Wakefield Calculations and Impedance Database Challenges for the European XFEL Project at DESY Igor Zagorodnov ICFA mini-Workshop on “Electromagnetic wake fields and impedances in particle accelerators“ Erice, Sicily April 2014

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 2 Overview  The European XFEL Project  Wakefield Calculations for the XFEL  Cavity and Coupler Wakes  Collimators  High-Frequency Impedances  Resistive, Roughness, Oxide Layer Wakes  Wakefields in Undulator Section  Impedance Database  Start-to-End Simulations with Wakes  Impact of Wakes on FEL Performance  Challenges

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 3 The European XFEL Project

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 4 The European XFEL Project Linac Coherent Light Source (LCLS) Spring-8 Angstrom Compact Laser (SACLA) European XFEL LocationUSAJapanDeutschland Start of commissioning Accelerator technology normal conducting superconducting Number of light flashes per second Minimum wavelength 0.15 nm0.1 nm0.05 nm Length of the facility 3000 m750 m3400 m

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 5 The European XFEL Project Gun 4 accelerator modules 12 accelerator modules main linac 3 rd harmonic RF SASE1 laser heater dogleg collimator BC2 BC1 BC0 bunch compressors σ s = 2 mm I peak = 50 A Q = 1 nC σ s = 1 mm I peak = 100 A E = 130 MeV σ s = 0.1 mm I peak = 1 kA E = 600 MeV σ s = mm I peak = 5-10 kA E = 2400 MeV Layout

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 6 Cavity and Coupler Wakes cavities + 9 belows =12m12m Cryomodule 1 Cryomodule 2 Cryomodule 3  Wakes for short bunches up to 50um have been studied  To reach the steady state solution 3 cryomodules are considered  For longitudinal case the wakes were studied earlier by A. Novokhatski et al *. The transverse results are calculated with ECHO **. ** Weiland T., Zagorodnov I, The Short-Range Transverse Wake Function for TESLA Accelerating Structure, DESY, TESLA , 2003 * Novokhatski A, Timm M, Weiland T. Single Bunch Energy Spread in the TESLA Cryomodule, DESY, TESLA , 1999 Wakefunctions of TESLA Cryomodule

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 7 Cavity and Coupler Wakes a – iris rtadius, g – cavity gap One-cell structure Periodic structure - fit parameters K.L.F.Bane, SLAC-PUB-9663, LCC-0116, 2003 Wakefunctions of TESLA Cryomodule

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 8 Cavity and Coupler Wakes Comparison of numerical (points) and analytical (lines) integral parameters for the third cryomodule Wakefunctions of TESLA Cryomodule

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 9 Cavity and Coupler Wakes Comparison of numerical (grays) and analytical (dashes) transverse wakes Transverse wake of TESLA Cryomodule

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 10 Cavity and Coupler Wakes Coupler Kick

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 11 Cavity and Coupler Wakes Coupler Kick

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 12 Cavity and Coupler Wakes Coupler Kick

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 13 Cavity and Coupler Wakes TESLA Report , DESY, 2004 Transverse Deflecting Structure

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 14 Cavity and Coupler Wakes Transverse Deflecting Structure

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 15 Cavity and Coupler Wakes Transverse Deflecting Structure

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 16 Cavity and Coupler Wakes Transverse Deflecting Structure

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 17 Cavity and Coupler Wakes Transverse Deflecting Structure

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 18 Cavity and Coupler Wakes Third-Harmonic Section

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 19 Cavity and Coupler Wakes Third-Harmonic Section

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 20 Collimator Wakes The bunch moves very close to the aperture wall! Tapered Collimators

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 21 Collimator Wakes I.Zagorodnov et al, DESY, TESLA , 2003 M.Dohlus et al., DESY, FEL Report , 2010

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 22 Collimator Wakes Zagorodnov I., Bane K., Wakefield Calculations for 3D Collimators, in Proceedings of EPAC 2006 Conference, Edinburgh, Scotland, 2006 (SLAC-PUB-11938) Short/Long 3D Step Collimators Kick factor vs. collimator length. A round collimator (left), a square or rectangular collimator (  = 0.3 mm, right).

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 23 Collimator Wakes Zagorodnov I., Bane K., Wakefield Calculations for 3D Collimators, in Proceedings of EPAC 2006 Conference, Edinburgh, Scotland, 2006 (SLAC-PUB-11938) Short/Long 3D Step Collimators long short

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 24 Collimator Wakes Short/Long Round Collimators shortlong short

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 25 High-Frequency Impedances, Optical Approximation

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 26 High-Frequency Impedances Transverse Impedance of Laser Mirror of RF Gun k y (0,0), V/pC k y (d), V/pC/ m k y (q), V/pC/ m Analytical Numerical k y (0,0), V/pC k y (d), V/pC/ m k y (q), V/pC/ m Analytical Numerical

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 27 High-Frequency Impedances Transverse Impedance of OTR Screens

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 28 High-Frequency Impedances Longitudinal Impedance of Round-to-Rectangular Transitions in Bunch Compressors

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 29 High-Frequency Impedances Impedances of Round Misaligned Pipe M. Dohlus et al, High Frequency Impedances in European XFEL, DESY , 2010

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 30 High-Frequency Impedances

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 31 Resistive, Roughness, Oxide Layer Wakes The effect of the oxide layer and the roughness can be taken into account through the inductive surface impedance M.Dohlus. TESLA , 2001 A.Tsakanian et al, TESLA-FEL Round Resistive Pipe with Roughness and Oxide Layer

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 32 Resistive, Roughness, Oxide Layer Wakes Round vs. Elliptical pipe Loss, V/pC Spread, V/pC round elliptical Mathcad script for arbitrary shape with roughness and oxide layer (author M. Dohlus)

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 33 Wakefields in Undulator

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 34 Wakefields in Undulator NElementfromto Effective LengthMaterialConduct. Relax. Time Oxid layer Rough ness mm 1/Omm/msecnm 1Eliptical pipe Aluminium3,66E+077,10E Pump Aluminium3,66E+087,10E Absorber/Round transition Copper5,80E+072,46E Round pipe Copper5,80E+072,46E Below BeCu 1742,78E+072,46E BPM Stainless Steel 3041,40E+062,40E Below BeCu 1742,78E+072,46E Round/Eliptical transition

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 35 Wakefields in Undulator Loss (Spread), V/pC step110 (43) taper 10mm74 (48) taper 20mm50 (43) step taper 10mm Absorber in 3D (2005)

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 36 Wakefields in Undulator Impedance of Eliptical-to-Round Transition with Absorber Dependence of the loss factor from the radius of the round pipe. The left graph presents the results without the absorber, the right graph presents the results with the absorber included. The black dots show the numerical results from CST Particle Studio.

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 37 Wakefields in Undulator Loss, V/pC Spread, V/pC Peak, V/pC pump pillbox Pillbox 2D/3D Pump

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 38 Wakefields in Undulator Energy Spread for Gaussian Bunch (25 μm)

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 39 Transitive Resistive and Geometrical Wakes in Undulator Wakefields in Undulator A.Tsakanian, PhD Thesis, 2010

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 40  There are hundreds of wakefield sources in XFEL beam line.  The bunch shape changes along the beam line.  Hence, a database with wake functions for all element is required.  The wake functions are not functions but distributions (generalized functions).  How to keep information about such functions?  We need a model. Impedance Database

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 41 singular part (cannot be tabulated directly) Wake function model regular part resistive inductive capacitive it describes singularities s -   Impedance Database

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 42 Pillbox Cavity Step-out transition Tapered collimator Impedance Database

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 43 Wake potential for arbitrary bunch shape derivative of the bunch shape Impedance Database

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 44 Impedance Database

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 45 Undulator wake for Q=1nC Total wake resistive wake bunch Impedance Database

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 46 Impedance Database Accelerator wakes. Q=1nC collimators cavities “warm” pipe

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 47 Impedance Database Longitudinal+Transverse Wakes 3D

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 48 Beam dynamics simulation (2010) ASTRA ( tracking with 3D space charge, DESY, K. Flötmann) W1 -TESLA cryomodule wake (TESLA Report , DESY, 2003) W3 - ACC39 wake (TESLA Report , DESY, 2004) TM - transverse matching to the design optics W3W3 W 1 TM 4W 1 TM 64W 1 12W 1 TM Full 3D simulation method (200 CPU, ~10 hours) CSRtrack (tracking through dipoles, DESY, M. Dohlus, T. Limberg) Start-to-End Simulations with Wakes

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 49 Start-to-End Simulations with Wakes CSRtrack+ASTRA (Guangyao Feng) Elegant (Hyunchang Jin) 2013 G.Feng et al. FEL Report , 2013

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 50 New Results and Comparison with Elegant Comparison with Elegant, Q = 1nC

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 51 New Results and Comparison with Elegant Comparison with Elegant, Q = 250 pC

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 52 total wake resistive wake bunch SASE for Nominal Bunch Parameters Mismatch and wake Q=1nC

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 53 Radiation Q=1 nC Averaged through 8000 slices +Wake+Taper +Wake SASE for Nominal Bunch Parameters

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 54 Mismatch and wake Q=250 pC Total wake resistive wake bunch SASE for Nominal Bunch Parameters

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 55 Radiation Q=250 pC Averaged through 2400 slices +Wake+Taper +Wake SASE for Nominal Bunch Parameters

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 56 Accelerator wakes. Q=1nC collimators cavities “warm” pipe Impact of Accelerator Wakes on SASE

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 57 Full wake Cavities wake Full wake Cavities wake current Impact of Accelerator Wakes on SASE Accelerator wakes. Q=1nC

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 58 full wake (full wake) x 4 (full wake) x 8 at z=85 m Beam matched in the peak current. Q=1nC current Impact of Accelerator Wakes on SASE

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 59 full wake (full wake) x 4 (full wake) x 8 Beam matched in the peak current. Q=1nC FWHM=0.14% FWHM=0.23% FWHM=0.6% Normalized spectrum at z=85 m Impact of Accelerator Wakes on SASE

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 60 Accelerator wakes. Q=250 pC. collimators cavities “warm” pipe Impact of Accelerator Wakes on SASE

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 61 Full wake Cavities wake Full wake Cavities wake Impact of Accelerator Wakes on SASE Accelerator wakes. Q=250 pC.

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 62 full wake (full wake) x 4 (full wake) x 8 Normalized spectrum at z=85 m FWHM=0.29% FWHM=0.30% FWHM=0.38% Impact of Accelerator Wakes on SASE Beam matched in the peak current. Q=250 pC

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 63 Summary Accelerator wake Bunch charge, nC Energy in the radiation pulse at z=175 m, mJ x x x Spectrum width at z=85m, % x x x We have considered only the longitudinal wake in a quite coarse model (adding the missed part of the accelerator wake at the undulator entrance). The transverse wakes are neglected. Impact of Accelerator Wakes on SASE

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 64 Challenges  Chamber Wakefields in Bunch Compressors  Impact of All (Longitudinal+Transverse) Wakes on the Results of Start-to-End Simulations  Transverse Impedance Database  Impact of Transverse Wakes on FEL Performance