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Jim Fuller edited Mode Visibility.tex
about 9 years ago
Commit id: c6f3715ee7abdcab8a80a965145cd01ff76d660b
deletions | additions
diff --git a/Mode Visibility.tex b/Mode Visibility.tex
index fedf975..cf4812b 100644
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\label{eqn:integral2}
T \simeq \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
$\omega $\omega=L_{\ell}$ and the lower boundary occurs where $\omega $\omega=N$).
For 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.