1. 4/10/2004SPARC Review Committee Orbit Correction S. Guiducci On behalf of the Beam Dynamics Group

2. 4/10/2004SPARC Review Committee Alignment errors To have enough safety margin then choice of the correctors strengths is based on the following set of alignment errors, which are larger than those expected from the alignement procedure. Angle at the gun exit  1.0 mrad Linac section position error  0.1 mm Linac section angle error  0.2/3 = 0.07 mrad

3. 4/10/2004SPARC Review Committee Location of the bpms Strip line beam position monitors (bpms): Two between gun and section 1. One after each section. One at the undulator entrance. Section 1Section 2Section 3 Gun Distance from gun (m)

4. 4/10/2004SPARC Review Committee Location of the dipole correctors There are x and y steerings in each position. Two steerings in front of each section allow to correct angle and position at the entrance. For space reason, the two correctors are not placed between the sections but on the sections (one near the entrance and one near the exit). This lowers the required strengths. Transfer line quadrupoles are mounted on movable slits and can be adjusted to correct the orbit. Quadrupole triplet

5. 4/10/2004SPARC Review Committee Orbit displacement in one section. Displacement Angle max ll xx  x’

6. 4/10/2004SPARC Review Committee Correctors strenghts The maximum correctors strengths allow to displace the beam by  x = ± 0.1 mm and  x’ = ± 0.07 mrad. The required field integral is calculated at the maximum energy achievable by each section. The integral of the magnetic earth field over the length covered by each corrector has been also added.

7. 4/10/2004SPARC Review Committee Correctors strenghts They have been designed all equal at the maximum strenght 4 Gm

8. 4/10/2004SPARC Review Committee Alignment procedure 1.Using one corrector for each bpm the beam is centered in the bpms. The result is limited by: Bpms resolution Bpms accuracy 2.To improve the orbit correction the Beam Based Alignment (BBA) method is used.

9. 4/10/2004SPARC Review Committee Effect of orbit errors on the emittance Simulations with HOMDYN including transverse and longitudinal wakes: Emittance evaluation including alignment errors. First correction: steer the beam centered in the bpms. Emittance evaluation with orbit correction. In progress: Statistic analysis with random errors in solenoid, linac sections and bpms. Implementation of a correction algorithm in HOMDYN (response matrix calculation, minimization method)

10. 4/10/2004SPARC Review Committee Hp: wake fields on space charge on space charge on centroid off B earth on, Bearth off in section 1(shielded by the solenoid iron) B earth off after BPM3 BPM on axis !!Solenoid field of the first travelling wave on steer1 BPM3 steer2 steer3 steering BPM Exercise: correction of the earth magnetic field BPM4 V. Fusco

11. 4/10/2004SPARC Review Committee The solenoid around the first travelling wave is on the coordinate x and y are coupled V. Fusco

12. 4/10/2004SPARC Review Committee First step-> determine the matrix element b, p, f, l Steering off Steer (horizontal) onSteer (vertical) on V. Fusco

13. 4/10/2004SPARC Review Committee Second step-> determine the angle (horizontal and vertical) for each steering The response matrix has been calculated with HOMDYN for each pair steering - bpm. The required strength is calculated solving the two by two system for each pair of steering - bpm. A minimization algorithm will be included in the code to calculate all the correctors. V. Fusco With the same method it will be measured on the machine.

14. 4/10/2004SPARC Review Committee Orbit in the Linac without (red) and with (blu) correction X (mm) V. Fusco

15. 4/10/2004SPARC Review Committee Orbit in the Linac without (red) and with (blu) correction V. Fusco Y (mm)

16. 4/10/2004SPARC Review Committee Horizontal normalized emittance with and without correction Compared with nominal emittance (no errors)  nx = 0.785  rad nominal

17. 4/10/2004SPARC Review Committee Vertical normalized emittance with and without correction Nominal emittance (red line)  ny = 0.785 mrad. nominal

18. 4/10/2004SPARC Review Committee Alignment procedure: an exercise Solenoid displaced by  x = 0.2 mm No bpms errors Can be corrected by two steering: CH2 = -0.13 mradCV2 = -0.076 mrad CH3 = -0.026 mradCV3 = 0.076 mrad Without correction:with correction: x max =660  mx max =20  m y max =1400  my max =88  m The main source of orbit error is solenoid misalignment.

19. 4/10/2004SPARC Review Committee Solenoid displaced by  x = 0.2 mm Without correction x y X max = 0.66 mm Y max = 1.4 mm

20. 4/10/2004SPARC Review Committee Solenoid displaced by  x = 0.2 mm After correction - Without bpms errors X max = 88  m Y max = 20  m x

21. 4/10/2004SPARC Review Committee Alignement procedure: an exercise Without correction Solenoid and section 1 displaced by:  x = 100  m MAD simulation Solenoid in 13 pieces at different energies No focusing effect in the RF sections X max = 326  m Y max = 701  m

22. 4/10/2004SPARC Review Committee First Correction: centre the beam on the bpms: Horizontal plane CHV2 = -30  rad Solenoid and sect. 1:  x = 100  m No focusing effect in the RF sections X max = 100  m Y max = 701  m CHV2

23. 4/10/2004SPARC Review Committee Displacement Angle Beam Based Alignment Vary the orbit displacement and find the minimum emittance. Repeat for orbit angle Horizontal plane Section 2 Solenoid alignment error  x = 100  m No focusing effect in the RF sections

24. 4/10/2004SPARC Review Committee Beam Based Alignment The orbit is corrected in section 2 It is unchanged in the other sections Horizontal plane Orbit bumps in section 2 Solenoid alignment error  x = 100  m No focusing effect in the RF sections Without BBA in sect. 2 With BBA in sect. 2

25. 4/10/2004SPARC Review Committee Beam Based Alignment BBA in section1: the beam is on the axis of the section Repeat the procedure for section 3 Repeat for the vertical plane Horizontal plane Solenoid and section 1:  x = 100  m No focusing effect in the RF sections Without BBA in sect. 1 With BBA in sect. 1

26. 4/10/2004SPARC Review Committee Evaluation of the emittance Homedyn simulations Horizontal + vertical plane earth magnetic field off wake fields on space charge on Solenoid and section 1:  x = 100  m Orbit Without correction With correction X (mm) V. Fusco

27. 4/10/2004SPARC Review Committee Nominal value  xn = 0.785 Without correction  x /  xn = 33%  y /  yn = 7% With correction  x /  xn < 1%  y /  yn < 1% Evaluation of the normalised emittance  x (  rad)  y (  rad) V. Fusco

28. 4/10/2004SPARC Review Committee Conclusions The set of beam steerings allows to align the beam on the axis of each linac section The limit of the orbit correction is due to the bpms resolution and accuracy With a Beam Based Alignment procedure the correction can be improved in order to cancel any sensible emittance growing effect.

29. 4/10/2004SPARC Review Committee Solenoid coils and TW displacements V. Fusco

30. 4/10/2004SPARC Review Committee Bunch’s centroid position along the structure without (black lines) and with (red lines) steering correction. V. Fusco

31. 4/10/2004SPARC Review Committee Normalized emittance behaviour along the structure without (black line) and with (red line) steering correction for the case of 0.05mm offset. Normalized emittance degradation without and with steering correction at the end of the TWs (z=12.0m). Nominal normalized emittance  xn = 0.785  rad V. Fusco

32. 4/10/2004SPARC Review Committee NO Wakes No Problems What about emittance? M. Ferrario

33. 4/10/2004SPARC Review Committee With Wakes Some Problem M. Ferrario

34. 4/10/2004SPARC Review Committee HOMDYN results: Wake field effects M. Ferrario

35. 4/10/2004SPARC Review Committee Centroids Equations of Motion M. Ferrario

36. 4/10/2004SPARC Review Committee Centroids Motion X Y Wake fields change polarisation M. Ferrario

37. 4/10/2004SPARC Review Committee Bane & Sands Wake Field Diffraction Model M. Ferrario

38. 4/10/2004SPARC Review Committee Posizioni bpms (di riserva) Il bpm all’ingresso della sezione ci permette di centrare il fascio all’ingresso della sez. Per correggere l’angolo dobbiamo centrare il fascio sul bpm successivo che sta a ~3m di distanza. 2 bpms tra le sezioni non hanno risoluzione sufficiente a misurare l’angolo; l’errore sull’angolo e’: Dx’= 2Dxris/Ds ~ 0.13 mrad Dxris= risoluzione bpm ~20  m (?) Dx= distanza tra I bpms ~0.3 m maggiore dell’angolo che vogliamo correggere.

39. 4/10/2004SPARC Review Committee Effetto del disallineamento sull’emittanza Trasp. di Valeria Uno spostamento di 100 mm delle sezioni Caso peggiore Sez1: +100mm, sez2: -100mm, sez3: +100mm Da’ un aumento di emittanza di … Percio’ vogliamo correggere molto meglio.

40. 4/10/2004SPARC Review Committee Emittance change BUMP xx  x /  xn 00.79mm mr1.25 100  m 0.78mm mr0.07 200  m 0.79mm mr1.25