Filename: pscan_muons_001030.psThis document describes four momentum scans performed on the M13 channel---two with a beryllium 1AT1 target, and two with graphite. The scans were performed by Glen Marshall and Robert MacDonald. The muon and positron rates were measured for a series of magnetic field settings of the first dipole magnet (B1) of the M13 channel. The B1 magnet selects the channel momentum, and the purpose of these scans was to calibrate the B1 magnetic field (according to an NMR probe) to the well-known surface-muon edge momentum (29.79 MeV/c). Since this edge should be very sharp, the measured width of the edge also gives the momentum bite of the channel for the chosen F1 slit setting.
Filename: momentumscan_technote.ps
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\begin{document}
\title{Summary of M13 Momentum Scans of Surface Muon Edge\\
(\twist Technote 52)}
\author{Robert MacDonald\\\twist\\University of Alberta}
\date{8 March, 2001}
\maketitle
\pagenumbering{roman}
\begin{abstract}
This document describes four momentum scans performed on the M13
channel---two with a beryllium 1AT1 target, and two with graphite.
The scans were performed by Glen Marshall and Robert MacDonald.
The muon and positron rates were measured for a series of magnetic
field settings of the first dipole magnet (B1) of the M13 channel.
The B1 magnet selects the channel momentum, and the purpose of these
scans was to calibrate the B1 magnetic field (according to an NMR
probe) to the well-known surface-muon edge momentum (29.79 MeV/c).
Since this edge should be very sharp, the measured width of the edge
also gives the momentum bite of the channel for the chosen F1 slit
setting.
Summary of the momentum scan results:
\begin{center}
\begin{tabular}{|l|r|r|}
\hline
\textbf{Beryllium target} & \textbf{30 Oct.} & \textbf{5 Dec.} \\
\hline
B1 Field at Edge (Gauss) & $879.6 \pm 0.4$ & $876.5 \pm 0.4$\\
Momentum bite & 2.1\% & 1.3\%\\
\hline
\hline
\textbf{Graphite target} & \textbf{13 Nov.} & \textbf{20 Nov.}\\
\hline
B1 Field at Edge (Gauss) & $878.7 \pm 0.4$ & $877.8 \pm 0.4$ \\
Momentum bite & 1.6\% & 1.7\% \\
\hline
\end{tabular}
\end{center}
The momentum bite results are in agreement with the (very rough)
estimate of 2\% momentum bite for the F1 horizontal slit setting of 25
mm.
\end{abstract}
%\tableofcontents
%\listoffigures
%\listoftables
%\clearpage
\pagenumbering{arabic}
\setcounter{page}{1}
\section{About the Momentum Scans}
\label{sec:pscan}
The momentum scans were taken using two different targets at 1AT1.
The beryllium target was in place for the 30 October and 5 December
scans. The graphite target was in place for the 13 and 20 November
scans. (All scans took place in 2000.) The scans were performed by
Glen Marshal and/or Robert MacDonald.
An initial tune, at a momentum slightly below the surface muon edge,
was chosen to be the ``reference momentum.'' The channel momentum was
scaled by percentages relative to this reference. The B1 and B2
bender magnets were scaled by their NMR readings; the quadrupoles were
scaled by their DAC values.
About the November 13 scan: A coarse scan was performed, starting at
the reference momentum and going up to 20\% higher, in various step
sizes. Additional points were then filled in on the surface muon
edge, as well as points down to 10\% below the reference momentum.
The same scale percentages were used for the later two scans (20 Nov.
and 5 Dec.) described here, but scaling monotonically from -10\% to
+20\%. It was hoped this would reduce any hysteresis in the
quadrupole magnets.
The first scan (30 Oct.) used different (slightly coarser)
percentages, but was also done monotonically in an attempt to avoid
hysteresis effects.
For all but the 30 Oct. scan, the detector at the end of the M13
channel consisted primarily of a set of scintillators and an aluminum
target, arranged as shown in figure \ref{fig:apparatus}. $M1$ is a
thin scintillator used for counting muons, and is relatively
insensitive to positrons. Surface muons stop in the aluminum. For
these reasons, $(M1\cdot\bar{P})$ was used as a muon ID. Positrons
pass through the entire setup undeterred, so a coincidence of $E
\equiv (P \cdot E1 \cdot E2)$ is a good positron ID.
\begin{figure}
\begin{center}
\includegraphics{pscan_apparatus.eps}
\caption[Schematic diagram of apparatus.]{Schematic diagram of
apparatus. M1, P, E1, and E2 are scintillators. WC1 and WC2 are wire
chambers (WC1 is pushed against the end of the beam pipe). Al is a
set of aluminum sheets. (Not to scale.)}
\label{fig:apparatus}
\end{center}
\end{figure}
Two wire chambers were also part of the apparatus, but were used for
other beam studies. They are included in the diagram for
completeness.
The 30 Oct. scan used a similar apparatus, but without the wire
chambers (the apparatus used was for the \musr studies).
The data was taken using visual scalers, set to accumulate over 10
second intervals. Scalers counted $M1$, ``clean'' muons
$(M1\cdot\bar{P})$, positrons, and the T1 ion chamber (which puts out
pulses at a rate proportional to the proton current in the BL1A
beamline). The rates were then normalized to proton current by
dividing by the T1Ion scaler.
\section{Muon Flux, Surface Muon Edge, and Momentum Bite}
\label{sec:muflux}
%\subsection{Beryllium 1AT1 Target}
%\label{sec:Be}
%\subsection{Graphite 1AT1 Target}
%\label{sec:C}
Figures \ref{fig:pscan_muons_Be} and \ref{fig:pscan_muons_C} show the
normalized muon flux as a function of the B1 NMR reading (in Gauss),
for both scans on each target. The shape is approximately as
predicted: the muon rate rises with momentum until it reaches the
surface muon edge, at which point it falls sharply. It resumes
rising, but more slowly, after the edge---at these momenta, the only
muons are ``cloud'' muons.
\begin{figure}
\begin{center}
\includegraphics[angle=90, width=3in, height=3in]{pscan_muons_001030.ps}
\includegraphics[angle=90, width=3in, height=3in]{pscan_muons_001205.ps}
\end{center}
\caption[Normalized muon flux vs. B1 NMR reading, Be
target.]{Normalized muon flux vs. B1 NMR reading, \textbf{Be
target}. Left: October~30. Right: December~5. Muon flux is
normalized against the T1 Ion Chamber rate, which is proportional
to the BL1A proton rate.}
\label{fig:pscan_muons_Be}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[angle=90, width=3in, height=3in]{pscan_muons_001113.ps}
\includegraphics[angle=90, width=3in, height=3in]{pscan_muons_001120.ps}
\end{center}
\caption[Normalized muon flux vs. B1 NMR reading, C
target.]{Normalized muon flux vs. B1 NMR reading, \textbf{C target}.
Left: November~13. Right: November~20. Muon flux is normalized
against the T1 Ion Chamber rate, which is proportional to the BL1A
proton rate.}
\label{fig:pscan_muons_C}
\end{figure}
The minima and maxima of these graphs are summarized in table
\ref{tab:pscan_muons_minmax}. Of particular interest is the graphite
(C) target data. The minima (mostly cloud muons) are roughly the same
between the two scans, but the maxima (mostly surface muons) differ by
a factor of almost two. The graphite target split in two during the
November beam studies, and it is not known when this happened; the
difference in surface muon flux may be due to this break.
\begin{table}[tbp]
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Date & Target & Min. Flux & Max. Flux \\
\hline
Oct. 30 & Be & 0.066 & 0.73 \\
Dec. 5 & Be & 0.043 & 0.74 \\
\hline
Nov. 13 & C & 0.14 & 6.3 \\
Nov. 20 & C & 0.13 & 2.7 \\
\hline
\end{tabular}
\caption{Minima and maxima of normalized muon flux graphs from
figures \ref{fig:pscan_muons_Be} and \ref{fig:pscan_muons_C}.}
\label{tab:pscan_muons_minmax}
\end{center}
\end{table}
The curves are not quite as smooth as expected. Some of the jitter in
the November 13 data could be attributed to hysteresis (the data was
not taken in order of momentum), but not so for the other scans.
Moreover, the shape of these jitter ``features'' is reproduced in
three of the four graphs (and the fourth---from 30 Oct.---was taken
using different equipment).
Figures \ref{fig:pscan_muons_zoom_Be} and
\ref{fig:pscan_muons_zoom_C} show an expanded view of the surface
muon edge for each scan. The ``10\%'' and ``90\%'' levels correspond
to 10\% and 90\% of the range between the minimum and maximum muon
fluxes.
\begin{figure}
\begin{center}
\includegraphics[angle=90, width=3in,
height=3in]{surfacemu_closeup_001030data.ps}
\includegraphics[angle=90, width=3in,
height=3in]{surfacemu_closeup_001205data.ps}
\end{center}
\caption[Closeup of surface muon edge, Be target.]{Closeup of surface
muon edge, \textbf{Be target}. Normalized as in figure
\ref{fig:pscan_muons_Be}. The horizontal dashed lines show the
10\% and 90\% levels, and the vertical dashed lines show where the
momentum scan crosses those levels. The boxed point shows the
halfway-point between those levels, ie. the surface muon edge (at
$879.6 \pm 0.4$ Gauss (left graph) and $876.5 \pm 0.4$ Gauss
(right graph)).}
\label{fig:pscan_muons_zoom_Be}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[angle=90, width=3in,
height=3in]{surfacemu_closeup_001113data.ps}
\includegraphics[angle=90, width=3in,
height=3in]{surfacemu_closeup_001120data.ps}
\end{center}
\caption[Closeup of surface muon edge, C target.]{Closeup of surface
muon edge, \textbf{C target}. Normalized as in figure
\ref{fig:pscan_muons_C}. The horizontal dashed lines show the
10\% and 90\% levels, and the vertical dashed lines show where the
momentum scan crosses those levels. The boxed point shows the
halfway-point between those levels, ie. the surface muon edge (at
$878.7 \pm 0.4$ Gauss (left graph) and $877.8 \pm 0.4$ Gauss
(right graph)).}
\label{fig:pscan_muons_zoom_C}
\end{figure}
Let $B$ represent the magnetic field in B1 (that is, the B1 NMR).
Then $B_{10}$, $B_{50}$, and $B_{90}$ are the $B$ values for the 10\%,
50\%, and 90\% levels.
The 10\% and 90\% levels were chosen because the derivative of the
edge shape should approximate a Gaussian curve. In this case, the B1
NMR values for the 10\% and 90\% levels should roughly correspond to
the half-maximum points of the Gaussian's peak. Therefore, the
difference $B_{90} - B_{10}$ should give the ``width'' of the edge,
and $B_{50}$ should occur at exactly the surface muon edge.
The 10\% and 90\% levels are shown as dashed horizontal lines in
figures \ref{fig:pscan_muons_zoom_Be} and \ref{fig:pscan_muons_zoom_C}; the
corresponding B1 NMR values are shown as dashed vertical lines. The
boxed point shows the position of $B_{50}$---the surface muon edge of
29.79 MeV/c. This point occurs at the field values shown in table
\ref{tab:pscan_results}. (The uncertainty in the field values
represents the precision to which the B1 magnet can be set, as limited
by the coarseness of the power supply control (DAC). A detailed error
analysis has not yet been done, so this may not be the only source of
error on these points.) The fields for the graphite target momentum
scans agree within error. The beryllium target results, however, vary
significantly.
\begin{table}[tbp]
\begin{center}
\begin{tabular}{|l|r|r|}
\hline
\textbf{Beryllium target} & \textbf{30 Oct.} & \textbf{5 Dec.} \\
\hline
B1 Field at Edge (Gauss) & $879.6 \pm 0.4$ & $876.5 \pm 0.4$\\
Momentum bite & 2.1\% & 1.3\%\\
\hline
\hline
\textbf{Graphite target} & \textbf{13 Nov.} & \textbf{20 Nov.}\\
\hline
B1 Field at Edge (Gauss) & $878.7 \pm 0.4$ & $877.8 \pm 0.4$ \\
Momentum bite & 1.6\% & 1.7\% \\
\hline
\end{tabular}
\caption{Summary of momentum scan results, both targets.}
\label{tab:pscan_results}
\end{center}
\end{table}
One possible explanation for the difference in beryllium target
results is beam tuning: the 5~December scan was taken during beam tune
studies, and the tune used was probably not exactly the same as that
used for the other scans. (In fact, it was probably a better tune
(closer to what \twist will likely use).)
Figures \ref{fig:deriv_Be} and \ref{fig:deriv_C} show plots of the
``derivative'' of the surface muon edge. The derivative was
calculated as the difference in y positions (normalized flux) of
adjacent points, divided by the difference in x positions (B1 NMR).
They are plotted at the centres of their B1 NMR intervals. Vertical
lines show the positions of $B_{10}$, $B_{50}$, and $B_{90}$. All of
these plots are vaguely Gaussian, some moreso than others; with all
curves, with both curves $B_{10}$ and $B_{90}$ occur near the half-max
points of the curves, and $B_{50}$ occurs roughly in the middle of the
peak. Note that uncertainties in these ``derivatives'' were not
calculated.
\begin{figure}
\begin{center}
\includegraphics[angle=90, width=3in, height=3in]{naive_deriv_001030.ps}
\includegraphics[angle=90, width=3in, height=3in]{naive_deriv_001205.ps}
\end{center}
\caption[``Derivative'' of surface muon edge, Be
target.]{``Derivative'' (slope of segments between data points) of
surface muon edge, \textbf{Be target}. Vertical lines show
$B_{10}$, $B_{50}$, and $B_{90}$ (see text). These plots do not
include uncertainties.}
\label{fig:deriv_Be}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[angle=90, width=3in, height=3in]{naive_deriv_001113.ps}
\includegraphics[angle=90, width=3in, height=3in]{naive_deriv_001120.ps}
\end{center}
\caption[``Derivative'' of surface muon edge, both
scans, C target.]{``Derivative'' (slope of segments between data
points) of surface muon edge, \textbf{C target}. Vertical lines
show $B_{10}$, $B_{50}$, and $B_{90}$ (see text). These plots do
not include uncertainties.}
\label{fig:deriv_C}
\end{figure}
The magnetic field $B$ should be directly proportional to the channel
momentum $p$. Therefore
\begin{equation}
\label{eq:bite}
\frac{dB}{B} = \frac{dp}{p} .
\end{equation}
Thus we can calculate the momentum bite $dp/p$ from the width of the
surface muon edge:
\begin{equation}
\label{eq:dB}
\frac{dp}{p} \approx \frac{|B_{10} - B_{90}|}{B_{50}}
\end{equation}
The momentum bite results are listed in table \ref{tab:pscan_results}.
No error analysis has yet been done on momentum bite, but the results
are in good agreement with the 2\% momentum bite estimated by Jaap
Doornbos. (The width of the F1 horizontal slit defines the momentum
bite. Jaap Doornbos calculates a momentum bite of (very roughly) 1\%
per 1.25 cm slit width; the slit was set to 2.5 cm wide for these
scans.)
\section{Positron Flux}
\label{sec:eflux}
The surface muon edge should have little to no effect on the M13
positron flux---the flux should increase approximately linearly with
momentum---so this flux can be used as a check. Figures
\ref{fig:pscan_e_Be} and \ref{fig:pscan_e_C} show the normalized
positron flux as a function of B1 NMR. The flux was normalized
against the T1 ion chamber as with the muon flux.
\begin{figure}[p]
\begin{center}
\includegraphics[angle=90, width=3in,
height=3in]{pscan_positrons_001030.ps}
\includegraphics[angle=90, width=3in,
height=3in]{pscan_positrons_001205.ps}
\caption[Normalized positron flux vs. B1 NMR reading, Be
target..]{Normalized positron flux vs. B1 NMR reading, \textbf{Be
target}. Positron flux is normalized against the T1 Ion
Chamber rate, which is proportional to the BL1A proton rate.}
\label{fig:pscan_e_Be}
\end{center}
\end{figure}
\begin{figure}[p]
\begin{center}
\includegraphics[angle=90, width=3in,
height=3in]{pscan_positrons_001113.ps}
\includegraphics[angle=90, width=3in,
height=3in]{pscan_positrons_001120.ps}
\caption[Normalized positron flux vs. B1 NMR reading, C
target.]{Normalized positron flux vs. B1 NMR reading, \textbf{C
target}. Positron flux is normalized against the T1 Ion
Chamber rate, which is proportional to the BL1A proton rate.}
\label{fig:pscan_e_C}
\end{center}
\end{figure}
As the graphs show, the positron flux does seem to scale linearly with
channel momentum. There are kinks in the curves, however. For the
November 13 data, these may be due to some hysteresis in the
quadrupoles, since the data points were not taken in a single series.
(The dipole magnets B1 and B2 should not be subject to hysteresis,
since the magnetic fields for those were set by NMR.)
The kinks in the other scans are probably not due to hysteresis, since
the data was taken in order of momentum---any hysteresis should affect
all points in roughly the same way. They could be due to some
non-linearity or scaling problems in the quadrupoles.
It is worth noting that most of the features of these curves are in
the same places on both graphs for a given target (though different
for the different targets). This suggests that hysteresis is probably
not the cause.
\end{document}
Filename: pscan_apparatus.eps
Filename: pscan_muons_001030.ps
Filename: pscan_muons_001113.ps
Filename: pscan_muons_001120.ps
Filename: pscan_muons_001205.ps
Filename: surfacemu_closeup_001030data.ps
Filename: surfacemu_closeup_001113data.ps
Filename: surfacemu_closeup_001120data.ps
Filename: surfacemu_closeup_001205data.ps
Filename: naive_deriv_001030.ps
Filename: naive_deriv_001113.ps
Filename: naive_deriv_001120.ps
Filename: naive_deriv_001205.ps
Filename: pscan_positrons_001030.ps
Filename: pscan_positrons_001113.ps
Filename: pscan_positrons_001120.ps
Filename: pscan_positrons_001205.ps