Pan, Z. Chao, A. Deng, X.J. Huang, W.-H. Li, R.K. Li, Z.Z. Tang, C.-X. JACoW Publishing Geneva, Switzerland A new concept is proposed for minimizing the longitudinal emittance of a low momentum compaction factor (low-alpha) storage ring which has the capability to stably store sub-femtosecond electron bunches for the first time. This storage ring is designed for Steady-State microbunching (SSMB) to generate kW level average power EUV radiation. The proposed design approach can be applied to any quasi-isochronous storage rings to yield very high radiation power due to longitudinal coherence of the radiation. We obtain an optimal lattice design by minimizing global and local momentum compaction factors simultaneously and the result of single-particle tracking shows that the electron beam with equilibrium rms bunch length of about 40 nm can be stored in this ring. We also clarify in this type ring, the horizontal emittance will be fixed when beam energy, dipole bending angle and cell tune is fixed. In this type ring, the calculation for IBS effect will be different with traditional rings, we point out where the difference is and give a more convenient calculation for it.