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Matteo Cantiello edited Magnetic Trapping.tex
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\section{Magnetic Trapping}
We can now understand In the
behavior of waves and oscillation modes in red giants with magnetic cores. Waves with angular frequency $\omega \sim \omega_{\rm max}$ are excited via convective motions near following we show how the
surface presence of
the star. As a strong magnetic core in
other red giants, 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}
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 } \, ,
\end{equation}
where $r_1$ and $r_2$ are the boundaries of the evanescent region (in this case, RGB stars can provide the
upper boundary occurs where $\omega trapping mechanism required to explain the lower boundary occurs where $\omega visibility oftransmitted energy flux through the evanescent region is $T^2$, while the fraction of reflected energy is $R^2=1-T^2$. dipole modes in suppressed $\ell =1 $ stars.