  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.
