This is just a first third attempt to look at the FNAL base to get some idea about the effects of rate.
  See attached pdf

Simulation 1:
rate=  12000 PE / (2 uS)

Simulation 2:
rate=1200 PE/(2 uS)

Note on rates,

What is simlated here is 1200 photo electrons at a rate (period= 2 microseconds).
That corresponds to about 3 GeV/microsecond /channel

If there was 1 collision per microsecond  of a 100 GeV beam and if id
deposited 1/5 of its energy as EM energy in the 700 large cells, that would be a
deposited energy of 20 GeV/700 per cell = .03 GeV/cell.  That is an average rate
of <10 Photoelectrons per second.

This would be a larger number of Photo electrons at 250 GeV.