S.Ritz 25 March 01, Updated 29 March 01
At the 23 March meeting of the beam test subgroup, Eduardo suggested we begin thinking seriously about the arrangement of the towers for the beam tests. More than one configuration is possible, of course, but that means more rigging time and incremental costs of more fixtures, etc.
Three classes of studies drive the choice of layout: PSF studies, CAL resolution studies, and background rejection studies. The first two are mainly considered here.
Some simple facts about LAT geometry are illustrated here. I ran the simulation, launching 1 GeV (around our "sweet spot" energy) gammas from (x,y,z,theta,phi) = (150, 20, 100, 55, 0). I used the AO version of the simulation (since it is the version most carefully validated at this point) -- the flight geometry is slightly different but that doesn't matter here. Here is a typical event viewed in the XZ plane:
It is clear that a 2x2 arrangement of towers for off-axis PSF studies is probably not very useful. Note that in a sizable number of events, significant energy is deposited in the left-most towers in this view (distributions are forthcoming). For the ~on-axis studies of the PSF, two towers should be sufficient (4 towers are not needed, so the on-axis studies can proceed in the early part of the beam test). For ~on-axis studies of the energy resolution, the 2x2 arrangement may be more useful, and that must also be studied. It may also be difficult with only 4 towers to do off-axis PSF studies over a meaningful range of phi.
Here is the same event viewed from the front of the instrument, looking back along -Z:
The 4x1 configuration of the beam test is represented by the 2nd row of towers in this view, and the surrounding rows of towers can be used to analyze the leakage. To get an idea of the leakage visually, here is the same event in the YZ plane:
There is some leakage to surrounding towers, but it is not very large. I am working on making the histograms, but this is a fairly represtative event.
It is also important to consider events at lower energy (where the multiple scattering can widen the event) and at higher energy (where the measurable shower is wider). At 20 MeV, the events are very short and are very well contained transversely. At 100 MeV, a few percent of the events scatter into neighboring towers after passing through several layers, but this is not very important for the PSF measurement since most of the pointing information comes from the first 2-3 measurements which are contained in the 4x1 towers. IF we need the calorimeter for the energy measurement (i.e., no external tag), this could be a significant problem for E>100 MeV.
The effective area is falling rapidly with incidence angle in the region around 55 degrees, so we will want to measure this region carefully in the beam test and do detailed comparisons with the simulation. This doesn't appear to be possible with a 2x2 tower arrangement.
The 4x1 configuration is also better for most calorimeter studies, since a greater number of radiation lengths are presented to off-axis particles. Similarly, for backsplash studies the 4x1 configuration gives a wider range of tile distances from the core of the shower.
Thus, for both PSF and CAL studies, the 4x1 configuration is a higher priority. The 2x2 configuration allows us to integrate over phi more effectively, but over a reduced range of theta values (probably less than 20-25 degrees).