Matteo Cantiello edited Magnetic Trapping.tex  about 9 years ago

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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.