deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index b74f53e..b0d6924 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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%Modes suppressed via the magnetic greenhouse effect have an extra source of damping determined by the rate at which energy leaks through the evanescent region separating the acoustic cavity from the g-mode cavity.   Waves with angular frequency $\omega \sim \omega_{\rm max}$ are excited via convective motions, the waves propagate downward as acoustic waves until their frequency is less than the local Lamb frequency for waves of angular degree $\ell$, i.e., until $\omega < L_{\ell}$. At this boundary, part of the wave flux is reflected, and part of it tunnels through.   The degree of reflection is determined by the tunneling integral through the evanescent region. The transmission coefficient is   \begin{equation}\label{eqn:integral} can be approximated as   \begin{equation}  \label{eqn:integral2}  T= \exp{\int^{r_2}_{r_1} i k_r dr}  \simeq \exp{\int^{r_2}_{r_1} - \frac{\sqrt{\ell(\ell+1)}}{r} dr } \bigg( \frac{r_1}{r_2} \bigg)^{\sqrt{l(l+1)}}  \, , \end{equation}  where $r_1$ and $r_2$ are the boundaries of the evanescent region (in this case, the upper boundary occurs where $\omegaFor waves of the same frequency, larger values of $\ell$ have larger values of $r_2$, thus equation \ref{eqn:integral2} demonstrates that high $\ell$ waves have much smaller transmission coefficients through the evanescent zone.  The fraction of transmitted energy flux through the evanescent region is $T^2$, while the fraction of reflected energy is $R^2=1-T^2$. Let's assume that for suppressed modes, any mode energy which leaks into the g-mode cavity is completely lost.   %via the magnetic greenhouse effect.