deletions | additions       diff --git a/Magnetic Trapping.tex b/Magnetic Trapping.tex  index 774e773..c4f676f 100644  --- a/Magnetic Trapping.tex  +++ b/Magnetic Trapping.tex 
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Let's first consider waves that are transmitted at $r_{\rm MG}$. The incoming magneto-gravity waves couple to pure Alfven modes in the cavity $r  On the other hand magneto-gravity waves that are reflected at $r_{\rm MG}$ never couple directly to Alfven modes. However, as the reflecting boundary can not be spherically symmetric (since $\nabla \cdot \textbf{B} = 0$ 0$)  and purely poloidal fields are unstable), the incoming $\ell=1$ wave is also scattered into higher $\ell$ modes. Similarly to pure Alfven modes, these waves can not couple back to acoustic modes in the envelope, their tunneling integral being very large. Therefore they are effectively trapped in the magneto-gravity cavity.