherent, high repetition rate x-ray source with widely tunable wavelength is desired for a variety of experimental applications. A free electron laser (FEL) powered by an electron beam from a superconducting linac can reach the desired peak and average x-ray power levels with transverse coherence. However, generating longitudinally coherent x-ray pulses is a significant challenge, especially at high repetition rate. This paper presents a one-dimensional theoretical and numerical investigation of a method to achieve longitudinal coherence and high repetition rate simultaneously. We propose a “radiator-first” configuration, wherein an FEL oscillator follows a high gain harmonic generation (HGHG) FEL. The oscillator generates seed power that is directed upstream to initiate the HGHG process in a following electron bunch. This configuration allows for the generation of radiation at short wavelength, which is highly sensitive to energy spread, to occur before the longer wavelength oscillator, whose performance is not seriously degraded by the beam heating in the upstream radiator. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass, 1D map is derived using a semianalytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft x-ray FEL.