deletions | additions       diff --git a/Magnetic_fields_can_provide_the__.tex b/Magnetic_fields_can_provide_the__.tex  index a8bece3..44be1a6 100644  --- a/Magnetic_fields_can_provide_the__.tex  +++ b/Magnetic_fields_can_provide_the__.tex 
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Magnetic fields can provide the mechanism for trapping oscillation mode energy in the core by altering gravity wave propagation. The nearly horizontal motions and short radial wavelengths of gravity waves in RGB cores will bend radial magnetic field lines, creating strong magnetic tension forces. {\bf Thebuoyant  acceleration created by required to restore  a wave with horizontal  displacement $\xi_r$ in the radial direction $\xi_{\rm h}$  is $\sim \! \xi_r N^2$, \xi_{\rm h} \omega^2$,  whereas the magnetic tension acceleration due to ahorizontal wave displacement $\xi_{\rm h}$ in a  radial magnetic field of strength $B_r$ is $\xi_{\rm h} B_r^2 k_r^2/(4 \pi \rho)$, where $k_r$ is the radial wavenumber and $\rho$ is the density. Gravity waves are strongly altered by the magnetic fields when these two forces are equal, which for dipole waves occurs at a critical magnetic field strength (see supplementary online material)} \begin{equation}  \label{eqn:Bc}  B_c= \sqrt{\frac{\pi \rho}{2}} \, \frac{\omega^2 r}{N} \, . 
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