deletions | additions       diff --git a/Magnetic Trapping.tex b/Magnetic Trapping.tex  index 5cdab80..e974e1a 100644  --- a/Magnetic Trapping.tex  +++ b/Magnetic Trapping.tex 
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\subsection{Magnetic Greenhouse Effect}  Regardless of whether magneto-gravity waves are transmitted or reflected at $r_{\rm MG}$, we show here that strong magnetic fields will effectively trap waves in the radiative core of a red giant star. We refer to this process as the magnetic greenhouse effect, because it acts as a filter that allows gravity waves to enter the radiative core, but prevents them from escaping. However, the magnetic greenhouse effect arises not from the alteration of incoming wave frequencies, but rather due to modification of the angular wavenumbers. Such angular modification originates from the inherently non-spherical magnetic field structure of even the simplest field configurations.  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