  Non-evaporable getter (NEG) coating is widely required in the next generation
of light sources and circular $e^+e^-$ colliders for small vacuum pipes to
improve the vacuum level, which, however, also enhances the high-frequency
resistive-wall impedance and often generates a resonator-like peak in the
terahertz frequency region. In this paper, we will use the parameters of the
planned Hefei Advanced Light Facility (HALF) storage ring to study the impact
of NEG coating resistive-wall impedance on the longitudinal microwave
instability via particle tracking simulation. Using different NEG coating
parameters (resistivity and thickness) as examples, we find that the impedance
with a narrow and strong peak in the high frequency region can cause
micro-bunching instability, which has a low instability threshold current and
contributes to a large energy spread widening above the threshold. In order to
obtain a convergent simulation of the beam dynamics, one must properly resolve
such a peak. The coating with a lower resistivity has a much less sharp peak in
its impedance spectrum, which is helpful to suppress the micro-bunching
instability and in return contributes to a weaker microwave instability.
