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    User name johna

    Log entry time 18:17:58 on March 18,1998

    Entry number 4629

    keyword='statistics' vs current calculation

    Here is a calculation for 'best current' taking into account more than the
    ideal statistics without deadtime, tracking efficiency, etc... so that we can
    try and figure out a good current for running. Counts and S/B are based on
    running so far. Assumption is 6000 counts in the remaining time if we run
    at 3000 microAmps. Our best guess is currently 7000 counts, so 6000 seems
    to be a 'safe' estimate.

    Stat1 is the 'raw' statistical uncertainty for the subtracted counts (sqrt(S+B)/S)

    Stat2 includes the uncertainty in determing the background (sqrt(B)/sqrt(10) if
    we use 10 background peaks to determine the background. Using 10 peaks,
    it makes little difference.

    Stat3 includes the effect of assuming a 1% uncorreleated systematic uncertainty
    between the signal counts and the background counts, due to a difference in
    the analysis of the events (tracking efficiency or acceptance might change due
    to different focal plane distributions, the energy distributions may be different,
    ...). Because the systematic uncertaincy is 'magnified' by the S/B ratio, this
    is worse for the higher currents.

    L/Tsys is an estimate for the uncorrelated uncertainty between the 1pass and 2pass
    data. I'm assuming a 2% uncertainty (which is low but possible, to my understanding) plus the BCM uncertainty, which is .2microA/I_beam.
    For currents of 20microAmps and above, the BCM uncertainty is 1% or less,
    and is not a large contribution


    I(microA).........20.......25.......30.........40
    Signal cts ........4000...5000...6000.....8000
    Background.....3200...5000...7200.....12800
    S/B...................0.8......1.0......1.2........1.6
    Stat1(%)...........2.12....2.00....1.91......1.80
    Stat2(%)...........2.17....2.05....1.97......1.86
    Stat3(%)...........2.82....2.86....2.95......3.20

    L/Tsys(%)........2.24....2.15....2.11......2.06
    Total(%)...........3.60....3.58....3.62......3.81

    This indicates that anywhere between 20 and 30 microAmps is ideal. If we
    lose 2 or 3 days of running time due to a major failure, a higher current would
    be somewhat favored. If the systematical uncertainty in seperating the signal
    and background is larger than 1%, then the lower currents would be significantly
    favored. If the L/Tsys errors are significantly larger, then it doesn't make much
    difference, as the statistics will not be a significant error. We have lowered the
    beam current to 30 microAmps for the moment. I would recommend going to
    25 (or even 20), but we are going to think about it more before going below 25.

    I did not take the tracking efficiency into account. At 30 microAmps, we measure
    an 78% tracking efficiency. However, as this includes real pions, random pions,
    and 10-20% protons at beta=0.2, the 'real' tracking efficiency may be >95% for
    the good pions. At 40 microAmps, the SOS fid efficiency was ~5% lower. This
    could be partially due to a modified real/random, but it could also be a true
    loss of efficiency due to the high singles rates in the SOS. If this is a real loss
    of events, then the higher currents will give a worse statistical uncertainty than
    shown above. Similarly, any other rate dependant effects should favor the low
    current, but as far as I can see, none of them are exceptionally large effects:
    deadtime is only about 5% at 40 microAmps, the tracking efficiency is only
    <=5% lower, and deadtime due to coincidence blocking is probably about
    3-5% at 40 microAmps).