A naive look at the occupancy

Ocupancy in the Endcap

In order to have an idea of the ocupancies expected in the SLHC forward tracker a very simple simulation has been made. You can skip part of this stuff and go directly to where the sugar is.

We have used Pythia to simulate ttbar events with different numbers of pileup events: none, 100, 200, 300 and 400. Why ttbar ? We have chosen this process since the cross section is quite high and, also, because many people will be interested in that sort of topologies. However, having said that, it is obvious that after >100 pile up events, the interesting topology has very little to say...

The Pythia events are processed by Geant4, where the only physical process simulated has been the transport of the particles in a magnetic field. So, there are no conversions, nor particles escaping the moderator in this simulation.

The geometry is as suggested in the straw-man layout: 5 disks, covering up to |eta|=2.5, with an external radius of 950 mm and located at Z=1200, 1650, 2100, 2600 and 3050 mm.

The pictures below show the geometry together with sample events for different number of pileup events simulated.

No pileup	pileup 300	pileup 400

We have calculated the hit density per cm2, which is shown in the pictures below for each of the disks. Also shown is the hit density as a function of the radius.

No pileup	pileup 300	pileup 400

From the pictures above one can see that z does not have a strong effect on the occupancy. The picture below shows the averave hit density, for the smaller z, as a function of the transverse radius for different pileup scenarios:

The occupancy as a function of eta can be parametrized as

and the picture below shows the fit of that function to the simulated data

The hit density is uniform w.r.t phi and has this dependency on R and z. This is the density that will be used in a toy simulation program to evaluate the occupancy of the different sensor shapes. The fit parameters are linear w.r.t the number of pile up events as shown below

From the formulas above one estimates the mean number of hits for a given sensor in a given location and then, assuming a Poisson distribution, one generates the actual number of hits for a given event. The hit positions are supposed to follow the hit density distribution shown before.

The results

Using the parametrization described above I have analyzed the occupancy with 400 pileup events for different sensor geometries. Those are based on the stave concept described here and shown in the picture above. I have considered staves with no short strips, so the sensors have the best shape to be accomodated in a 6'' wafer and with short strips, so the sensors have a length with should be a multiple of the short strip length. For the latter, I have considered 2 different situations: 1) the pitch decreases radially and 2) the pitch is fixed to 75um in all the rings, which also means that the number of channels is a sensor is reduced for the inner radii. I have tried with 2.5cm strips up to a given radius.

You can see 3 plots. The one at the top is the occupancy for a sensor with 10 128 channels ASICS, that is, 1280 channels per side in the case of fixed interstrip angle. If the pitch is fixed, the number of channels is smaller. For that plot, what is really shown is the maximum occupancy or, in other words, the occupancy plus 3 times the occupancy spread. The plot in the middle shows the percentage of the strips that only see one and only one hit, while the plot at the bottom shows the expected number of hits in a sensor. The error bars on the X axis represent the radial extent of the sensors.

From the occupancy plot is is clear that:

• The occupancy is too high with long strips (red curve) up to a certain radius. From the plot this value should be around 60cm. Using short strips (2.5cm) below 60cm the occupancy goes down to the 2% level and is still high (around 3%) for the first ring with long strips.

• Using a fixed pitch does not degrade very much the occupancy figure provided that we can cope with 3% otherwise we need to have the pitch decreasing with the radius (that is, the interstrip angle is constant)

• The plot of the percentage of strips with only one hit, it seems that short strips below 60cm helps keeping that number close to 99%

So, I guess it is clear that we need short strips for R<60cm. We still need to now what is the effect of a fixed pitch, instead of a fixed interstrip angle, on the momentum resolution and, also important, the pattern recognition. We need to know what is the allowed level of "confusion", which can be estimated by the number of hits/strip/event.

Below there a couple of pictures showing the occupancy, again average + 3 sigma, as a function of the radius and the strip length for different values of the pitch

-- CarlosLacasta - 21 Feb 2007