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Impedance Budget from LINAC to SASE2

Impedance Budget from LINAC to SASE2. Igor Zagorodnov Beam Dynamics Group Meeting 3.12.07. overview wake sources = geometric & resistive (=surface effects) definitions (average & rms) collimator : geometric, surface effects, all ~40%

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Impedance Budget from LINAC to SASE2

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  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. 6000 5000 4000 3000 2000 1000 0 -50 0 50 100 • 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=10W/m ) Bunch shape from S2E simulations by Martin Dohlus

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

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

  7. Collimator bunch resistive total

  8. (T.Wohlenberg) Pipe (resistive+oxid layer+roughness) Aluminium bunch wake

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

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

  11. Kicker bunch resistive total

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

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

  14. s0 characteristic distance: Monopole TermLongitudinal Impedance Per Unit Length A. Tsakanian 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. transverse  A.T.

  15. TOTAL (LINAC to SASE2) pipe bunch collimators kickers

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

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

  18. TOTAL (SASE2) 1 4 2 3 5 6 7 8 Katrin Schuett, ZM1 Dirk Lipka, MDI bunch Geometric Total wake (for comparison)

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

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