deletions | additions       diff --git a/methods.tex b/methods.tex  index a48bd75..ca962b6 100644  --- a/methods.tex  +++ b/methods.tex 
...
\label{eq:sat_solution}  i(s) = \frac{s-s_{T}}{L}  \end{equation}  The transition to a saturated maser occurs at $s_T$, where $i(s)=1$. At that point, $i_0$ is negligible. Although the intensity growth of a saturated maser is linear, this regime represents the maximum efficiency that the pumping process can produce \citep{Elitzur_1992}. It represents the steady-state between the energy exhausted by stimulated emission and the energy provided by the pumping mechanism.  \subsection{Line Narrowing}  \label{sub:line_narrow} 
...
\subsection{Beaming}  \label{sub:beaming}  The exponential growth of the maser also leads to a spatial narrowing of the observed maser source. This process is referred to as {\it beaming}. Figure \ref{fig:geometry} shows the effect of this beaming in a filamentary configuration. A light ray enters from the right side, propagating through a saturated maser region (dark grey), towards the left. It hits an unsaturated region in the middle (white) where the the ray is beamed into a smaller peaked region. This occurs because this central region has the longest path length along the line-of-sight. The exponential increase with the path length leads to a significantly higher intensity ray in the center. Due to this, and the requirements needed for stimulated emission to occur, detected maser emission tends to be confined to very small regions. This result holds generally for other choices of the structure geometry