We present an analysis of the performance of a broadband secondary radiation source based on a high-gradient laser-plasma wakefield electron accelerator. In more detail, we report studies of compact and ultra-short X-ray generation via betatron oscillations in plasma channels. For the specific working point examined in this paper, determined by the needs of other experiments ongoing at the facility, at ∼0.02 Hz operation rate, we have found ≲106 photons emitted per shot (with a fluctuation of 50%) in the soft X-rays, corresponding to a critical energy of ∼0.8 keV (with a fluctuation of 40%). The source will be implemented for experiments in time-domain spectroscopy, e.g., biological specimens, and for other applications oriented to medical physics.