| Summary: | We present a scheme to generate synchronised THz and soft X-ray radiation pulses by using a free-electron laser oscillator driven by a high repetition rate (of order 10–100 MHz) energy recovery linac. The backward THz radiation in the oscillator cavity interacts with a successive electron bunch, thus producing few <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup></semantics></math></inline-formula> soft/hard X-ray photons per shot (namely <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>12</mn></msup></semantics></math></inline-formula>–<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>13</mn></msup></semantics></math></inline-formula> photons/s) via Thomson/Compton back-scattering, synchronised with the mJ-class THz pulse within the temporal jitter of electron beams accelerated in the superconducting cavities of the linac (less than 100 fs). Detailed simulations have been performed in order to assess the capability of the scheme for typical wavelengths of interest, between 10 and 50 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">μ</mi></semantics></math></inline-formula>m for the TeraHertz radiation and 0.5–3 nm for the X-rays.
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