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Resistive Effects in Ceramic Kicker Chamber. Roughness Effects in Undulator Chamber.

Resistive Effects in Ceramic Kicker Chamber. Roughness Effects in Undulator Chamber. Andranik Tsakanian, Uni Hamburg. DESY, 16 April 2007. Topics. Impedance Structure Investigation for Ceramic Kicker Vacuum Chamber with metallic coats. Resistive and Geometrical Wakes.

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Resistive Effects in Ceramic Kicker Chamber. Roughness Effects in Undulator Chamber.

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  1. Resistive Effects in Ceramic Kicker Chamber.Roughness Effects in Undulator Chamber. Andranik Tsakanian, Uni Hamburg DESY, 16 April 2007

  2. Topics • Impedance Structure Investigation for Ceramic Kicker Vacuum • Chamber with metallic coats. • Resistive and Geometrical Wakes. • Influence of Surface Roughness in Undulator Chamber on • the Beam. DESY, 16 April 2007

  3. - combination of Bessel functions. Single layer cylindrical tube Impedance Structure Investigation of Ceramic Kicker Vacuum Chamber with Metallic Coats. Longitudinal Impedance. Monopole term. M. Ivanyan, V. Tsakanov, Phys. Rev. ST-AB, 2004 DESY, 16 April 2007

  4. Metallic type layers Good approximation - the smallness of each layer skin depth with respect to the layer inner radius Single layer tube DESY, 16 April 2007

  5. Ceramic type layers with metallic coats Good approximation: Metallic layer Ceramic layer * Actually for all the practical applications, the formula (*) is valid and well approximates the exact solution. DESY, 16 April 2007

  6. TSHGS Parameters Numerical Examples Ceramic Kicker Vacuum chamber: Ceramic with Titanium-Stabilized High Gradient Steel (TSHGS) coats Vacuum Chamber Parameters Parameters from T. Wohlenberg DESY, 16 April 2007

  7. 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. s0 characteristic distance: Longitudinal Impedance Per Unit Length. Monopole term. DESY, 16 April 2007

  8. Resistive wall longitudinal wake potentials of Gaussian bunch with 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. Resistive Wall Wakes . DESY, 16 April 2007

  9. Geometrical longitudinal wake potentials of Gaussian bunch Geometrical Wakes . DESY, 16 April 2007

  10. R.m.s. distortion Surface Roughness in Undulator Section . Measurement data from T. Wohlenberg DESY, 16 April 2007

  11. Where is spectral density defined as Fourier Transformation of Autocorrelation function: Surface Impedance where Inductance define as . G.V.Stupakov, SLAC-PUB-8208, 1999 M.Dohlus, M.I. Ivanyan, V.M. Tsakanov, TESLA-FEL 2000-26,2000 M.Dohlus. TESLA 2001-26, 2001 DESY, 16 April 2007

  12. Wake Potential of Corrugated pipe . DESY, 16 April 2007

  13. R.m.s. value of the roughness in Arithmetical Mean Roughness Abbreviations DESY, 16 April 2007

  14. Summary • Impedance Structure for Ceramic Kicker Vacuum Chamber was • Investigated. For Kicker was shown that Wake Potential for two • layer tube can be estimated by single layer tube formula. • Was analyzed the transition Wakes influence on the beam. • Influence of surface corrugation in Undulator vacuum chamber on the beam was • calculated. Acknowledgements: Thanks to Martin Dohlus, I. Zagorodnov,T. Wohlenberg, M. Ivanyan and V. Tsakanov for stimulating discussions.

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