MC study for optimizing the Timing Counter
P.W. Cattaneo
Geometrical acceptance
Geometrical optimization of TC in and with the newest magnetic field.
TC is simulated covering and 1 m long to measure the electron intersection with a cylinder at given radius.
Simulations with/without energy loss and with/without point like target to distinguish the contributions to inefficiency.
With point like target and no dedx the range is about . With full target and dedx the range is somehow around
(depends a little on the radius).
For the minimal is
!
"!
for larger efficiency drops very quickly.
This range is covered by 15 slabs 5 cm each.
R(cm) 25 26 27 28 29 30 31 32
-114 -118 -122 -127 -134 -143 -140 -140
#%$
+18 +16 +13 +10 +7 +3 -1 -5
In the direction,
is dictated by mechanis.
For fixing the maximal only hit on TC during the second turn are considered.
Multiple turn hits are better avoided.
Efficinecy are defined for electrons !
and appropriate . They must be multiplied by the angular efficiency 0.0675.
Maximal efficiency (with true target) for is reached with maximal as
# $
for larger efficiency drops very quickly.
R(cm) 25 26 27 28 29 30 31 32
#%$
86 89 91 94 97 100 90 86
"!$#
59 62 64 67 70 73 63 59
The efficiency for signal and for Michel background with no boundary in and , full target and only second turn are
R(cm) 25 26 27 28 29 30 31 32
% &'&( *)
+ 88.7 90.1 91.8 93.4 95.1 84.8 68.3 49.9
% &'&, .-0/2103
+ 33.7 30.6 27.1 22.4 17.9 12.5 7.9 4.6
Realistic configurations with energy loss Tried two different configurations:
2 layer: Inner 0.5 cm thick Outer 2.0 cm thick 1 layer: Outer 2.0 cm thick
A range of inner radii from 28.0 to 30.0 with 0.5 cm steps.
Without applying the cuts in and and energy but requiring hit in the second turn on the outer layer
First configuration :
R(cm) 28.0 28.5 29.0 29.5 30.0
% & & ( *)
+ 88.0 86.0 82.3 75.4 66.9
% & & , .-0/ 1 3
+ 17.9 15.3 12.8 10.4 8.2 Second configuration :
R(cm) 28.0 28.5 29.0 29.5 30.0
% & & ( *)
+ 91.0 90.9 89.5 86.5 80.3
% & & , .-0/ 1 3
+ 21.1 18.8 16.3 13.8 11.2
The reference is the ! + efficiency obtained at !
in the first configuration. The background should correspond approximately to a counting rate of 1MHz every
muon decay.
Corresponding to in the second configuration with reduced background.
Realistic efficiencies
Finally putting together all the cuts geometric and on the en- ergy loss in the layers, but not requiring explicitly the hits are in the second turn (it is almost forced by the limited length of the counter )
First configuration :
R(cm) 28.0 28.5 29.0 29.5 30.0
% & & (
*)
+ 85.2 84.7 84.3 80.2 72.3
% & & , .-0/ 1 3
+ 19.7 17.3 14.9 11.8 9.6 Second configuration :
R(cm) 28.0 28.5 29.0 29.5 30.0
% & & ( *)
+ 93.3 93.6 93.0 88.8 82.4
% & & , .-0/ 1 3
+ 23.1 20.4 17.7 14.7 12.1
For example at in the second configuraion there is a slight improvement in the signal efficiency and in background suppression compared to any radius in the first.
One layer versus two layers
The only reason to have two layer is to reduce the trigger rate.
Covering a band identified by the calorimeter requires 4 slabs.
With additional information on z, only two are required.
Alternatively a smart choice of three slabs with one layer give an extra 6-7% inefficiency (to be confirmed).
In this case the background rate would increase only of a fac- tor 1.5.
From the previous tables at fixed background count, the 2 layer has about 5% larger inefficiency equivalent to the loss due to using three slabs in the trigger.
The two layers configuration should also gives further ineffi- ciency in the timing measure due to the extra interaction in the inner layer.
The trigger rate would not increase at all if the ratio of the charge can be used to measure z within 20 cm, that seems quite a reasonable goal.
Therefore the 1 layer solution is a interesting alternative to the traditional 2 layers with large saving of money and work .
