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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.