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{\Large \bf TRIUMF Experiment E614 \\}
{\Large \bf Addendum to Technical Note 33 \\}

\vspace{0.4cm}

{\Large \bf Cosmic Rays: calibration uses \\}

\vspace{0.4cm}

\rm{\bf M. Shotter, TRIUMF summer student \\}
\rm{\bf D. Gill, TRIUMF\\}

\vspace{0.4cm}

\rm{\bf 10 August 1999 \\}

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\begin{abstract}
    This addendum deals with some of the points raised in connection with 
TN-33: Use of cosmic rays for calibration of drift planes. The yoke was 
incorporated into GEANT, the positions where the useful cosmics crossed the 
yoke were histogrammed, and the statistics were calculated without the 
contribution from the dense stacks. Matters useful to the simulation of high 
energy particles with E614 GEANT are also listed here.\\
\end{abstract}

{\large \bf Notes on simulating cosmics\\}

    The cosmic ray particles we are dealing with are a fair bit more energetic
than particles of the type previously simulated with E614 GEANT, and we need
to consider if we need to change settings within GEANT to properly simulate
them. In particular, the ERAN card in the \verb+ e614.ffcards + file needs
to be changed to deal with the higher energies. Unfortunately GEANT is
picky over what values it allows (segmentation errors result) so it seems 
safest to stick to the default values given in the GEANT manual:

\begin{verbatim}
ERAN 0.00001 1000. 90
\end{verbatim}
   
   The first two entries give the minimum and maximum energies the process 
cross-sections are calculated for, in GeV. The third is the number of
logarithmic energy bins used in this range.

   Note that we also want the maximum track length (MAXS) to be fairly long,
say 10m, as it is the high angle cosmics with long tracks in EVOL that
we are interested in. With the field off, we can extend EVOL and WORL
in the \verb+ ugeom.F + file to look at cosmics at even higher angles;
I have done this in my simulation.

   A problem was encountered while simulating high-energy muons. At the
boundary between two materials, just before the muon crossed into the new 
material, the step size went down to the minimum displayable value (which
was actually less than the minimum value set in the STPL card) and the
simulation continued with the particle on the boundary, until the simulation
was finally terminated after 30000 steps. In this time the particle remained
in the material just before the boundary and very slowly drifted along the
boundary in some direction (I expect this drift is a result of some errors or
approximations made in the tracking routine). This hanging of the program
occurred not every time such a muon crossed a boundary, but every 50 events
or so. Favorite places to hang were the air-iron interfaces and in the G10
lamels in the detector, although it was by no means limited to just these
materials or locations. Changing the minimum step size in STPL had
absolutely no effect on the simulation.

   The only ways found to alleviate these problems was to turn down the
energy of cosmic rays to below about 100MeV (this is not really acceptable
for simulations of cosmic rays), and to change the epsil parameter in
the STPL card, the precision to which the volume boundaries and the tracks
are calculated. In the absence of any real understanding of the problem,
which seems to be part of the CERN muon tracking routine, I took the
second approach. In the \verb+ material.F + file I changed epsil to 0.002
for the non-sensitive materials, while keeping it at 0.00002, the E614
default, for the sensitive materials, which need to have a good accuracy
to calculate for example the position of wires in the chambers. This seemed
to provide a fix to the problem. If we are interested in having a high
accuracy and understanding of GEANT in this energy regime this problem will
need to be looked into.\\ 

{\large \bf Addition of yoke to E614 GEANT \\}

   The current design of yoke was added to the \verb+ ugeom.F + file, and will
probably be incorporated into the next version of GEANT. At the moment
the modeling of the yoke is fairly rough, with the only holes in the
yoke being along the beamline. The dimensions used will be obvious from
the \verb+ ugeom.F + file. It was found to be necessary to use a `MANY'
volume where the beam enters the yoke.\\ 



{\large \bf Refinements of simulation \\}

   The dense stacks were excluded from the current simulation. The only
detectors used to get cosmic ray information were the drift chamber pairs.
This obviously will lengthen the length of time needed to collect the
required data.

   Furthermore, the position that the useful cosmic rays crossed the yoke was
histogrammed, this will help position the scintillator or triggering 
detector.\\


{\large \bf Results of simulation \\}

   2100000 particles were sent through a window having measuring 
2070cm by 290cm in z and x respectively; the extra length in z was to
simulate the passage of near-horizontal cosmic rays through the detector,
from the direction in which these will be of greatest use to us.
To do this I had to lengthen WORL and EVOL as described above. 

 This corresponds to 269 seconds of cosmics (four and a half minutes).

 The resulting graphs are Figures 1 to 5.


\begin{figure}
\begin {center}
\epsfysize=18cm
\epsffile{tn33addfig1.eps}
\end{center}
\caption{No. of cosmics crossing detector planes}
\end{figure}

\begin{figure}
\begin {center}
\epsfysize=18cm
\epsffile{tn33addfig2.eps}
\end{center}
\caption{No. of useful cosmics crossing detector planes}
\end{figure}
 
\begin{figure}
\begin {center}
\epsfysize=18cm
\epsffile{tn33addfig3.eps}
\end{center}
\caption{Position of hits to side of yoke}
\end{figure}
 
\begin{figure}
\begin {center}
\epsfysize=18cm
\epsffile{tn33addfig4.eps}
\end{center}
\caption{Position of hits to end of yoke}
\end{figure}
 
\begin{figure}
\begin {center}
\epsfysize=18cm
\epsffile{tn33addfig5.eps}
\end{center}
\caption{Postion of hits to top of yoke}
\end{figure}

\newpage

   Figure 2 (No. of useful cosmics) appears to have a slightly odd shape, as
it is not a smooth decrease of odd/even planes as you would expect (like
Figure 1). This could well be due to the low number of statistics we have
in this region. Another possible effect would be the grouping together of 
pairs in the detector, they are not evenly spaced. This would favour
multiples of 4 planes, and could explain the larger peak at 16; 
however this does not account for the low value of 20.

   The integrated flux here is 432, which translates to 8-9 days at 5000
per wire.

   The cosmics are entering the detector in roughly the expected regions.
The useful places to put the scintillator are on the ends ( -128 to 128
in x, -20 to 128 in y), and on the top of the yoke (-100 to 100 in x, -150
to -70 in z, mirrored at opposite end). This is equivalent to 10.8 m$^2$ of
scintillator or equivalent material (to trigger on about 98 percent
 of the cosmics).\\


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