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Frequency upconversion of laser-generated photons by inverse Compton scattering for applications such as nuclear spectroscopy and gamma-gamma collider concepts on the future ILC would benefit from an increase of average source brightness. The primary obstacle to higher average brightness is the relatively small Thomson scattering cross section. It has been proposed that this limitation can be partially overcome by use of laser pulse recirculation. The traditional approach to laser recirculation entails resonant coupling of low-energy pulse train to a cavity through a partially reflective mirror [ 1]. Here we present an alternative, passive approach that is akin to "burst-mode" operation and does not require interferometeric alignment accuracy. Injection of a short and energetic laser pulse is achieved by placing a thin frequency converter, such as a nonlinear optical crystal, into the cavity in the path of the incident laser pulse. This method leads to the increase of x-ray/gamma-ray energy proportional to the increase in photon energy in frequency conversion. Furthermore, frequency tunability can be achieved by utilizing parametric amplifier in place of the frequency converter.