Systematic errors with the "final" collimator
Estimates have been made of the effects of position, size, direction and energy modulation for the "final" collimator geometry of early August, 2005, Juliette's row 20 (http://www.phys.vt.edu/~jmammei/coll_opt.html) with minitorus off and rectangular bars 18 cm wide. Results are given also for the best version of the upstream collimator with handlebar-shaped bar, Juliette's row 11, and for the March'05 version of the "Boston" upstream collimator with 15 cm wide bar. Calculations were made with the following assumptions:
False asymmetry: no more than 6 × 10-9 from each source.
Position modulation: the beam moves with helicity as x± = x0 ± δx, with δx = 20 nm. The nominal beam position is x0 = 0. Results assume identical bars and QTOR fields. Results are given also for how precisely bars need to be aligned in the radial direction and how closely magnetic fields in QTOR segments should match so that the added uncertainty in the asymmetry is no more than 6 × 10-9.
Size modulation: The beam diameter is D± = D0 ± δD, with D0 = 200 µm for the unrastered beam.
Direction modulation: The direction of the beam on target is θ± = θ0 ± δθ, with θ0 = 60 µrad (0.6 mm @ 10 m).
Energy modulation: Beam energy is E± = E0 ± δE. The nominal beam energy is 1.165 GeV.
Beam parameters that cause a false asymmetry of 6 × 10-9 |
|||||
|---|---|---|---|---|---|
Source of Error |
Error goes as |
Condition |
"Final #20" |
"Upstream #11" |
"Boston" |
| Position modulation | x0δx |
δx = 20 nm |
x0 < 0.71 mm |
x0 < 0.4 mm |
x0 < 0.3 mm |
Positioning bars in radial direction |
" |
δr < 19 mm |
δr < 5 mm |
δr < 5 mm |
|
Matching QTOR sectors |
" |
δB/B < 1.6% |
δB/B < 0.4% |
δB/B < 0.4% |
|
| Size modulation | D0δD |
D0 = 200 µm |
δD < 0.4 µm |
δD < 0.24 µm |
δD < 0.18 µm |
| Direction modulation | θ0δθ |
θ0 = 60 µrad |
δθ < 1.4 µrad |
δθ < 0.4 µrad |
δθ < 0.4 µrad |
| Energy modulation | δE |
E = 1.165 GeV |
δE/E < 6 × 10-9 |
δE/E < 3 ×10-9 |
-- |
The figures below show how the conditions vary with the radial position of the inner edge of the Cerenkov bars (nominal value 313 cm) for the final collimator if nothing else is changed.
(a) Variation of rate. As the bar is moved out, more of the radiative tail is seen, and then the lower edge of the elastic peak starts to be cut.
(b) Position modulation: condition on x0.
(c) Size modulation: condition on δD.
(d)
Position modulation: condition on radial position of Cerenkov bars.
(e)
Direction modulation: condition on δθ.
(f) Energy modulation: condition on δE/E.
The event rate increases a little if the bars are moved outward, but conditions on beam parameters become tighter.
JB, 31 August 2005 @ UM