1. Institut Theorie Elektromagnetischer Felder Technische Universität Darmstadt, Fachbereich Elektrotechnik und Informationstechnik Schloßgartenstr. 8, 64289 Darmstadt, Germany mueller@temf.tu-darmstadt.de, www.TEMF.de Lab Report TEMF, TU Darmstadt W. Ackermann, R. Cee, R. Hampel, W.F.O. Müller, S. Setzer, T. Weiland, I. Zagorodnov TESLA Collaboration Meeting INFN, Frascati, 05/26/03

2. 1 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Outline  RF Design of a Booster for PITZ (R. Cee)  Dark Current Simulations for the PITZ-RF-Gun (W. Ackermann, S. Setzer)  Wake Fields in Long Structures e.g. Collimators (I. Zagorodnov)

3. 2 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03  /2-accelerating mode  /2-coupling mode Booster Geometry coupling window 2 cells coupling cell (cc) nose cone (drift tube) y z 2 cells P P Biperiodic Structure operated in the  /2-mode accelerating cell (ac)

4. 3 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03  /2-Modes Tuning Procedure accelerating cell tuning E E r ac = 84.275 mm  am = 1.300 GHz coupling cell tuning MM r cc = 64.791 mm  cm = 1.300 GHz end cell tuning E r ec = 85.290 mm  am = 1.300 GHz

5. 4 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Tuned Cavity with Nine Cells am = 1.29999 GHz EzEz ac = 1.3007 GHz; k 2 ac = -0.1% cc = 1.3040 GHz; k 2 cc = -0.6% k 1 = -10.1%; Dispersion CurveField on Axis z

6. 5 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Final Layout Design parameters: r acell 84.275 mm r irisin 12.0 mm r irisout 28.0 mm r ccell 64.791 mm r endcell 85.290 mm l hccell 3.0 mm l win 14.0 mm l hacell 40.6525 mm r winin 35.0 mm r winout r ccell a win 40.0° Geometry: r irisin r ccell r irisout l nose l win l hccell l hacell r acell quality factor Q22,470 eff. shunt imp. R s 24.2 M  /m R s /Q 1.1 k  /m field flatness2.1 % Electrical properties: y x y z a win r winin r winout

7. 6 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Beam Dynamics Simulation (ASTRA) booster Transverse Emittance and Beam Width Energy max. |E z |-field in gun50.0 MV/m max. |B z |-field in gun200.0 mT max. |E z |-field in booster30.0 MV/m booster z-position1.9 m Field parameters: # of macro particles1000 bunch charge-1.0 nC plateau length / rise time20.0 ps / 2.0 ps rms-bunch width (uniform)0.75 mm Beam parameters:

8. 7 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Outline  RF Design of a Booster for PITZ (R. Cee)  Dark Current Simulations for the PITZ-RF-Gun (W. Ackermann, S. Setzer)  Wake Fields in Long Structures e.g. Collimators (I. Zagorodnov)

9. 8 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Potential dark current emitting areas MWS model of the RF-Gun Fowler-Nordheim equation Accelerating FieldSolenoid Field PITZ RF Gun

10. 9 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Equation of motion Integration in time Implicit approximation Used Leap-Frog Tracking Algorithmus

11. 10 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Trajectories of electrons starting at the iris (E = 40 MV/m, I sol = 100 A) Start from Iris

12. 11 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Trajectories of electrons starting at the cathode (E = 40 MV/m, different launching phases) Start from Kathod

13. 12 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Dark current vs. Solenoid current (E = 40 MV/m) Measurement vs. Simulation

14. 13 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Dark Current vs. El. Field Strength (Different solenoid currents) Fowler-Nordheim

15. 14 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Outline  RF Design of a Booster for PITZ (R. Cee)  Dark Current Simulations for the PITZ-RF-Gun (W. Ackermann, S. Setzer)  Wake Fields in Long Structures e.g. Collimators (I. Zagorodnov)

16. 15 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Short bunches in long structures new code (ECHO) zero dispersion in longitudinal direction. staircase free (second order convergent) moving mesh easily (mesh step = time step) longitudinal + transversal Motivation

17. 16 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Transverse wake function 1 8 1 8 1 8 8 cavities + 9 belows =12m12m 3 cryomodules = 36 meters Cryomodule 1 Cryomodule 2 Cryomodule 3 Transverse wakes for short bunches up to have been studied. To reach steady state solution the structure from 3 cryomodules is considered. For longitudinal case the wakes were studied earlier by Novokhatski-Timm- Weiland *. The transverse results are new **. ** Weiland T., Zagorodnov I, The Short-Range Transverse Wake Function for TESLA Accelerating Structure, DESY, TESLA-2003-19, 2003 * Novokhatski A, Timm M, Weiland T. Single Bunch Energy Spread in the TESLA Cryomodule, DESY, TESLA-1999-16, 1999

18. 17 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Transverse wake function The wake functions at short distance are approximately related by (1) (2) a – iris rtadius, g – cavity gap One-cell structure Periodic structure - fit parameters – relations (1), (2) hold exactly – only relation (2) holds exactly K.L.F.Bane, SLAC-PUB-9663, LCC-0116, 2003 Different behavior!

19. 18 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Single-Cell Structure Middle cell with pipe radius - cell period in the TESLA cavity Wake functions obtained from the fit of numerical data to analytical formulas Comparison of numerical (points) and analytical (lines) integral parameters for the TESLA single-cell structure.

20. 19 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Periodic Structure Structure of 144 cells cells are required to reach steady state solution Comparison of numerical (pionts) and analytical (lines) integral parameters for the periodic structure Fit parameters

21. 20 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 TESLA Structure Comparison of numerical (points) and analytical (lines) integral parameters for the third cryomodule 1 8 1 8 1 8 Like periodic structure!

22. 21 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 TESLA Structure Comparison of numerical (grays) and analytical (dashes) transverse wakes Comparison of numerical (grays) and analytical (dashes) longitudinal wakes for the third cryomodule

23. 22 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 TESLA Structure Kick factor/V/pC/m Numeri -cal Analyti- cal TDR 1000138137153 700109108130 50085.485.1111 40072.572.299.6 30058.157.986.8 25050.250.179.6 12528.828.356.9 7518.218.144.3 5012.812.636.3 Loss factor/V/pC Numeri- cal Analyti- cal TDR 100086.490.290.4 70095.995.895.6 500105104103 400110 108 300117116114 250122120117 125135133128 75138141134 50143146138 Comparison of numerical and analytical loss factors for the third cryomodule TDR formula for transversal wake shows one cell behavior and overestimates the kick Comparison of numerical and analytical kick factors for the third cryomodule Correct! Overestimates!

24. 23 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Collimators Longitudinal wake dependence on the collimator angle

25. 24 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Collimators Transverse wake dependence on the collimator angle Zagorodnov I.,Weiland T., Bane K., Numerical Calculation of Small-Angle Collimator Wakefields for Short Bunches, DESY, TESLA-2003-18, 2003 The numerical results and analytical estimations of K. Yokoya confirm each other up to extremely small angles and short bunches. K. Yokoya, Impedance of Slowly Tapered Structures, Tech. Rep. SL/90-88 (AP), CERN, 1990.

26. 25 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Comparison with experiment sigma, mm Kick factors, V/pC/mm MeasuredSimulatedAnalytical 1.21.20 0.11.2681.34 0.651.40 0.11.9082.48  mrad 19mm 51mm 1.9mm Geometry of experiment collimator at SLAC (the real device has a square form) Coincide! Differ?!

27. 26 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03 Collimator Form Optimization Collimator geometry optimization. Optimum d ~ 4.5mm Geometry of the “step+taper” collimator Work together with M.Dohlus and M. Koerfer (DESY)

28. 27 TEMF, TU Darmstadt TESLA Meeting, INFN, Frascati, 05/26/03