New Cosmic Muon Stand at Fermilab, 1999

1. Introduction.

The new Cosmic Muon Stand at Fermilab has been in operation since Nov. 1998. It is used for the test of the CMS Endcap Muon Cathode Stip Chambers and its electronics. The stand was designed by E.Borisov with contributions from Yu.Bonushkin, A.Korytov, Yu.Pischalnikov and O.Prokofiev and built with help of N.Chester. Assembling and work on scintillation counters were done by Y.Pischalnikov, trigger - S.Medved, DAQ and online software - A.Bujak, data taking - S.Medved, offline software and data analysis - A.Bujak, N.Terentyev.

Here we present some measurements characterizing the scintillation counters of this stand. The counters serve as a trigger on cosmic muons and the common stop for the TDCs. There are total 24 counters assembled in two rows, top and bottom. Each from these counters is readout by two photomultipliers (PMT, total 48). The current trigger requires the coincidence of signals from four photomultipliers of two counters - the bottom and the top which form the vertical hodoscope. The trigger is OR of these 12 hodoscopes. As a common stop for TDCs of scintillation counters and front end anode electronics of the chamber the latest in time signal from the coincidence of four photomultipliers is used. The goal of the measurements was to estimate the averaged time resolution of the signal from PMT and to estimate the contribution of the trigger time vs coordinate dependence into the CSC anode "bunch crossing efficiency". The data were analyzed and presented here by N.Terentyev.

2. The Muon Track Coordinate and Angle distributions.

The distribution of PMT hits, time distributions and trigger PMT distributions are presented in Fig.1. The PMTs corresponding to hodoscopes 3,7,8 and 9 have less hits than others. We will see later (in coordinate distributions) that these hodoscope are short of hits at the edges. The peak at 410 nsec in TDC distributions are signals from trigger counters. Trigger PMT distribution shows that we have triggers from bottom counters only (PMT=1,2 or 5,6 or 9,10 etc) because the muon travels about 9 nsec from top counters to bottom and the bottom counters almost always have signal later than the top counters (at the equal cable delays).

The coordinate distributions for the top and bottom counters of all 12 hodoscopes (in nsec) are given in Fig.2 and plane angular distribution (for all hodoscopes, in the vertical plane parallel to the counters) - in Fig.3 . Here the coordinate for example for the hodoscope #1 (in nsec) is given by the formula (1):

	Xb = (tdc1-tdc2)/2 for the bottom counter and 
	Xt = (tdc3-tdc4)/2 for the top counter				(1)

where TDC is Le Croy 3377 TDC count (with 0.5 nsec bin width) . The plane angle was measured thru Xb and Xt as:

	tan(theta) = (Xb - Xt)/h					(2)
where Xb,Xh were rewritten in cm using the length of the counter of 235 cm and the light signal travel time of 15 nsec. The vertical distance between counters in hodoscope h is 275.6 cm. The mean of angular distribution in Fig.3 is not zero because no attempt of counter alignment was made in the analysis.

3. Trigger time resolution.

The sum of two signals from the top counter in each hodoscope
	SUM = tdc3 + tdc4  						(3)
was used to estimate the time resolution of the trigger (per one PMT). But first because the time of the trigger as a TDC common stop depends from the muon coordinate Xb in the bottom counter such dependence should be taken into account. The SUM vs Xb distributions are presented in Fig.4 for hodoscopes 1-4 and the corresponding correction is:
	SUM = tdc3 + tdc4 - 2*abs((tdc1 - tdc2)/2)			(4)  
One more correction is due to the angle dependence of the muon track:
	SUM = tdc3 + tdc4 - 2*abs((tdc1 - tdc2)/2)
			  - 2*v*h*(SQRT(1 + ((Xb-Xt)/h)**2) - 1)	(5)
The possible contribution of the signal amplitude to the trigger timing was ignored. We don't have control on it. Also the discriminator level was set low enough to make such contribution small. The SUM vs Xb distributions after corrections above are presented in Fig.5 for hodoscopes 1-4. Note that at the edges of counters the SUM distributions are slightly different. The means of SUM in slices of Xb at -6 < Xb < 6 are in Fig.6 for all hodoscopes.

In calculation of the time resolution of trigger the contribution due to angle dependence was also ignored (it is less than 0.16 nsec according to the simulation with random distribution of the hits in top and bottom counters). Now, in terms of absolute time:
	 tdc3 = Tr - t3   tdc4 = Tr - t4  
         tdc1 = Tr - t1   tdc2 = Tr - t2				(6)
where Tr, t1, t2, t3 and t4 are absolute time of the trigger and PMT 1 thru 4 signals. Therefore (4) becomes:
	SUM =  Tr - (t3 + t4) + t1 if trigger from t2 (Tr = t2)
	SUM =  Tr - (t3 + t4) + t2 if trigger from t1 (Tr = t1)		(7)
and the variance of the SUM is:
	D(SUM) = D(Tr - t3 - t4 + t1) = 4*D(t)				(8)
if we assume that all 4 time signals in given hodoscope have one and the same resolution. The resolutions obtained as sqrt[D(SUM)]/2 are given in Fig.7 for all hodoscopes in the same slices as means in Fig.6 . Both parameters were found from the fit by gaussian distributions. The means and resolutions for each hodoscope (without dividing on slices in Xb) are shown in Fig.8 . One can see that resolutions are within the interval of 0.8-1.0 nsec. The time resolutions, measured earlier on the bench were 0.5 nsec (A.Korytov) and 0.6 nsec (S.Medved,Yu.Pischalnikov).

4. Trigger contribution to the anode front end "bunch crossing identification efficiency".

The correction to the single plane time distributions from the anode front end is 2 times less than in (5) because SUM in (5) has two entries of Tr. It is pictured in Fig.9 for all 12 hodoscopes together. Note that the observed RMS is only 2.3 nsec.

Since the RMS of the second arrival time distribution is about 5.0 - 6.0 nsec for the data from the Cosmic Muon Stand the contribution of biased trigger with RMS of 2.3 nsec does not look to be significant. The resulting RMS is only slightly higher by about 0.2-0.3 nsec. Therefore the efficiency of the "bunch crossing identification" goes down by maximum 1-1.5% (see Fig.10 ).
Last modified: Fri Apr 30 18:00:00 CST 1999