1. Impedance Budget from LINAC to SASE2 Igor Zagorodnov Beam Dynamics Group Meeting 3.12.07

2. overview wake sources = geometric & resistive (=surface effects) definitions (average & rms) collimator: geometric, surface effects, all ~40% pipe: surface effects ~40% kicker: geometric, surface effects, all ~20% total total vs. pipe radius comparison with effects in LINAC comparison with SASE2 ~SASE2 / 2 total vs. pipe radius normalized to SASE2

3. SASE2 SASE1 (W.Decking)

4. -50050100 0 1000 2000 3000 4000 5000 6000 Wakefield sources - Resistance of the pipe (r ~ 20 mm, L=456 m, Aluminium) - Collimators (r=2 mm, L=50 cm, 4 items, TIMETAL 6-4 ) - Kickers (r=10 mm, L=10 m, 3 items, R/L  m ) Bunch shape from S2E simulations by Martin Dohlus

6. Collimator (geometrical wake) Optical approximation: the geometrical wake repeats the bunch shape.

7. TIMETAL 6-4 alloy (Titanium) (E.Schutz MVA) http://www.timet.com/timetal6-4frame.html Collimator (resistive wake) M.Dohlus. TESLA 2001-26, 2001 K.L.F.Bane, G.V.Stupakov, SLAC-PUB-10707, 2004

8. Geom.Res.Total Loss7543321086 Spread457365791 Peak-1518-833-2272 Collimator total resistive bunch

9. Aluminium resistivetotal Loss8.49.0 Spread8.59.3 Peak-19.8-21 Pipe (resistive+oxid layer+roughness) wake bunch (T.Wohlenberg)

10. Kicker (geometrical wake) (T.Wohlenberg)

11. Kicker (resistive wake) (T.Wohlenberg)

12. Geom.Res.Total Loss227659886 Spread137412519 Peak-457-1222-1544 Kicker total resistive bunch

13. M. Ivanyan, A. Tsakanian, Phys. Rev. ST-AB, 2006 Analytical solution for the fields inside tube for finite Lorenz factor Perform the ultrarelativistic limit A.W. Chao, SLAC-PUB- 2946, 1982 A. Piwinski, DESY-94-068, 1994 Usual Approach Tube with finite thickness Method: matching technique Problem: fields are diverges in outer space for Tube with infinite thicknessskin-depth < tube thickness Solution in General Case B. Zotter, S. Kheifets, 1997. A. Tsakanian

14. Ceramic Kicker Vacuum chamber: Ceramic with Titanium-Stabilized High Gradient Steel (TSHGS) coats TSHGS Parameters Vacuum Chamber Parameters Impedance of XFEL Ceramic Kicker Vacuum Chamber with Metallic Coats. Ceramic Parameters A. Tsakanian

15. Longitudinal monopole impedance as function of dimensionless wave number for several cases of vacuum chamber material: 1. Ceramic with TSHGS coats. 2. TSHGS single layer tube with finite and infinite thickness. 3. Copper single layer tube. s 0 characteristic distance: Monopole Term Longitudinal Impedance Per Unit Length A. Tsakanian transverse  A.T.

16. Pipe (456m) Collimators (4 items) Kickers (3*10m) Total Loss41034343265911105 Spread4222316415578682 Peak-9680-9088-4633-22595 TOTAL (LINAC to SASE2) collimators pipe bunch kickers

17. Energy losses between LINAC and SASE2 vs. pipe radius R Spread Loss

18. Energy spread due to wakefields between LINAC and SASE 2 bunch Energy from S2E simulations by Martin Dohlus after LINAC Before SASE2 bunch

19. 1 23 4 5678 Katrin Schuett, ZM1 Dirk Lipka, MDI GeometricTotal Loss0.69e41.77e4 Spread0.33e41.89e4 Peak-1.2e3-4.67e4 TOTAL (SASE2) Total wake bunch Geometric (for comparison)

20. Energy spread between LINAC and SASE2 vs. pipe radius R (normalized to the spread in SASE2) total collimators kickers pipe R=20mm