Systematic error in the energy calculation neglecting 2nd order terms in the calculation of dL


Purpose of this analysis is to estimate the systematic error on the 1st order calculation of dL, neglecting the higher order terms of the beam displacement. This is done in one particular case: considering the reference orbit as the central orbit. This is the case that one wants to study because, in the general case, one has to consider the variation of the displacement of the reference orbit along s (position around the ring). This quantity is difficult to measure in practice because the BPM system is not "absolutly" calibrated.

Considering the central orbit as reference orbit, it is possible to exactly calculate the orbit length for a general orbit as
L = cyclic int (sqrt ( f(s) ) ) ds , where
f(s) = (1+X/ro)^2 + (dX/ds)^2 (for bent sections) and
f(s) = 1 + (dX/ds)^2 (for straight sections)
(X: beam displacement at the position s, with respect to the reference orbit;
ro: average bending radius of the bent sections)

Because the reference orbit is the central orbit, it is NOT possible to use this "exact" calculation to get physical results. ALL OF THIS IS A TEST OF THE 1st ORDER ALGORITHM TO CALCULATE dL.

It has been compared the "exact" dL with the 1st ord. dL for the stable run

 run stack  res
 704   3   chi2
 706   3   chi2
 707   3   chi2
 708   3   chi2
 709   3   chi2
 839   6   psip
1011   8   psip
1313  19    1p1
1314  19    1p1
1315  19    1p1
1424  21   chi1
1425  21   chi1
1431  21   chi1
2015  22   psip
2202  38   chi2
2218  39   psip
2399  50    1p1
2421  52    1p1
2422  52    1p1
2440  54    1p1
2450  55    1p1
2451  55    1p1
2452  55    1p1
3014  56    1p1
3022  57    1p1
3023  57    1p1
3025  57    1p1
3026  57    1p1
3047  58    1p1
3050  58    1p1
3079  60   jpsi
3091  61    1p1
3092  61    1p1
3149  63    1p1
3150  63    1p1
3151  63    1p1
3194  65   chi1
3288  74   chi1
in three different configurations of BPM saturation:
  • Sat. OK: the configuration used is the correct one for the given run
  • No Sat. BPMs: all the BPM are considered NOT saturated for all the run
  • Lot of Sat. BPMs: the BPM are considered saturated for all the run like in run 2369 (stack 49 etac). This is one of the worst situation:
    Saturated BPMs: 104 106 108 204 206 306 406 508 603 606 608
    BPMs close to saturation: 101 103 506 601
  • The results are summarized in this plot:

    In average, the 1st order dL understimate the "real" dL for 80 um (Sat. OK value). Furthermore, the error slightly depend upon dL: in the case of Sat. OK (slope = 1.002), this means that the 1st order calculation of dL = 10 mm is underestimated by 60 um and of dL = -10 mm by 100 um. This is an error of /e835/people/15 KeV in energy in the worst case.

    These are the table of data:
    correct saturation pattern for the given run
    BPMs considered NOT saturated
    BPMs considered saturated like in run 2369


    Last update of this page -- Tue Mar 3 15:10:50 CST 1998

    useful links:

    E835 Home Page

    E835 run info table: alphanumerical ; only numerical (useful for paw)
    Offline energy calculation stack per stack
    Golden Data Stream and DSTs Page
    Luminosity Home Page

    ACNET run number stack per stack
    BPM saturation history
    Single Value Decomposition Threshold Plots
    Beam Position and Angle at the target from BPMs
    Systematic error in the energy calculation neglecting 2nd order terms in the calculation of dL
    BPM position vs time stack per stack

    Maintained by Gabriele Garzoglio.
    Comments, problems or questions -- please send mail.