In the storage rings, the electron beams go to the equilibrium state. One of the equilibrium parameters is the natural emittance which is determined by the radiation damping and quantum excitation effects. In other words, the equilibrium emittance is determined by the magnet lattice regardless of the initial beam. Theoretically the minimum emittance and its optimal conditions for uniform bending magnet have been well demonstrated. However, the minimum condition doesn't include the damping partition number. In this paper, we tried to calculate the minimum emittance including the damping partition number. The results shows that the minimum emittance condition and the minimum emittance value is slightly changed by including the damping partition number.

Due to the small vacuum apertures, impedance serves as a significant cause of beam instabilities in the 4th generation storage ring. These instabilities are directly affected by the bunch charge, thereby placing a limit on the maximum achievable beam current within the storage ring. The Korea-4th generation storage ring (Korea-4GSR) is currently under construction with the aim of reaching a maximum beam current of 400 mA. To meet this goal, we've conducted estimations and optimizations of the current storage ring’s impedance. In this presentation, we show the impedance of Korea-4GSR and the corresponding instabilities.