deletions | additions       diff --git a/In_stars_with_field_strengths__.tex b/In_stars_with_field_strengths__.tex  index 8833958..b456f00 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 dipole 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 Alfv\'en  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 (supplementary online text). 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}. The same effect occurs for 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 resulting oscillation modes 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.  
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