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In the following we show how the presence of a strong magnetic field in the core can provide the trapping mechanism (Magnetic Greenhouse Effect) required to explain the visibility of suppressed dipole modes in RGB stars.  \subsection{Magneto-Gravity Waves}  The very high radial order of the g-modes in the core of a red giant  imply a large amount of transverse shear that will be resisted by the  bending of the radial component of a magnetic field. A simple   estimate of field strength needed to impact the   transverse restoring force gives $B^2\approx \rho \omega^2/k_r^2$.   Since the g-mode is in the WKB limit, we know that  $\omega^2=k_\perp^2 N^2/k_r^2$, which we use to obtain the local  radial wavenumber $k_r$, and derive the local radial   magnetic field of $B^2\approx \rho\omega^4/N^2 k_\perp^2$ needed to   resist the g-mode propagation. A more careful calculation (see  supplementary materials) gives (your current equation 5).  In the absence of a magnetic field, linear incompressible adiabatic waves (appropriate for the radiative interior of a red giant) obey the WKB dispersion relation   \begin{equation}  \label{eqn:gravdisp}