1. Transverse Emittance Measurement in the Linac4 Dump Line and the LBE Measurement Line K. Hanke T. Hermanns B. Mikulec With many thanks for discussions and contributions from various colleagues and in particular A. Lombardi, G. Bellodi and C. Carli!

2. Outline Introduction Measurement Principle Emittance measurement proposal for Linac4 Dump line  Summary Dump line Upgrade proposal for LBE line  Summary LBE line B. Mikulec Linac4 Beam Coordination Committee 3 November 20092

3. 3 Geographical Overview LT.BHZ20 LTB.BHZ40 Linac4 Transfer Line Dump Line LBE Line LBS Line LBE Line LBS Line

4. 3-Monitor Method Beam can be described in 2-dimensional phase space by an ellipse  emittance = πarea of ellipse (area of ellipse constant if no non-linear forces) The evolution of phase space coordinates (transfer matrix) can be related to the evolution of the ellipse (Twiss) parameters.  3 linear equations Furthermore, there is a proportionality between beam size σ and the emittance:  σ 2 = εβ ⇒ It is sufficient to know transfer matrices and beam sizes at 3 locations to calculate the emittance (=3-Monitor Method). Assumptions:  Emittance should be nearly constant between 3 measurement locations  Avoid non-linear effects/elements between the 3 monitors (space charge!)  Phase space planes decoupled  In presence of dispersion, emittance has to be corrected for B. Mikulec Linac4 Beam Coordination Committee 3 November 20094

5. Calculation of Emittance Input: transfer matrices (TRACE-3D) and beam sizes (Path) at the 3 monitor positions. The combination of the 2 simulation programs allows to account (at least in approximation) for space charge effects. Compare calculated emittance with emittance simulated by Path. B. Mikulec Linac4 Beam Coordination Committee 3 November 20095

6. 6 Measurement Principle Determine beam sizes at three different positions  Here: configuration for vertical beam size measurement Layout such that phase space ellipses turn by approximately  =60° from position to position for optimal sampling  Reduces errors in determination of ellipse y y‘

7. Linac4 Dump Line B. Mikulec Linac4 Beam Coordination Committee 3 November 20097

8. Layout of Linac4 Dump Line Use 2 quadrupoles to optimise ellipse angles (different settings for horizontal/vertical emittance measurement)  1 st quadrupole already foreseen (accelerator type; max. 20 T/m)  2 nd quadrupole (transfer line type; ~11.4 T/m) has to be added as well as 3 retractable 2-D monitors (screen + camera)  add 1 transformer to measure percentage of beam going to dump line; possibility to select transfer matrices corresponding to certain beam current range Due to stripping and multiple scattering, the 3 measurements have to be done sequentially. Screens (1 mm thick alumina foils proposed by BI) can stand a max. pulse length of 100 μs (same value is used for dump design) B. Mikulec Linac4 Beam Coordination Committee 3 November 20098

9. Parameters of Dump Line B. Mikulec Linac4 Beam Coordination Committee 3 November 20099 Horizontal measurementVertical measurement Monitor position [mm after L4 exit] 579083909550 same α 28.7772.952-8.25011.4801.025-3.345 β [mm/mrad]82.8961.0097.12832.4220.5493.222 Dump entry [mm after L4 exit] 10300 same Beam size (h/v) at dump entry [mm] h: 3.731v: 13.332h: 10.689v: 2.338 Dump core [mm after L4 exit] 11900 same Beam size (h/v) at dump core [mm] h: 7.495v: 16.705h: 13.585v: 4.628 Positions of the 3 monitors and the dump entry/core as well as ellipse parameters at 3 monitors for 65 mA (ellipse values from Trace 3-D)  design dump entry for min. beam radius of 14 mm x 14 mm rms (particle angle and steering errors not included!)

10. Dump Line: Beam Sizes at 65 mA B. Mikulec Linac4 Beam Coordination Committee 3 November 200910 Horizontal measurementVertical measurement MonitorM1M2M3M1M2M3 rms beam size [mm] 6.9110.8281.9844.2290.6071.299 Rms beam size evolution for horizontal (left) and vertical (right) measurement vertical horizontal M1M2M3M2M3M1

11. B. Mikulec Linac4 Beam Coordination Committee 3 November 200911 Dump Line: Monitor Resolution Assume following resolution for the 3 monitors for all presented results:  200 μm / 50 μm / 200 μm Fill histograms at the corresponding binning with the 3 beam distributions  Use a Gaussian fit to these distributions to extract the beam size Remark: the distributions are not really Gaussian  potential for improvement Vertical measurement, 65 mA: monitor 1 monitor 2 monitor 3

12. Dump Line: Beam Distributions Horizontal measurement, 65 mA: monitor 1 monitor 2 monitor 3 Vertical measurement, 65 mA: monitor 1 monitor 2 monitor 3 B. Mikulec Linac4 Beam Coordination Committee 3 November 200912

13. B. Mikulec Linac4 Beam Coordination Committee 3 November 200913 Dump Line: Emittance at 65 mA With approx. known starting conditions (transfer matrices), the emittance measurement at monitor 1 is feasible with an error <5% wrt prediction horizontal vertical Horizontal measurementVertical measurement αβεαβε Path value22.216764.39190.741710.574530.13330.5936 Reconstr. value21.225661.57050.775910.221229.17800.6131 rel. deviation-4.46%-4.38% +4.60% -3.34%-3.17% +3.28% Δ J (geometric mismatch) -0.23%-0.14% Some emittance growth between M1 and M3 (6.0% and 3.7%, respectively)

14. Dump Line: 20/40/65 mA Studies made with beam input distributions for 20, 40 and 65 mA  Rms beam size at monitor 2: smallest for 20 mA and vertical measurement (0.345 mm)  Emittance deviations for hor./vert. measurement: 40 mA: +4.00%/+2.67% 20 mA: +1.39%/+0.82%  Using the 65 mA transfer matrices in the calculation, but beam size measurements from different beam current conditions, the deviation to the reference emittances stays always below 5%.  In principle one could correlate easily the ‘correct’ transfer matrix to the beam current range in use, but this seems not necessary propose a kind of look-up table for a few different beam current ranges correct transfer matrix can automatically be selected with the transformer reading The results are stable with varying beam current, even using only 1 set of transfer matrices. B. Mikulec Linac4 Beam Coordination Committee 3 November 200914

15. Dump Line: Additional Studies Longitudinal emittance changes: Concern as transition between bunched Linac4 beam to an unbunched beam Studies dividing long. emittance by a factor of 2 for the nominal current; determine new transfer matrices (keeping original beam size values)  Emittance deviations: 4%/3% (hor./vert. measurement) Emittance growth between Linac4 exit and monitor 1: Correction required to obtain Linac4 emittance value from emittance determined at monitor 1 B. Mikulec Linac4 Beam Coordination Committee 3 November 200915 Horizontal measurementVertical measurement Beam current [mA] 654020654020 Correction factor -30.2%-21,6%-6,2%-9.5%-11.4%-3.6%

16. Summary Dump Line (1) A layout for a 3-monitor emittance measurement has been proposed  New equipment: 1 TL quadrupole, 1 transformer, 3 retractable alumina screens + cameras Despite difficult conditions (space charge, emittance growth along the line, longitudinal beam development), the emittance can be determined with a reconstruction error smaller than specified (<10%)  if the initial beam distribution is approximately known  with measurement precision of the monitors of order of 200/50/200 μm The emittance is determined for monitor 1; due to emittance growth after the Linac4 exit this value has to be corrected as mentioned to obtain the Linac4 emittance ➣ Respecting the above-mentioned conditions, the transverse emittance measurement using 3 monitors in the dump line is very reliable and could be used during standard Linac4 operation B. Mikulec Linac4 Beam Coordination Committee 3 November 200916

17. Summary Dump Line (2) ! But: This method seems not suitable in the Linac4 dump line for the Linac4 commissioning phase  With a 50% change of α and β (realistic order of magnitude after information from A. Lombardi, despite prior determination of these values with the 12 MeV diagnostic line), the error could increase to up to 30%/7% (hor./vert.) For the Linac4 commissioning phase it should be possible to use the same hardware setup, but apply a ‘forward’ method [1]  Measure the 3 beam profiles (or produce a quadrupole scan)  Simulate the quadrupole scan with a multiparticle code and vary the input parameters (Twiss parameters and emittance) such that the measurement results are best reproduced; this will yield the ‘real’ beam parameters  A. Lombardi might have a person to study this ‘forward’ method [1] C. Oliver, P.A.P. Nghiem and C. Marolles, Transverse Emittance and Energy Spread Measurements for IFMIF-EVEDA, Proceedings of the Workshop on Transverse and Longitudinal Emittance Measurement in Hadron- (Pre-) Accelerators, Bad Kreuznach, Germany, 11-12/12/2008. B. Mikulec Linac4 Beam Coordination Committee 3 November 200917

18. LBE Line B. Mikulec Linac4 Beam Coordination Committee 3 November 200918

19. Layout of LBE Line Layout upgrade proposal with constraint to keep Linac3 ion characterisation possible 2 existing quadrupoles to produce the beam waist will have to be modified or exchanged (max. 2.25 T/m); power converters to be changed It has to be checked if cooling for LTB.BHZ40 is sufficient with increased current 3 retractable alumina monitors + cameras have to be added 1 transformer probably needs to be replaced Dump to be installed (max. 100 μs pulse length) Steerer magnet to be displaced downstream B. Mikulec Linac4 Beam Coordination Committee 3 November 200919

20. Parameters of LBE Line B. Mikulec Linac4 Beam Coordination Committee 3 November 200920 Horizontal measurementVertical measurement Monitor position [mm from LTB.BHZ40 entrance] 95361208113529 same α 8.2730.450-3.9712.399-0.010-1.360 β [mm/mrad]22.5300.3955.4867.1171.0843.065 Positions of the 3 monitors and ellipse parameters at the 3 monitors for 65 mA (values from Trace 3-D)

21. LBE Line: Beam Sizes at 65 mA B. Mikulec Linac4 Beam Coordination Committee 3 November 200921 Horizontal measurementVertical measurement MonitorM1M2M3M1M2M3 rms beam size [mm] 3.8250.5101.9472.2530.9061.541 Rms beam size evolution for horizontal (left) and vertical (right) measurement horizontal M1M2M3 vertical M2M3M1

22. LBE Line: Resolution Horizontal measurement:Vertical measurement: B. Mikulec Linac4 Beam Coordination Committee 3 November 200922 Monitor resolutions of 10, 50, 100, 200, 500 and 1000 μm have been studied. Error band corresponds to worst possible combination of the fit errors for the 3 beam size measurements Also here a monitor resolution of 200 μm / 50 μm / 200 μm is proposed.

23. B. Mikulec Linac4 Beam Coordination Committee 3 November 200923 LBE Line: Emittance at 65 mA The emittance measurement at monitor 1 is feasible with an error ~1% wrt the prediction  In the LBE line, the emittance evolution is flat except for hor. dispersion at start horizontal vertical Horizontal measurementVertical measurement αβεαβε Path value7.923521.43510.68242.28456.76960.7495 Reconstr. value7.905221.32620.68322.30046.75940.7414 rel. deviation-0.23%-0.51% +0.12% +0.70%-0.15% -1.08% Δ J (geometric mismatch) -0.05%-0.04%

24. LBE Line: Systematic Studies Solution converges very quickly (no additional iteration required where new transfer matrices are calculated with the first result) Vary quadrupole field and monitor positions:  Quadrupole field errors should not be too critical as quadrupoles have been avoided between monitors; conservative estimate of ±1% field error for both quadrupoles  Vary monitor positions by ±5 mm  Choose largest deviation and calculate determine error (square root of quadratic sum)  Max. error of 0.69%/0.21% (hor./vert. measurement) Simulate measurement with 5 monitors instead of 3  No significant error improvement; deviation of emittance <1%  Test different combinations of 3 monitors Stable, even with less ideal monitor positions; all combinations yield errors <3.3%/1.6% (hor./vert. measurement) Proposed layout seems good choice B. Mikulec Linac4 Beam Coordination Committee 3 November 200924

25. LBE Line: Additional Studies Longitudinal emittance changes: Set longitudinal emittance to half of its nominal value (to 194.4 deg keV); determine new transfer matrices (using nominal beam size values)  Emittance deviations stay at same level as for nominal longitudinal emittance Vary input beam parameters: Use approximately half of the value for α and β as input Calculate emittance with the new beam sizes (estimated from Trace 3-D this time), but use the nominal transfer matrices Deviation from reconstructed α and β to the nominal (=~doubled) reference value lie between -45% to -47% Deviation of reconstructed emittance: -3%/0.23% (hor./vert. measurement) B. Mikulec Linac4 Beam Coordination Committee 3 November 200925

26. LBE Line: Summary A layout for a 3-monitor emittance measurement has been proposed, compatible with ion emittance measurement using the old setup  New equipment: 2 quadrupole power supplies (maybe also exchange magnets), 1 transformer, 3 retractable alumina screens + cameras, dump  Displace 1 steerer The proposed layout yields very stable solutions with errors <1.5% Systematic error studies show the robustness of the layout To be kept in mind: In case input beam parameters would differ significantly from the predicted parameters, the ‘forward’ method could also be an option, although for the LBE line the conditions look very robust. B. Mikulec Linac4 Beam Coordination Committee 3 November 200926

27. Backup Slides B. Mikulec Linac4 Beam Coordination Committee 3 November 200927

28. Dump Line: Phase Space Plots @ 65 mA Initial distribution at Linac4 exit:Beam at monitor 1 (hor. measurement): B. Mikulec Linac4 Beam Coordination Committee 3 November 200928

29. LBE Line: Phase Space Plots @ 65 mA Horizontal measurement (M1):Vertical measurement (M1): B. Mikulec Linac4 Beam Coordination Committee 3 November 200929

30. LBE Line: Convergence of Solution The solution converges very quickly after 1 st iteration (10 -3 % difference from 1 st to 2 nd iteration)  iteration 0 corresponds to reference value B. Mikulec Linac4 Beam Coordination Committee 3 November 200930