1. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 1 Micro bunch evolution and „turbulent beams“ Sabrina Appel, Oliver Boine-Frankenheim, Thomas Weiland Beam physics for FAIR Bastenhaus, 6 July 2010

2. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 2 Outline  Introduction and Motivation  Beam quality  Multi-stream instability  Longitudinal space charge  Costing beam  Bunch beam  Micro bunch evolution  Envelope equation  Simulation  Measurement of the micro bunch parameter  Summary

3. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 3 Micro bunch evolution Measurement at SIS18  Time signal and frequency spectrum U 28+ SIS18 f SIS = 214 kHz T SIS = 4.67 μs ≈ 1 turn injection + ‘Schottky’ pickup (≈ 10-100 MHz) f UNILAC = 36 MHz BB12 ‘Micro bunch’ pickup (≈ 32-500 MHz) + Long. Emittance measurement E10  The long. beam quality is essential  Limit by the rf bucket  σ should be routinely measure  Difficult: Mutli-stream instability  The initial micro bunch parameter are imporant  They depends on  Injected longitudinal beam quality (form UNILAC)  Space charge effects in the transfer channel  Manipulated by two buncher cavities at the TK

4. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 4 Measurement results Micro bunch structure  ~ 1 turns inj.  U 73+  N ≈8×10 7  low current  debunching time:  theoretical:

5. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 5  Momentum spread dp/p: σ >0.5 ×10 -3  Jump of momentum spread at 3 mA  Momentum variation with current Measurement results Momentum spread dependence on UNILAC current  Momentum spread σ Momentum spread σ / 10 -3 UNILAC Current / mA FAIR design value August 09 Momentum spread σ / 10 -3 + Measured at 12 MHz ∆ Measured at 25 MHz ♢ Measured at 20 MHz Turns  Experiment: Constant UNILAC currents, number of injected turns is varied  Momentum spread increasing with the number of injected turns ⇒ parasitic loss in TK or broad band impedance in SIS18+ multi-stream instability? Ar 18+

6. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 6 Theoretical Model Filamentation of Phase Space  Single turn injection  Because the rf is off the debunching of bunches causes filamentation in phase space  Space charge leads to multi-steam instabilities  A turbulent coherent current fluctuation spectrum develops Length Δp/p

7. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 7 Multi-stream instability  With critical number of filaments:  Time to reach M thr -filaments: SimulationMeasurement

8. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 8 Longitudinal Space Charge  For an arbitrary perturbation of costing beam : A. M. Al-khateeb, Analytical calculation of the longitudinal space charge and resistive wall impedances in a smooth cylindrical pipe, PRE 2001  Cut-off harmonic:  Z 0 =337 Ω vacuum impedance

9. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 9 Stokes ‘ Law: With radial E-Field and azimuthal B-Field Final result: With geometry (integration) factor: Longitudinal Space Charge

10. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 10 Longitudinal Space Charge Longitudinal electric field for a ellipsoidal bunch  Nonlinearity of E z for long bunches  The g-Factor dependent on bunch length for dependent for short bunches  Reiser, Theory and design of charged particle beams Some literature:

11. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 11 Geometry-factor for bunched beams  3 D calculation with EM-Studio  Linear fit on E z to estimate the g-factor  Short bunches the field is linear  For long bunches became nonlinear Long bunch g=2.2 b/a=2 Short bunch g=0. 6 b/a=2

12. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 12 SIS18 region Geometry-factor for bunched beams b/a=2 z m /a=5 z m =6 m  PIC-Code:  Describe approximate the longitudinal E-Field  Discrepancy at the end, but there less particles  A constant geometry-factor can be used for SIS18 simulation

13. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 13 SIS18 region Geometry-factor for bunched beams  Also on the 3D calculation with EM-Studio linear fit for g  Bunches with offset: Dependency of g-factor for small offset is near to analytic solution and can be negligible  We found for a costing beam a modified g-factor  The dependency is logarithmic

14. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 14  Envelope equation for linear rf (Φ<90°) and space charge force: Longitudinal Simulations codes Simulation for linear space charge effects in TK 160 m E10B12 TK SIS18 UNILAC  z m bunch length, RF is a focusing force  Space charge force and emittance term have defocusing effects.  The code is used to optimize the buncher voltages for low momentum spread.  Bunchers are optimized for no current: Weak space charge Space charge dominant s / m ϕ /deg ( f=36 MHz) Linear rf (Φ<90°)

15. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 15  The integration of the Envelope equation give the longitudinal invariant  With the Total momentum spread Total momentum spread after a long drift follow: Envelope equation Total momentum spread

16. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 16 Longitudinal emittance measurement  To get small transversal plane the rhomb and quadrupoles is used  The dispersion is needed to monitor the energy spread (normal compensated)  To gain the phase distribution (or length) rf-chopper is used

17. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 17 Longitudinal emittance measurement l3l3 Linear transformation: D G : Dispersion on Profile grid F C : 47.93 °Vm/mm u A c : Chopper Amplitude f c =108 MHz: Copper frequency A: Mass of Ion in u

18. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 18 Longitudinal emittance measurement  In the TK the max. momentum spread larger than the FAIR design value  With buncher the max. momentum in SIS18 lower than the FAIR design value

19. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 19 Longitudinal emittance measurement  Initial parameter for Code the measurement parameter of micro bunch  Bunchers are optimized for I=3mA  For lowest current in agreement  For the other currents the measured max. momentum higher than as expected

20. 6 July 2010 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Sabrina Appel | 20 Summary ▪ Introduction and Motivation -Beam quality -„turbulent beams“ (Multi-stream instability) ▪ Longitudinal space charge -For costing beam -Bunch beam ▪ Micro bunch evolution -Envelope equation -Simulation -Measurement of the micro bunch parameter ▪ Summary