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\documentclass{chowto}

\title{Design of the SOS Lucite Detector}
\howtotype{reference}
\author{Liguang Tang}
\category{sos} 
\date{June 10, 2003}
\begin{document}

\begin{abstract}
This Howto outlines the purpose of the SOS Lucite detector 
and its design parameters.  General information on mechanical 
installation and electronics setup are also given.

\end{abstract}

\section{Purpose}

This detector was designed and used as part of the particle
identification to suppress protons from lighter particles, 
kaons and pions. It is a total internal reflection type of 
detector.  The Lucite material (C(CH$_3$)CO$_2$CH$_3$ polymer) 
has an index of refraction n = 1.49, so that the threshold 
$\beta$ for Lucite \v{C}erenkov radiation is 0.672.  

The outside medium is air with an index of about 1.  In such 
case, the total internal reflection takes place when the 
incident radiation angle is larger than the so called 
critical angle which is defined by:

sin($\theta_{\rm critical}$) = 1/n,

about 42.16 degrees.  Therefore, there is a threshold $\beta$ 
beyond which the total internal reflection will take place and 
the \v{C}erenkov radiation will in principle remain 
transmitting inside of the Lucite to the ends, where PMTs are 
attached.  This threshold can be found by

$\beta_{\rm TIR} \ge 1/\sqrt{n^-1}$,

corresponding to threshold at $\beta$ = 0.905.  In general with 
normal incident, with a momentum above 1.06 GeV/c radiations from 
kaons will be collectable through TIR.  On the other hand, protons 
need to have a momentum above 2.0 GeV/c in order to have 
collectable TIR radiation.   Thus, proton rejection can be done 
by Lucite \v{C}erenkov detector up to the maximum SOS momentum,
while the minimum momentum for the desired lighter particles 
depends on the mass of such particle, as an example of kaons 
mentioned above.


\section{Design and Installation}

\v{C}erenkov radiation has a continuous energy spectrum, 
with a stronger intensity in the short wavelength, in the 
ultra-violet region.  In order to minimize the scattering and 
absorption loss, UV transmitting Lucite material was used for 
the SOS Lucite detector.

The detector consists of eight horizontal Lucite bars, each 
one has a thickness of 2.54 cm and an active area of 40 x 13.7 
cm$^2$.  Tapper light guide with the same material reduced the 
cross section over a 15 cm length to fit a 3 in Phillip PMT 
mounted at each end.  Each bar was individually wrapped by 
black Teflon foil to seal outside light and absorb the escaped 
none - TIR radiation.

The eight bars were mounted on a common holding frame.  This 
frame was then attached to the supporting frame that holds the 
S2Y and S2X scintillators, in front of the S2Y.  Thus, this 
detector is ahead of S2Y.


\section{Electronics setup}

There were total of 16 analog signals sent to upstairs counting 
house patch panel.  Due to the low gain of PMTs and attenuation 
in long transmission, the signals are small for split.  Thus,
the signals were first sent to a 10 times linear amplifier.  Then 
it was splitted: 2/3 went to ADC and 1/3 to the 16-channels 
CAMAC discriminator that can provide a sum output signal.

The PMT HVs were adjusted by single photo-electron peak.  A 
common threshold was used for the discriminator module.  Single 
output from the sum was used in the PID trigger system.  If this 
signal is sent further to another discriminator, by changing the 
threshold level one can select requirement of signal from one-PMT, 
or two-PMTs, or so on.  Due to variation of incident angles, only 
one-PMT requirement was commonly used.

\section{Performance}

This detector was mainly used in the kaon experiments in the past 
with SOS as the kaon arm.  It was found that with the above 
mentioned electronics setup, background protons in trigger were 
reduced by a factor of 3.  More detailed analysis in the offline 
can reduce it further.  However, the angular spread of the 
incident particles was sufficiently large to cause certain level 
of overlap for the summed ADCs bwteen those from protons and kaons.
Thus, to maintain no more than 2 % kaon loss, small per centage of 
protons remained in the data and were further rejected by other mean, 
such as TOF.


\end{document}

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% $Log: SOS_Lucite.tex,v $
% Revision 1.2  2003/06/19 18:26:58  saw
% Minor cleanup
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% Revision 1.1  2003/06/12 16:15:47  saw
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