deletions | additions       diff --git a/Magnetic Constraints.tex b/Magnetic Constraints.tex  index 0e034d9..2cba625 100644  --- a/Magnetic Constraints.tex  +++ b/Magnetic Constraints.tex 
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somewhere in the g mode cavity. For incoming dipole waves with $k_\perp = \sqrt{\ell(\ell+1)}/r = \sqrt{2}/r$, magnetic suppression requires field strengths of at least % $B_c(\ell=1) = \sqrt{\pi \rho r \omega^2/(2 N)}$.  \begin{equation}  \label{eqn:Bc_l1}  B_c(\ell=1) = \sqrt{\frac{\pi \rho}{2} \rho}{2}}  \, \frac{\omega^2 r}{N}. \end{equation}  In red giant cores, the right hand side of equation \ref{eqn:Bc} is typically minimized at the peak in $N$ corresponding to the sharp density gradient within the H-burning shell. Therefore, gravity waves are most susceptible to magnetic alteration in the H-burning shell. The observation of a star with depressed dipole modes thus provides a {\it lower limit} to the internal magnetic field strength, given by equation \ref{eqn:Bc}, evaluated in the H-burning shell. This lower limit corresponds to a minimum {\it radial} field strength. Magnetic suppression via horizontal fields can also occur, but in general requires much larger field strengths (see Supplementary Material).