deletions | additions       diff --git a/In_stars_with_field_strengths__.tex b/In_stars_with_field_strengths__.tex  index 1dfe945..43baa22 100644  --- a/In_stars_with_field_strengths__.tex  +++ b/In_stars_with_field_strengths__.tex 
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In stars with field strengths exceeding $B_c$ (equation \ref{eqn:Bc}) somewhere in their core, incoming dipolar gravity waves will become evanescent at the radius $r_{\rm MG}$ where $B>B_c$. At this point, the waves must either reflect or be transmitted into the strongly magnetized region as Alfven waves. An analogous process occurs in the Sun's atmosphere, where outwardly propagating magneto-acoustic-gravity waves become magnetically dominated as they propagate upward. In general, the reflection or transmission of the wave depends on the geometry of the magnetic field (\cite{Zhugzhda_1984}).   In RGB cores, the reflection/transmission process modifies the waves such that they will become trapped in the radiative zone (see Supplementary Material). Incoming $\ell=1$ magneto-gravity waves can transmit energy into a continuous spectrum (\cite{Reese_2004,Levin_2006}) of Alfven waves with a broad spectrum of $\ell$ values \cite{Rincon_2003}, even for simple field geometries. \cite{Rincon_2003}.  The same effect occurs formagneto-gravity  reflected waves. The location of $r_{\rm MG}$ is a function of latitude, because the magnetic field cannot be spherically symmetric. Even in the simplest case of a purely dipolar magnetic field, any oscillation modes created by the waves will contain a broad spectrum of $\ell$ (\cite{Lee_2007,Lee_2010}). In reality, the field will likely have a complex geometry containing both poloidal and toroidal components (\cite{Braithwaite_2004,Braithwaite_2006,Duez_2010}), and dipole waves will inevitably scatter into higher $\ell$ waves in the presence of a strong magnetic field. %Let’s first consider waves that are transmitted into Alfven waves at $r_{\rm MG}$. The number of Alfven modes that can be excited is likely very high, due to the fact that the magnetic field has a large range of values and a non-trivial geometry in the region (stable magnetic equilibria require a mixture of toroidal and poloidal magnetic fields, (\cite{Braithwaite_2004,Braithwaite_2006,Duez_2010}). The Alfven waves will travel along field lines and could eventually transmit their energy back into magneto-gravity waves. However, even if this occurs, the energy will be spread over a large number of $\ell$ values.