HOMDYN ( H igher O rder M odes DYN amics) Massimo.Ferrario@LNF.INFN.IT Acknowledgements:

1. HOMDYN (Higher Order Modes DYNamics) Massimo.Ferrario@LNF.INFN.IT Acknowledgements: J. B. Rosensweig, L. Serafini, J.P. Carneiro, J. Clendenin, H. Edwards, V. Fusco, L. Giannessi, M. Migliorati, A. Mosnier, D.T. Palmer, L. Palumbo, Ph. Piot, M. Quattromini ,T. Ronsivalle, J. Sekutowicz, F. Tazzioli.

2. Historical motivation: Superconducting Photo-injectors Requirements: Relativistic and Non-Relativistic Beams ==> Space Charge Effects Long term multi-bunch beam cavity interaction (msec-1000 bunches) ==> Transients, Beam Loading, HOM excitation

3. Space Charge Self Consistent Code and Reasonable CPU Time

4. The HOMDYN model Normal Modes Expansion of Cavity fields We describe the field evolution under the slowly varying envelope approximation for each resonant mode Analytical propagation of field from bunch to bunch, including an external generator Longitudinal and Transverse Beam Laminarity We describe the bunch dynamics of a uniform charged cylinder under the Multi-Slice approximation Analytically computation of slice Space Charge Fields

6. Artistic view of the Envelope Equations

7. Dx(t) L(t) Rs(t) Dt Multi-Slice approximation and Envelope Equations:

8. Space Charge Field: Aspect Ratio: Longitudinal Component (on axis) Radial Component (on envelope)

9. Rs Rs L g = 10 g = 1 g = 5

10. Beam Generation and Cathode Image Charges: e+ e- No Image Charges With Images Charges

11. Y X Elliptical cross section bunch R*

12. Space Charge Solenoid Quadrupoles Undulator RF Focusing SW+TW Beam Line

13. Cylindrical Symmetry Elliptical Symmetry

14. Undulator (Compressor?) Lc

15. TW structures

16. Wake Fields Convolution with a Uniform charge distribution Delta Wake Function V/pc/m MV/m m m Wake field along a 40 mm bunch

18. Comparison with PARMELA/UCLA ==> good agreement

19. Comparison HOMDYN with ASTRA (Ph. Piot)

21. Gun 9-cells TESLA structure Quads PepperPot Experimental validation at the A0 photoinjector (J. P. Carneiro et al.) 1.6 cells gun, 1.3 GHz, 40 MV/m peak field, 1.3 KG solenoid 9 cells Tesla structure, 1.3 GHz, 15 MV/m accelerating field Solenoid Scan @ 8nC Emittance (mm-mrad) computed by HOMDYN and PARMELA/Orsay

22. Homdyn Parmela

23. INPUTDECK FIELD.SEK FIELD.POI HOMDYN HBUNCH.OUT HTWISS.OUT HSCREEN.OUT HSPACE.OUT HFEL.OUT HSLICES.OUT HSUM.OUT

24. INPUTDECK - 1 (the beam line) t0 TEND H1 NLOOP iprint IPR2 -1.d-1 200.d-9 1.d-12 3000 1 10 ZETA0 ZSTOP EMEV SPREAD 0.00045d0 33.d0d0 1.d-6 0.d0 MAXB reprate IPART CHARGE DLBUNCH IGA carflut LCOOP 1 1000 1 1.d-9 -11.653d-12 55 0.d0 300.d-6 ISAVE IREAD ZSAVE 0 0 8.1d0 iflat 0 XEMIT XBUNCH XPRIME ITWISS 0.3d-6 1.d-3 0.d0 0 YEMIT YBUNCH YPRIME ICAT BZCAT 0.3d-6 1.d-3 0.d0 0 0 IPOI ISOL ISHIELD IQUAD ICAV IFOUR ITWA ISWA IWIG iplas ifoil ZSCREEN 3 0 0 13 1 0 2 0 1 0 0 33.d0 ISCAN STEP 11 -0.1d0

25. INPUTDECK - 2 (the bunch) t0 TEND H1 NLOOP iprint IPR2 -1.d-1 200.d-9 1.d-12 3000 1 10 ZETA0 ZSTOP EMEVSPREAD 0.00045d0 33.d0d0 1.d-6 0.d0 MAXB reprate IPARTCHARGE DLBUNCH IGA carflut LCOOP 1 1000 1 1.d-9 -11.653d-12 55 0.d0 300.d-6 ISAVE IREAD ZSAVE 0 0 8.1d0 iflat 0 XEMIT XBUNCH XPRIME ITWISS 0.3d-6 1.d-3 0.d0 0 YEMIT YBUNCH YPRIME ICAT BZCAT 0.3d-6 1.d-3 0.d0 0 0 IPOI ISOL ISHIELD IQUAD ICAV IFOUR ITWA ISWA IWIG iplas ifoil ZSCREEN 3 0 0 13 1 0 2 0 1 0 0 33.d0 ISCAN STEP 11 -0.1d0 HREAD.COR

26. INPUTDECK - 3 (integration step) t0 TENDH1 NLOOP iprint IPR2 -1.d-1 200.d-9 1.d-12 3000 1 10 ZETA0ZSTOP EMEV SPREAD 0.00045d0 33.d0d0 1.d-6 0.d0 MAXB reprate IPART CHARGE DLBUNCH IGA carflut LCOOP 1 1000 1 1.d-9 -11.653d-12 55 0.d0 300.d-6 ISAVE IREAD ZSAVE 0 0 8.1d0 iflat 0 XEMIT XBUNCH XPRIME ITWISS 0.3d-6 1.d-3 0.d0 0 YEMIT YBUNCH YPRIME ICAT BZCAT 0.3d-6 1.d-3 0.d0 0 0 IPOI ISOL ISHIELD IQUAD ICAV IFOUR ITWA ISWA IWIG iplas ifoil ZSCREEN 3 0 0 13 1 0 2 0 1 0 0 33.d0 ISCAN STEP 11 -0.1d0

27. saving output data in HBUNCH.OUT and HTWISS.OUT every dt1=TEND/NLOOP saving output data in HSPACE.OUT every dt2=dt1*IPR2 t0 TEND H1 NLOOP iprint IPR2 -1.d-1 200.d-9 1.d-12 3000 1 10 ZETA0 ZSTOP EMEV SPREAD 0.00045d0 33.d0d0 1.d-6 0.d0 MAXB reprate IPART CHARGE DLBUNCH IGA carflut LCOOP 1 1000 1 1.d-9 -11.653d-12 55 0.d0 300.d-6 ISAVE IREAD ZSAVE 0 0 8.1d0 iflat 0 XEMIT XBUNCH XPRIME ITWISS 0.3d-6 1.d-3 0.d0 0 YEMIT YBUNCH YPRIME ICAT BZCAT 0.3d-6 1.d-3 0.d0 0 0 IPOI ISOL ISHIELD IQUAD ICAV IFOUR ITWA ISWA IWIG iplas ifoil ZSCREEN 3 0 0 13 1 0 2 0 1 0 0 33.d0 ISCAN STEP 11 -0.1d0 HSAVE.COR Zw INPUTDECK - 4 (the output) saving outputs every DZ=ZSCREENin files HSCREEN.OUT and HFEL.OUT

28. INPUTDECK - 5 (parameters scan) t0 TEND H1 NLOOP iprint IPR2 -1.d-1 200.d-9 1.d-12 3000 1 10 ZETA0 ZSTOP EMEV SPREAD 0.00045d0 33.d0d0 1.d-6 0.d0 MAXB reprate IPART CHARGE DLBUNCH IGA carflut LCOOP 10 1000 1 1.d-9 -11.653d-12 55 0.d0 300.d-6 ISAVE IREAD ZSAVE 0 0 8.1d0 iflat 0 XEMIT XBUNCH XPRIME ITWISS 0.3d-6 1.d-3 0.d0 0 YEMIT YBUNCH YPRIME ICAT BZCAT 0.3d-6 1.d-3 0.d0 0 0 IPOI ISOL ISHIELD IQUAD ICAV IFOUR ITWA ISWA IWIG iplas ifoil ZSCREEN 3 0 0 13 1 0 2 0 1 0 0 33.d0 ISCANSTEP 11 -0.05d0 Range of the parameter scan MAXB*STEP

29. INPUTDECK - 6 (elements) SOLMAP ZSOLEN BMAX 'sanel' 1.3223500d0 0.06d0 'sanel' 4.900d0 0.0d0 'gtfbz' 0.000d0 0.27d0 ZQUAD QGRAD QLENGTH 8.636d0 4.7828d0 0.132d0 8.918d0 -4.7828d0 0.132d0 12.60d0 -0.2281d0 0.132d0 12.882d0 0.2281d0 0.132d0 14.875d0 4.8562d0 0.132d0 Z0CAV FI0 EPEAK IRISWF 0.d0 27.5d0 120.d6 -11.6d-3 ZK taug rfoff 0.00045d0 -10.d-6 0.801d0 nmod ik itrans 1 0 0 MODO WN QEX USTOR VSFH 'new45' 2856.d6 23616.74 0.39478e-05 0.999892d0 MODO Z0FR DNCEL ZINC WN PSI FI0 EP bl IRISWF 'twnew' 1.5d0 86 0.05248467 2856.d6 120. -8. 33.33d6 1 11.6d-3 Z0TWA FI0TW EPTWA 5.d0 -13.d0 33.33d6 Z0WIG ZPER NW BRMS KX NMODULES DRIFT 18.1d0 3.d-2 71 0.504d0 0.d0 6 0.36d0

31. HomDyn HomeWork for the SPARC project