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Jim Fuller edited Magnetic Trapping.tex
about 9 years ago
Commit id: c5273bdc293abea93ec93e64f5e060eb6a3b6995
deletions | additions
diff --git a/Magnetic Trapping.tex b/Magnetic Trapping.tex
index 274d0e4..f7c9ebd 100644
--- a/Magnetic Trapping.tex
+++ b/Magnetic Trapping.tex
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\begin{equation}
T = \exp{\int^{r_2}_{r_1} i k_r dr} \simeq \exp{\int^{r_2}_{r_1} - \frac{\sqrt{l(l+1)}}{r} dr } \, ,
\end{equation}
where $r_1$ and $r_2$ are the boundaries of the evanescent region (in this case, the upper boundary occurs where $\omegaThe fraction of transmitted energy flux through the evanescent region is $T^2$, while the fraction of reflected energy is $R^2=1-T^2$.
The wave which has tunneled through the evanescent region into the radiative core continues to propagate inward as a gravity wave, as magnetic effects are likely negligible near the top of the radiative zone. As the wave propagates inward, however, the background magnetic field strength likely increases ($B \propto r^{-3}$ in the simple case of a dipole field).