Note on Non-linearity of FMS cells

 There has been a long discussion about the fact that the FMS cells seem to be characterized by a very non-linear response, with the number of observed photons per Gev of energy much greater (~30% greater) for large energy photons (E>40 GeV) than the  more common lower energy photons (E<10 GeV).

Stephen and I were looking at some of the radiation damaged cells (not yet exposed to sun).  They look like this.

What is strikingly clear is that the radiation damage is showing the shower shape distribution.  This radiation damage is clearly causing much of the non-linear behaviour
that we observe.

I want to note several points.

1) Remember that the non-linearity from the FMS is much less than was seen in the FPD. That too was large but could be simulated fairely well.  The nonlinear effects were  less than what we have seen in the FMS.
2) The FMS glass was stacked for Run 7 and useful data from PP events were not significantly analyzed until Run 9 and most data that I have analyzed came from Runs 11,12 and 13. 
3) The LED pulser was used to monitor the gains of the phototubes. In Run 11 the loss of pulse height was about 20% per month however the reduction in pi0 signals was less than 1/2 of this. This can be understood by noting that the effects of radiation are seen in the first 2 to 7 radiation length of the cell.  The LED signals pass through the full length of the cell while 50% of the signal from showers comes from downstream of the shower max.
4) In the small cells, by Run 13 the LED signals had fallen by ~ an order of magnitude, however it was mysterious that pi0 measurement were far less impacted. Probably the nonlinearity has continually gotton worse over time in run 13 but that has not been studied in detail.

I seems clear to me now that much of our confusion was based in not appreciating that the radiation damage was in the shower max region and not downstream of that region. Clearly as the cells blackened, about half of the light continued to be observed from the region beyond shower max. This provided plenty of light for pi0 analysis but lead to extremly non-linear response, with soft photons that give up most of their energy in the damaged region, they have much reduced signal. Higher energy showers deposited more of their energy in the region of the cell that was undamaged.

This suggests that for very high energy showers, the performance of the FMS was likely quite good, as most of the energy of these events is deposited in the undamaged region.

We have never tried to simulate the FMS with a profile of radiation damage along the z axis.