1. 8 th February 2006 Freddy Poirier ILC-LET workshop 1 Freddy Poirier DESY ILC-LET Workshop Dispersion Free Steering in the ILC using MERLIN

2. 8 th February 2006 Freddy Poirier ILC-LET workshop 2 Scope: Differences between curved and straight machines –Scans with various BPM resolution and orbit weight (1 to 5  m) –Model of BPM linear scale error –Impact of BPM noise –Impact of Iteration –Model of Beam jitter

3. 8 th February 2006 Freddy Poirier ILC-LET workshop 3 Lattice Simple lattice from TESLA TDR ~ 9.5 km long lattice, 6852 structures, 191 BPMs 60 o FODO  max = 172 m constant beta lattice 6 cryomodules / fodo cell Cell length 99.5 m 500 GeV machine studied Vertical kink between cryomodules (2.7  rad). Injection emittance  y = 20 nm, injection On-energy = 5 GeV Initial Uncorrelated energy spread 2%

4. 8 th February 2006 Freddy Poirier ILC-LET workshop 4 Dispersion Free Steering Minimisation of the absolute trajectory of the beam (wrt to a design orbit) and the difference orbit when the energy is changed W diff : Constrain on difference orbit (nominal = 5  m) W abs : Constrain on absolute orbit (nominal = 360  m) DFS technique is applied on segment of the linac: –40 quads –20 quads overlapping Constant Energy Difference at beginning of each segment = 20% –At beginning of linac: On-energy beam = 5 GeV Off-Energy beam = 4 GeV –Beam artificially changed (i.e. no gradient modification) Assume launch condition is re-establish for Off-energy pulse.

5. 8 th February 2006 Freddy Poirier ILC-LET workshop 5 Normal Conditions Transverse Quadrupole300 µmWrt to CM axis Rotation Quadrupole300 µrad Transverse BPM Alignment error200 µmCM Transverse RF Structure300 µmCM Rotation RF Structure300 µradCM Cryomodule Offset200 µmAccel. Ref BPM Resolution5 µm (10 µm in TDR) Nominal weight:

6. 8 th February 2006 Freddy Poirier ILC-LET workshop 6 Definitions Nb of runs / Bin  y [nm] Nominal parameters Wdiff = 5  m  cut  cut [nm] W diff = BPM noise (1 to 10  m) 41.7nm 90% 90% Limited Normalised Emittance 500 (200) runs with a new set of generated random numbers 1. Binned histogram 2. Calculate the integral and plot for latter scan the emittance for a 90% level. 90% Limited Corrected Emittance Same procedure as normalised emittance + Energy correlation numerically removed Equivalent of a perfect dispersion bump at exit of linac

7. 8 th February 2006 Freddy Poirier ILC-LET workshop 7 DFS Scans 90% limit normalised vertical emittance BPM from 1 to 5  m Wdiff: 1 to 5  m  Dependance of projected emittance (  y ) to both the weight and BPM.  Substantial gain with better BPM resolution BPM\Wdiff12345 13130 3132 23433 34 34037363536 44642414038 55450464442 Normalised emittance scans Difference between both straight and curved linac Maximum difference between curved and straight scenario< 3% In nm Curved machine Bpm= W diff =1 Bpm= W diff =5 Cv27 nm35 nm st27 nm35 nm

8. 8 th February 2006 Freddy Poirier ILC-LET workshop 8 Difference curved-straight W diff (  m) BPM resolution (  m) The difference between both straight and curved linac is defined at each scan point as: Each scan point = 500 runs (seeds) Maximum difference = 3% No real difference between linac following earth curvature and straight laser linac is observed.

9. 8 th February 2006 Freddy Poirier ILC-LET workshop 9 BPM response In previous study only BPM resolution was modeled (RMS error). In the following study spatial BPM response is modeled with a linear slope error: BPM offset a 1 = Gaussian random generated number centered on 1 with an rms error varying from 1 to 10%

10. 8 th February 2006 Freddy Poirier ILC-LET workshop 10 Emittance Growth - St Laser Straight Linac - Large impact of BPM slope error when orbit difference weight is small. - This impact can be minimized by taking a large weight at the cost of getting an emittance growth larger than the minimum possible at a slope error of 1%. Relative Emittance growth: is, in nm, the corrected normalized emittance at the 90% limit at the end of the linac =20 nm is the injection vertical emittance at the beginning of the linac. No iteration Slope\ Wdiff 12  m20  m 1%64%82% 10%173%82%

11. 8 th February 2006 Freddy Poirier ILC-LET workshop 11 Emittance Growth - Cv The relative emittance growth vs the orbit weight difference is in the following studied: Relative Emittance growth: is, in nm, the corrected normalized emittance at the 90% limit at the end of the linac =20 nm is the injection vertical emittance at the beginning of the linac. The number of runs (seeds) for each data point of the diagrams is 200. Slope error (%) minimum (nm) Minimum relative emittance growth W diff (  m) No error2735%1-4 1%2737%2-4 5%3681%11 10%3890%>55 37% Curved Machine BPM noise = 1  m

12. 8 th February 2006 Freddy Poirier ILC-LET workshop 12 Difference st-cv Difference in the 90% limit corrected emittance wrt orbit difference weight: The difference between each machine scenario is in overall more important with a slope error of 10% than with one of 1% and the absolute difference increases drastically for a low orbit difference weight Slope error (%)(nm) 1%81%3686%375% 10%82%36110%4332% At W diff = 20  m curvedstraight

13. 8 th February 2006 Freddy Poirier ILC-LET workshop 13 Impact of BPM noise - With a large weight W diff, the emittance growth is constant at a fixed slope error when BPM noise increases. - The emittance growth increases with the slope error. Curved Machine BPM from 1 to 10  m Slope error on BPM response = 1, 5 or 10% W diff =20  m No iteration Slope error % (nm)%<30nm (nm) 1%87%3773%43 5%92%3868%47 10%114%4356%52

14. 8 th February 2006 Freddy Poirier ILC-LET workshop 14 Impact of BPM Noise(2) Difference between both machine of the 90% limit emittance growth Difference between curved and straight machine on the emittance growth is less than 25%. Difference decrease with BPM slope error. BPM from 1 to 10  m Slope error on BPM response = 1, 5 or 10% W diff =20  m No iteration

15. 8 th February 2006 Freddy Poirier ILC-LET workshop 15 Impact of Iterations Iterations of Dispersion Free Steering correction within each segment BPM noise = 1  m Iteration impact studied for the curved geometry slope error a 1 =10% Error on energy of off-energy beam = 2% With 1 iteration, the 90% limit corrected emittance growth can be divided by 4 (at least) compared to no iteration. But impact of more than 2 iterations is not very clear. 160% 109%

16. 8 th February 2006 Freddy Poirier ILC-LET workshop 16 Beam Energy Jitter Deal with random jitter in the initial beam centroid, This perturbation is Propagated linearly through linac. launch condition Random jitter Sum of individual responses of upstream kicks. No additional sources assumed in linac

17. 8 th February 2006 Freddy Poirier ILC-LET workshop 17 Summary Differences between straight and curved machines: –When BPM linear slope error is at 10% –When Orbit difference weight is small  Care when optimising weight for DFS Large impact of BPM slope response error with Orbit difference Weight lower than 10  m (both), This impact can be minimised with a large orbit difference weight (20  m), The BPM noise does not seem to have an impact on emittance growth with a large weight –Beam jitter is now added to simulation: BPM noise expected to have here impact. Iterations provide a way to minimise the emittance growth when Orbit difference weight lower than 10  m. Simulation on the way to be more “realistic”

18. 8 th February 2006 Freddy Poirier ILC-LET workshop 18 A tentative interpretation 1 – smallest is best (BPM resolution) 2 – linear slope error results: smallest not enough. Have to know also well this error 3 – To be in a more stable area  higher orbit difference weight 4 – With this weight, BPM noise impact is reduced Possible solution: Iteration BPM noise expected to play a role when beam jitter in