deletions | additions       diff --git a/Magnetic Trapping.tex b/Magnetic Trapping.tex  index 5582a09..a25d860 100644  --- a/Magnetic Trapping.tex  +++ b/Magnetic Trapping.tex 
...
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  Magneto-gravity waves that are reflected at $r_{\rm MG}$ never couple directly to Alfven modes, however the reflecting boundary can not be spherically symmetric (since $\nabla \cdot B \textbf{B}  = 0$), implying that the reflected wave is scattered into high $\ell$ modes. But now these modes can not couple back to acoustic modes in the envelope, since the tunneling integral for high $\ell$ is very large. Therefore they are effectively trapped in magneto-gravity cavity.