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We describe a simple mechanism to transform bunches with matched longitudinalphase-space distributions from one RF system to a matched distribution of asecond RF system operating on a different harmonic and with a differentaccelerating voltage. The process is reversible and the longitudinal emittanceis preserved. Simple equations that characterize the procedure are given andapplications are discussed. In particular this method can be used to rapidlyshorten the bunch length in proton rings.

Longitudinal phase-space matching between radio-frequency systems with different harmonic numbers and accelerating voltages