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User name R. Michaels
Log entry time 15:36:40 on February 4,2000
Entry number 32570
keyword=predicted deadtime with high prescale
Earlier today there was a disturbing observation that
while at 50 microamps with prescale factor 5 the deadtime
was 3%, when we scaled to 10 microamps with psfact= 1
the deadtime was 27%. (This was for one dominant
trigger T1.) But this is predictable as follows. Consider
the probability to have >= K hits in time T at rate R.
This probability is the by definition deadtime for prescale factor K.
It is = Sum_(n>=K) (u_f^n exp(-u_f) / n!). where u_f is R*T
and the dominant deadtime we know is T = 120 +/- 10 microsec.
As an aside, if K=1 then since by definition deadtime + livetime =1
we get deadtime = 1 - exp(-R*T) which is approx RT if R is small.
Anyway, I predict for R= 2.4 kHz and K=1, deadtime = 25+/-2 %
For R = 12 kHz and K=5, deadtime = 1.2+/-2.1 %
The errors reflect how well I remember the parameter T.
The observed deadtimes 27% and 3% match well.
One amusing implication is that its better to run with
high prescale factors, but I'm not sure I could recommend it.