\label{fig:Prop}
{\bf Top:} Propagation diagram for a $M=1.6 \,M_\odot$, $R=6.6 \,R_\odot$, $\nu_{\rm max}=120 \,\mu{\rm Hz}$ RGB stellar model with a magnetized core. The red, blue, and green lines are the dipole Lamb frequency $L_1$, the buoyancy frequency $N$, and the magneto-gravity frequency $\omega_{MG}$ (defined in equation \ref{eqn:maggrav}), respectively. Regions are colored by the types of waves they support: the red region correspond is the acoustic wave cavity, the blue region is the magneto-gravity wave cavity, and the green region hosts only Alfven waves. The thick black line is the frequency of maximum power, $\nu_{\rm max}$, for this stellar model. Waves at this frequency behave like acoustic waves near the surface, gravity waves in the outer core, and Alfven waves in the inner core. {\bf Bottom:} Critical radial magnetic field strength, $B_c$ (equation \ref{eqn:Bc}) needed to suppress dipole oscillations. $B_c$ has a sharp minimum at the H-burning shell, which determines the minimum field strength $B_{c,\rm {min}}$ for dipole mode suppression.

%{\bf Middle:} Sound speed, $v_s$, gravity wave radial group velocity, $v_{g,r}$ (for $\omega=\omega_{\rm max}$), and Alfven velocity, $v_A$, as a function of radius. Waves travel at a group velocity of $v_s$, $v_{g,r}$, and $v_A$ for acoustic, gravity, and Alfven waves, respectively. {\bf Bottom:} Radial wave number, $k_r$, for a wave with $\omega=\omega_{\rm max}$, as a function of radius. We have plotted the wavenumbers of acoustic waves (p-waves), fast magneto-gravity waves (mg-waves), slow magneto-gravity waves (slow-waves), and Alfven waves (a-waves). The dashed blue line shows the wavenumber for gravity waves (g-waves) in the absence of a magnetic field. 