Skip to content

Adds distribution data for N-Body distribution #20

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
HunterBelanger wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Adds distribution data for N-Body distribution #20

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
Binary file modified ACEFormat.pdf
View file
Open in desktop
Binary file not shown.
39 changes: 29 additions & 10 deletions src/ContinuousEnergyNeutron.tex
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -831,21 +831,40 @@ \subsubsubsection{\var{LAW}=61---Like \var{LAW}=44, but tabular angular distribu
\end{description}

\subsubsubsection{\var{LAW}=66---$N$-body phase space distribution}\label{sec:LAW66}
\begin{LAWTable}{\var{LAW}=66 (From ENDF-6 \MF=6 \var{LAW}=6)}
\var{LDAT}(1) & \var{NPSX} & Number of bodies in the phase space \\
\var{LDAT}(2) & $A_{P}$ & Total mass ratio for the \var{NPSX} particles.
\label{tab:LAW66}
\end{LAWTable}
\begin{ThreePartTable}
\begin{TableNotes}
\item[$\dagger$] \label{tn:LAW66FractionInterpolationScheme}
\begin{description}
\item[\var{INTT}=1] histogram distribution, and
\item[\var{INTT}=2] linear-linear distribution.
\end{description}
\end{TableNotes}
\begin{LAWTable}{\var{LAW}=66 (From ENDF-6 \MF=6 \var{LAW}=6)}
\var{LDAT}(1) & \var{NPSX} & Number of bodies in the phase space \\
\var{LDAT}(2) & $A_{P}$ & Total mass ratio for the \var{NPSX} particles \\
\var{LDAT}(3) & \var{INTT} & Interpolation flag\tnotex{tn:LAW66FractionInterpolationScheme} \\
\var{LDAT}(4) & $N_{P}$ & Number of points in the distribution \\
\var{LDAT}(5) & $T(j),j=1,\ldots,N_{P}$ & Fraction of max energy \\
\var{LDAT}(5+$N_{P}$) & $\PDF(j),j=1,\ldots,N_{P}$ & Probability density function \\
\var{LDAT}(5+$2N_{P}$) & $\CDF(j),j=1,\ldots,N_{P}$ & Cumulative density function
\label{tab:LAW66}
\end{LAWTable}
\end{ThreePartTable}

The outgoing energy is
The outgoing center-of-mass energy is
\begin{align}
E_{\mathrm{out}} &= T(\xi)E_{i}^{\mathrm{max}} \\
E_{\mathrm{out}}^{\mathrm{CM}} &= TE_{i}^{\mathrm{max}} \\
\intertext{where}
E_{i}^{\mathrm{max}} &= \frac{A_{p}-1}{A_{p}}\left( \frac{A}{A+1}E_{\mathrm{in}}+Q \right) \\
\intertext{and $T(\xi)$ is sampled from:}
P_{i}(\mu,E_{\mathrm{in}},T) &= C_{n}\sqrt{T}\left( E_{i}^{\mathrm{max}}-T \right)^{3n/2-4}
E_{i}^{\mathrm{max}} &= \frac{A_{p}-1}{A_{p}}\left( \frac{A}{A+1}E_{\mathrm{in}}+Q \right). \\
\intertext{With $n=\mathrm{NPSX}$, the analytic distribution for $T$ is:}
P(T) &= C_{n}\sqrt{T}\left( 1 - T \right)^{3n/2-4} \\
\intertext{where $C_{n}$ is taken to be:}
C_{n=3} &= \frac{8}{\pi}\\
C_{n=4} &= \frac{105}{16} \\
C_{n=5} &= \frac{256}{7\pi}
\label{eq:LAW66}
\end{align}
The cosine of the center-of-mass scattering angle, $\mu_{\mathrm{CM}}$, is isotropic.

\subsubsubsection{\var{LAW}=67---Laboratory Angle-Energy Law}\label{sec:LAW67}
\begin{ThreePartTable}
Expand Down