  Using a nonlocal time-dependent theory of convection, we have calculated the
linear non-adiabatic oscillations of the Horizontal Branch (HB) stars, with
both the dynamic and thermodynamic coupling between convection and oscillations
carefully treated. Turbulent pressure and turbulent viscosity have been
included consistently in our equations of non-adiabatic pulsation. When the
coupling between convection and oscillations is ignored, for all models with
Teff <= 7350, the fundamental through the second overtone are pulsationally
unstable; while for Teff <= 6200 all the models are unstable up to (at least)
the 9th overtone. When the coupling between convection and oscillations is
included, the RR Lyrae instability strip is very well predicted. Within the
strip the most models are pulsationally unstable only for the fundamental and
the first few overtones. The turbulent viscosity is an important damping
mechanism. Being exclusively distinct from the luminous red variables (long
period variables), the HB stars to the right of the RR strip are pulsationally
stable for the fundamental and low-order overtones, but become unstable for
some oen of the high-order overtones. This may provide a valuable clue for the
short period, low amplitude red variables found outside the red edge of the RR
strip on the H-R diagram of globular clusters. Moreover, we present a new
radiation modulated excitation mechanism functioning in a zone of radiation
flux gradient. The effects of nonlocal convection and the dynamic coupling
between convection and oscillations are discussed. The spatial oscillations of
the thermal variables in the pulsational calculations have been effectively
suppressed.
