Time Of Arrival/R56 measurements Period 13

Background Dave Newton’s Parameter scans \\Dlfiles03\alice\Simulations\R56 AR1 (parameter scan).pdf Deepa’s sextupole studies from ALICE physics meetings.

TOA First Attempt # April 2012 Prelim results presented at \\Dlfiles03\Apsv4\Astec\Projects\ALICE\ALICE_Physics_Meeting\2012_05_01 \\Dlfiles03\Apsv4\Astec\Projects\ALICE\ALICE_Physics_Meeting\2012_05_01 R56 measured by TOF at AR2-BPM-01 and ST1-BPM-01. First measurement of post linac R56 at AR2-BPM3 (#2907) gave 150 mm, expect 280 mm naively And ELEGANT model of BURT _2351 on this shift predicts R56 = 450 mm – ARC is NOT isochronous for this BURT. AR1-Q1-4 are not the right values for isochronicity, and R56 is VERY sensitive to these quads. – Another reason for discrepancy could be because AR1-SEXT-01 was on (2.8 A), misalignment could affect R56 – Dipoles are not perfect symmetrical currents. On this shift in comp-chicane first 3 dipoles are symmetric and fourth one is 2 % weaker. AR2-Dipoles differ by < 0.5%. ELEGANT investigations suggest this alone isn’t enough to explain the discrepancy. – R51, R52?? Also attempted measurement of injector R56 but inconclusive. Try again in future. ELEGANT BURT _2351 post linac R56, AR1-SEXT-01 off Change in TOF (mm) vs fract change in beam energy

#2908 (Deepa, Julian) AR2-BPM-01 vs AR1 params (Q1/3, Q2/3, SEXT-01, SEXT-02) Indicates very strong effect from AR1-Q1,Q4, as expected. Trend of R56 AR1-SEXT-01 = 2 A for first point, = 0 A for other two points AR1-SEXT-02 = 0 A AR1-SEXT-01/2 = 0 A Nominal Q1,4 setting, first measurement was 150 mm (with AR1-SEXT-01 on), here it is 191 mm with AR1- SEXT-01 off Q2,3 nominal value Shouldn’t this be the same value as this? Shouldn’t this be the same value as #2907, 150 mm? Repeatability of measurements?

#2927 FJ/HA/Terry Atkinson Repeatability of Measurment AR1-SEXT-01 (A) R56 The difference between TOA for these two points was ~ 0.5 pS. Maybe a fluke? Wanted to get a more detailed scan of R56 vs Sext-01 to see trend. Scanned AR1-SEXT-01 0 A to 9 A then go back to repeat a point at 3 A BPM No particular trend observable but alignment of beam w.r.t quadrupole unknown Was the scope set up OK in this shift?

#2996, July 2012 Aim was combined effect of AR1 steering and AR1-SEXT-01 on R56. Attempt to use AR1-BPMs to judge trajectory. AR1-BPMs have new EMMA-style single bunch electronics. Also attempt beam-based calibration of AR1- BPMs Then tried R56 vs AR1-1 sextupole. #2996 took BPM calibration data.

#2998, 03 July 2012 R 56 measured as function of AR1-SEXT-01 Some trend visible but large fluctuations in data. Scope set-up unclear, treat this data with caution.

# July 2012 More studies of dependence of R56 on AR1-SEXT-01 Scope set up checked more carefully AR1 BPMs used more carefully Clearer trend of R56 vs AR1-SEXT-01 observable, but not the same as that indicated in previous shifts (#2998, #2908) Changing AR1Q1-4 from 2.19 to 2.23 changes R56 from ~ 150 mm to 175 ~mm. Shift data #2908 suggests R56 should be more sensitive than this. Changing compression chicane dipoles from 64.48, 64.51,64.51, A to uniformly 63.9 A (except for final dipole changed to 63.1 A to enable transport through undulator) changes R56 from 176 mm to 173 mm Deepa’s observation: AR1-SEXT-01 does not steer beam significantly on AR1-BPM-03. – Other Deepa’s analysis?

# Jul 2012 At first, repeated R56 vs AR1-SEXT-01 measurement. Also recorded AR1 BPM readings. Not sure what they tell us though. Again tested sensitivity of R56 to AR1Q1-4. Changed AR1Q1-4 from 2.19 to 2.23; this changes R56 from ~ 171 mm to 220 ~mm. Shift data #2908 suggests R56 should be more sensitive than this Then tested TOF sensitivity to AR1-SEXT-01 setting AR1-DIP-01 to different values. Prelim conclusion is that AR1-SEXT-01 doesn’t change R56 significantly for this set up, for various steerings through it. This conflicts with the behaviour seen in #3003

Simulated AR1-SEXT-01 Effect Just a rough study to get some idea of the effect Use ELEGANT to compute R56 with offset AR1-SEXTUPOLE of varying strength. K = 70 is approx. equivalent to 1 A. NB this is not a “design lattice”, this is a recently used BURT, where the ARC1 is not isochronous and the R56 with sextupole off is ~ 450 mm in the Elegant model. Only conclude from this that AR1-SEXT-01 can have both +ve and –ve effect on the R56 and that the effect can be sizable

# Jul 2012 Looked at some ‘scope’ issues. Particularly the ‘two-peak’ TOF. – We initially thought this might be due to the sampling rate of scope 20 Gsamples/sec, divided by 2 channels = 10 Gsamples/sec => Samples separated by 100 pS Changed sampling rate of scope to 10 Gsamples/sec total. Had NO EFFECT on the separation of the two peaks Then started measuring the TOA of the 2 nd, 3 rd, 4 th bunch in the train and again looked at the 2-peak separation. There seems to be a clear linear relationship.

# Jul 2012 Checked path length dependence on energy (linearity) in more detail – Was originally checked in #2907 Checked this with AR1-SEXT- 01/02 off and ON at 3 A Also checked TOF dependence on beam incident angle into chicane to probe R51, R52 of chicane. Preliminary result no obvious dependence seen. RMS residual between fit and points is ~ 3 pS. This is an indication of the minimum change in TOF we can measure with this method. Equivalent to a R56 difference of ~20 mm, if we can vary beam energy by 4% The blue points on the upper and lower graphs are the same data

# 3034 and # 3037 # 3034 spent looking more closely at scope ‘2-peak’ issue. Input from A. Wolski, S. Jamison, S. Hill. – Seems a feature of ‘long’ delay between scope trigger and measure. You see it even when trigger+measure is on the same BPM signal #3037 alternative method, use TOF location BPM as trigger and measure MO timing relative (a la buncher zero cross) No longer two peaks TOF distribution is approx gaussian with rms ~7 pS LA = 0.4 R56 measured with two different energy ranges 60 pC LA = 0.27

#3056 Fri 27 Jul 12 Shift 3 (FJ/AW) Path length vs beam energy in AR1 ONLY (use AR1-BPM-06) Used new scope. ‘Black’ EMMA lecroy scope 40 Gsamples/sec on all channels. TOF measured relative to MO signal (from EMMA collection of cables) EFFECT OF AR1-SEXT-01 (AR1-SEXT-01 OFF) EFFECT OF AR1Q1/4 EFFECT OF AR1-SEXT-01 compared to AR1-SEXT-02

#3058 Sun 29-Jul-12 Used LC1 GS to vary beam energy as alternative to LC2 GS

#3058 Sun 29-Jul-12 First measured path length vs energy for different AR1-Q1/Q4 Energy spread not carefully minimised

#3058 Sun 29-Jul-12 Then used LC1 to vary the energy Took path length vs energy for several different Ar1q1/4 settings (amps) 2.11, 2.15, 2.19, 2.23 Extract the R56 and T566 from the curves Error bars are statistical from the fit (Mathematica fit[“ParameterTable”])

#3058 Comparison with ELEGANT prediction. Systematic Errors Use ELEGANT matrix output to predict R56 and T566 vs AR1-Q1/4 for #3058 BURT. Some systematic differences between measurement and expectation, several candidates – Quad residual field (affects R56 AND T566, always) – Sextupole residual field (affects T566, amd R56 if misaligned) – Fit systematic errors (use cubic rather than parabolic?) (Tried this, cubic coeff very small, doesn’t make a big difference) – Uncertainty in what is the reference energy (i.e. which point is dp/p = 0 ?) It’s not very difficult to get model to match data by modest tweaks to the model. Is achieving perfect model/data agreement so useful?

# 3076 Mon 06-Aug-12 Shift 2 Same BURT as #3058 Post-chicane meas’ts vs AR1-Q1/4 (use AR2-BPM-01) Poorer fits but roughly similar systematic differences between ELEGANT and measurements as seen in #3058

#3076 Mon 06-Aug-12 Shift 2 Also tried to use ST2-BPM-04 immediately post-chicane (stripline BPM, been using only button BPMS until now) Need to measure timing of signal, and no ‘zero crossing’ feature On #3076 used but affected by amplitude? introduce artefacts ? Saw strange behaviour in path length vs E curve There is also (relative_level = 50% of max) should be more insensitive to amplitude. No time to try this on 3076.

#3086 Fri 10-Aug-12 Shift 2 Continued with ST2-BPM-04 immediately post-chicane for path length vs E vs AR1- Q1/4 – Used to measure BPM signal TOF – AR1-Q1/4 = 2.11, 2.17, 2.23 R56 in ST3 between ST2- BPM-04 and AR2-BPM-01

Summary Consistency of AR1 and post-chicane measurements (on separate shifts) #3058 ARC1 R56 #3086 Post-chicane R56 Separation of lines = R56 of chicane Red dashed line indicates AR1 isochronous condition

FEL AR1 setups How does the FEL AR1 set ups vary from shift to shift? Does the Q1/4 variation simply follow the variations in linac phase setting shift-to-shift?

Extra Notes

Chicane R56 Noticed that in ELEGANT, the R56 change over the the chicance (for all dipoles set to the design angle of 21.5°) was always 0.28 m, even if the upstream lattice (AR1) doesn’t close the dispersion through this chicane. One might naively think that R56 =  f(  )ds, where  is the disperions. So that if you don’t close the dispersion from AR1, then  and  ’ are non zero through the chicane and this will affect the R56 of the chicane. From linac exit to chicane exit, the transfer matrix is, apply AR1 matrix first, then chicane matrix Then the R56 from linac exit to chicane exit is, for ideal chicane See Chao and Tigner Sec “Single Element Optics” for general features of matrices of lattices with mid-plane symmetry about y So even if R16,26 (dispersion and dispersion’) of AR1.neq. 0, this expression holds, for ideal chicane The R16,26 of AR1 could easily be non zero (but probably not huge), since this is never checked routinely This is true for RECTANGULAR DIPOLES WHICH ARE ALL PARALLEL, see P. Williams Mathematica Notebook.

Transfer Matrix of ALICE Compression Chicane. To get R51 = R52 = 0, you need a chicane with RECTANGULAR DIPOLES which ARE ALL PARALLEL. Edge effects are crucial, if you don’t include the edge matrices you don’t get perfect cancellation of the R51, R52. A good ref is ‘Beam Trajectory Calculations in Bunch Compressors of TTF2’, P. Castro, DESY Technical Note 03-01, April 2003 which explains how to put the matrices together and gives the final result. This note is available on the web and at \\Dlfiles03\alice\Analysis\Period 14 data\AP_period13and14 Also P. Williams has a mathematica notebook which does the matrix computation for the ideal 4-dipole compression chicane. To model the rectangular parallel dipoles, you carefully chose edge and wedge combinations – First dipole. Normal incidence entry matrix (identity) then a wedge bend matrix, then an exit edge matrix (21.5°) – Second dipole. Entrance edge matrix (21.5°), then wedge bend matrix, then normal exit matrix (identity) – and so on … Also, see Hwyel and Peter’s paper ‘Modular Path Length Corrector’ at – This derives the transfer matrix for a compression chicane for ‘normal entry and exit from the dipoles’ i.e. wedge bends. – The transfer matrix has R51,52 elements which are non-zero but are small for small angle bends. ALICE Compression chicane does not have wedge bends. It has rectangular magnets which are tilted, not parallel. Thus ALICE compression chicane will not have zero R51,52 elements

ELEGANT tests of chicane R56 Simple lattice containing only chicane Chicane model is rectangular dipoles tilted by ½ the bend angle WHICH IS THE REALITY. This is approximated by bend dipoles with appropriate entrance/exit angles ST2DIP01:CSBEND, l = 0.408, angle = , e1 = , e2 = , k1 = 0; ST2DIP02:CSBEND, l = 0.408, angle = , e1 = , e2 = , k1 = 0; ST2DIP03:CSBEND, l = 0.408, angle = , e1 = , e2 = , k1 = 0; ST2DIP04:CSBEND, l = 0.408, angle = , e1 = , e2 = , k1 = 0; ELEGANT gives R56, R51, R52 = , ×10 -17, ELEGANT gives R56, R51, R52 = , ×10 -17, Now use model with parallel dipoles ST2DIP01:CSBEND, l = 0.408, angle = , e1 = 0, e2 = , k1 = 0; ST2DIP02:CSBEND, l = 0.408, angle = , e1 = , e2 = 0, k1 = 0; ST2DIP03:CSBEND, l = 0.408, angle = , e1 = 0, e2 = , k1 = 0; ST2DIP04:CSBEND, l = 0.408, angle = , e1 = , e2 = 0, k1 = 0; Conclusion. Not much difference in R56, R51, R52 for these two types of dipole. Interesting that R52 is not completely zero in parallel dipole chicane, according to ELEGANT. But R51,R52 small enough in both cases such that theory on slide 16 still holds ? Continued on next slide …

ELEGANT tests of chicane R56 Since R52_chicane ~ 300 micron, R26_arc would have to be ~ 3 to even have a small effect on the total R56 See Chao and Tigner Sec “Single Element Optics” for general features of matrices of lattices with mid-plane symmetry about y BUT WAIT! THERE’s more ….

ELEGANT tests of chicane R56 Now try a chicane with normal entrance and exit from each dipole !ST2DIP01:CSBEND, l = 0.408, angle = , e1 = 0, e2 = 0, k1 = 0; !ST2DIP02:CSBEND, l = 0.408, angle = , e1 = 0, e2 = 0, k1 = 0; !ST2DIP03:CSBEND, l = 0.408, angle = , e1 = 0, e2 = 0, k1 = 0; !ST2DIP04:CSBEND, l = 0.408, angle = , e1 = 0, e2 = 0, k1 = 0; ELEGANT gives R56, R51, R52 = , , So now, the R51, R52 are getting quite big!!!