1. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 1 GdfidL Simulations of ESA Prototype Collimators Jonathan Smith (Lancaster University/Cockcroft Institute)

2. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 2 Summary ● Methods of estimation ● ESA Run 1 & 2 Collimators (simulation results) ● New prototype collimator profiles ● Mesh stability ● Simulation of “real world” effects ● Comparison with other simulation packages

3. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 3 Methods of estimation ● Real beam tests ● Bench tests ● Analytical estimates ● Numerical simulation

4. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 4  =  /2rad r=4.0mm 4, 4  324mrad r=1.4mm 3, 3  324mrad r=1.4mm 2, 2  =324mrad r=2.0mm 1, 1 Revised 4-May-2006 Beam viewSide view (“DESY sandwich”) Collim. #, slot h=38 mm 38 mm L=1000 mm 7mm  r=1/2 gap As per last set in Sector 2, commissioning Extend last set, smaller r, resistive WF in Cu cf. same r, tapered

5. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 5  =  /2rad r=1.4mm 5, 4  166mrad r=1.4mm 6, 3  1 =  /2 rad  2 =166mrad r 1 =4.0mm r 2 =1.4mm 7, 2 r 1 =4.0mm r 2 =1.4mm   =289mrad   =166mrad 8, 1 Revised 4-May-2006 Beam viewSide view (“SLAC sandwich”) Collim.#, slot h=38 mm 38 mm 7 mm cf. collim. 4 smaller r 211mm cf. collim. 2, same r 31mm cf. collims. 4 and 6 133mm cf. collim. 7, and same step in/out earlier data

6. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 6 EM Simulations with GdfidL1 2 3 5 6 7 4 8

7. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 7 Wakefields @300µm (6 cells/sigma)

8. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 8 Wakefields @500µm (12 cells/sigma)

9. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 9 Mesh stability: Collimators 1&2 ● Only 3 decent points at 300µm for most collimators ● More at 500µm ● 1mm ~ OK – can use spline fit on data to get an estimate – not done so far – further analysis to see if this takes us closer to ECHO/PBCI.

10. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 10 What do we do about it? (1)

11. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 11 What do we do about it? (2)

12. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 12 Effect of mesh filtering…

13. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 13 Further collimator designs semi-circle, with[9]/without[10] flat, opposing demi-circles[10], 8 with flat[11].

14. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 14 More possible collimators 7 with flat [13], half exponential[14], 13 with shallower angle[15] exponential profile[16], 13 with ellipse connecting 4mm and 1.4mm aperture[17] 13 with ellipse connecting beam pipe radius and 1.4mm aperture (also see 9) [18] half cosine taper [19], raised cosine taper [20], tanh tapers [21] (set typically to the length of collimator 6)

15. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 15  166mrad r=1.4mm 12  =166mrad r =1.4mm 11  =166mrad r =1.4mm 10  166mrad r=1.4mm (1/2 gap) 6 Revised 27-Nov-2006 Beam viewSide view Collim.# h=38 mm 38 mm Roughened surface, compare with 12 As 10, in Ti-6Al-4V, polished, cf. 12 As 10, in OFE Cu, polished, cf. collim. 6, 13 Runs 3, 2007 Exists, from 2006 runs. For reproducibility ~211mm 1.4mm  =21mm   

16. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 16 non-linear taper r=1.4mm 16?  1 =  /2 rad  2 =50mrad r 1 =4.0mm r 2 =1.4mm 15  1 =  /2 rad  2 =166mrad r 1 =4.0mm r 2 =1.4mm 14  1 =  /2 rad  2 =166mrad r 1 =4.0mm r 2 =1.4mm 13 Revised 27-Nov-2006 Beam viewSide view Collim.# h=38 mm 38 mm cf. ? Polished, cf. collim. 13 Polished, cf. collims. 7, 11, 13 Polished, cf. collim. 7, 12, 13 Ti6Al4V OFE Cu =21 mm Form t.b.d. = 0.6    Ti6Al4V Runs 3, 2007 ~52 mm =21 mm  ~52 mm =21 mm   ~125 mm =21 mm

17. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 17 Variation of collimator kick with bunch length

18. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 18 Big gap?

19. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 19 Misallignment

20. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 20 GdfidL & PBCI ● TEMF working on ECHO/PBCI – 3D, moving mesh, conformal, non-dispersive solver s/σ σ/Δz=6 W ║ (s)/(V/pC) GdfidL PBCI With thanks to Mikko Kärkkäinen

21. Jonathan Smith, European LCW, 8 th January 2007, Daresbury 21 Conclusion EM simulations: MAFIA GdfidL ECHO Bench Tests (scaling?) Analytical Approach (Lancaster Theory Group) Beam Tests ESA Damage Studies ? Prediction of effect at IP (MERLIN) New designs Prediction of mechanical properties Now starting second iteration…