  We investigate the effect of a strong large scale magnetic field on the
reflection of high frequency acoustic modes in rapidly oscillating Ap stars. To
that end we consider a toy model composed of an isothermal atmosphere matched
onto a polytropic interior and determine the numerical solution to the set of
ideal magneto-hydrodynamic equations in a local plane-parallel approximation
with constant gravity. Using the numerical solution in combination with
approximate analytical solutions that are valid in the limits where the
magnetic and acoustic components are decoupled, we calculate the relative
fraction of energy flux that is carried away in each oscillation cycle by
running acoustic waves in the atmosphere and running magnetic waves in the
interior. For oscillation frequencies above the acoustic cutoff we show that
most energy losses associated with the presence of running waves occur in
regions where the magnetic field is close to vertical. Moreover, by considering
the depth dependence of the energy associated with the magnetic component of
the wave in the atmosphere we show that a fraction of the wave energy is kept
in the oscillation every cycle. For frequencies above the acoustic cutoff
frequency such energy is concentrated in regions where the magnetic field is
significantly inclined in relation to the local vertical. Even though our
calculations were aimed at studying oscillations with frequencies above the
acoustic cutoff frequency, based on our results we discuss what results may be
expected for oscillations of lower frequency.
