\section{Moderator: A time-of-flight source (pulsed)}
\label{s:moderator}
\index{Sources!Time of flight pulsed moderator}

\component{Moderator}{(System) Mark Hagen, SNS}{$r_s$, $E_0$, $E_1$, $z_f$, $w$, $h$, $\tau_0$, $E_c$, $\gamma$}{}{}
\mcdoccomp{sources/Moderator.parms}

The simple time-of-flight source component \textbf{Moderator} resembles
the source component \textbf{Source\_simple} described in \ref{source-simple}.
\textbf{Moderator} is circular with radius $r_s$ and focuses
on a rectangular target of area $w \times h$ in a distance $z_f$.
The initial velocity is chosen
with a linear distribution within an interval, defined by the
minimum and maximum energies, $E_0$ and $E_1$, respectively.

The initial time of the neutron is determined on basis of a
simple heuristical model for the time dependence of the
neutron intensity from a time-of-flight source.
For all neutron energies, the flux decay is assumed to be exponential,
\begin{equation}
\Psi(E,t) = \exp(-t/\tau(E)) ,
\end{equation}
where the decay constant is given by
\begin{equation}
\tau(E) = \left\{
\begin{array}{cc}
 \tau_0                               & ; E<E_c \\
 \tau_0 / [ 1 + (E-E_c)^2/\gamma^2 ]  & ; E \geq E_c
\end{array}
\right.
\end{equation}

The decay parameters are
$\tau_0$ (in $\mu$s), $E_c$, and $\gamma$ (both in meV).

Other pulsed source models are available from contributed components. See section \ref{sources-seealso}.
