Landau damping effects and evolutions of energy spread in small isochronous ring

This paper presents the Landau damping effects on the microwave instability of a coasting long bunch in an isochronous ring due to finite energy spread and emittance. Our two-dimensional (2D) dispersion relation gives more accurate predictions of the microwave instability growth rates of short-wavelength perturbations than the conventional 1D formula. The long-term evolution of energy spread is also studied by measurements and simulations.