A longitudinally coherent X-ray pulse from a high repetition
rate free electron laser (FEL) is desired for a wide
variety of experimental applications. However, generating
such a pulse with a repetition rate greater than 1 MHz is
a significant challenge. The desired high repetition rate
sources, primarily high harmonic generation with intense
lasers in gases or plasmas, do not exist now, and, for the
multi-MHz bunch trains that superconducting accelerators
can potentially produce, are likely not feasible with current
technology. In this paper, we propose to place an oscillator downstream of a radiator. The oscillator generates radiation that is used as a seed for a high gain harmonic generation (HGHG) FEL which is upstream of the oscillator. For the first few pulses the oscillator builds up power and, until power is built up, the radiator has no HGHG seed. As power in the oscillator saturates, the HGHG is seeded and power is produced. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass map is derived using a semi-analytic 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.