| Summary: | Low longitudinal emittance means small energy spread and short bunch length, which makes high-power short-wavelength coherent radiation possible. In a storage ring, due to quantum excitation, the equilibrium longitudinal emittance is mainly the overall contribution of all bend-related elements, such as bends, undulators and laser modulators. By introducing longitudinal Twiss function and analyzing the 6D one-turn map in 3D Twiss form, the longitudinal emittance contribution of all these elements is theoretically studied in this paper, and a general method for minimizing the storage ring equilibrium longitudinal emittance is proposed. An integrated optimization of longitudinal beta function shows, the longitudinal emittance scales as the third power of bending angle, and can be as low as subpicometer with a beam energy of 400 MeV in an ultimate state.
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