Experimental Studies for Surface Roughness Wakefield at Brookhaven Accelerator Test Facility

1. Experimental Studies for Surface Roughness Wakefield at Brookhaven Accelerator Test Facility Feng Zhou UCLA/BNL Accelerator Test Facility Brookhaven National Laboratory Upton, NY11973, USA

2. Outline of talk  Why to do the Experiment  Experimental Setup  Experimental Results  Summary

3. Why to do the experiment?  The next generation linac-based FELs will use very short bunches with large peak current. The impedance caused by sub-micro imperfections in the vacuum tube may generate an additional energy spread and energy loss. It has been pointed out with simulations that the surface roughness wakefield in the undulator pipe is the main source.  Some models have been developed, however, different predictions are presented. Our experiment is to test these models.

4. Brief review of typical models • Inductive wakefield model(Bane and Stupakov) The surface roughness was represented as a collection of bumps of a given shape randomly distributed over a smooth surface. If the bump dimensions are small compared to the bunch length, the impedance is purely inductive, which can be given by: where then: h g

5.  Synchronous mode The roughness wakefield is associated with the excitation of resonant modes when its phase velocity slows down until to the speed of light. Two types of bumps’ distributions are assumed. -Periodic bumps (byBorgins and Papas, 1950; Bane, 1999; Stupakov, 2000.) The frequency of the lowest mode:

6. Its wake function is: where p is the period, h is the bump’s height and g is the half width of the bump. The loss factor -Random bumps(by Novokhatski, 1997) The random distributed bumps are more close to the real roughness in the pipe. The surface roughness can be represented as a dielectric layer. The frequency of the lowest mode: where is the dielectric constant, usually is 1.5.

7. Wakefield comparison Inductive model: Energy spread: yes Energy loss: no *0.001 Synchronous mode: Energy spread: yes Energy loss: yes *0.001

8. Experimental setup  In order to observe the wakefield effects at ATF, the larger-scale bumps are artifically fabricated due to the shorter beam pipe length and longer pulse length. Three beam pipes are fabricated. Smooth pipe

9. 0.3 mm 1.2mm The bumps are not periodically distributed. 0.6 mm 1.2mm

11. Schematic layout of the ATF beam line and its diagnostics • Pulse length measurements • Intrinsic and final energy spread • Charge measurements • BPMs up and downstream of pipe Faraday cup Faraday cup Test pipe FPOP1 IPOP3 High energy slit IPOP2 IPOP1 FPOP2 IQ3 IQ2

12. Beam optics  The energy spread is measured in term of horizontal beam size  simulated spectrometer resolution: 40 MeV beam energy Test beam pipe

13. Alignment In order to suppress the transverse wakefield, the tolerance, misalignment of the beam pipe with the beam line and the straightness of the beam pipe, is rigorously controlled. The straightness of the pipe is controlled below 50 m. The laser alignment is also used to make sure the electron beam is overlapped with the laser beam.

14. Experimental results  The “smooth” beam pipe is measured. It is measured that the energy spread at the end of the test pipe is at the same level of intrinsic energy spread, ~0.05%. Test beam pipe induced contribution is neglected. 16 pixels, 0.32 nC, 6.5 ps 18 pixels, 0.22 nC, 4.5 ps 19 pixels, 0.4 nC, 9.33 ps Note: ~30 pixels corresponds to 0.1% energy spread

15. The small-bump’s beam pipe is measured. And the wakefield effects are observed. The typical beam images: 20 pixels, 0.31 nC, 6.3 ps 34.7 pixels, 0.3 nC, 4.8 ps 38.4 pixels, 0.29 nC, 3.6 ps Note that 12 pixels correspond to 0.1% energy spread

16. Energy spread for small-bump’s pipe

17. Energy spread for larger-bump’s pipe

18. Energy loss for larger-bump’s pipe

19. Summary and future plan  The measured energy spread shows that surface roughness wakefield can not be explained only by the inductive impedance since the energy loss and additional energy spread is observed.  It hints an isolated synchronous mode may exist in the beam pipe. A single frequency of synchronous mode is fitted well with the measurements for both the energy spread and energy loss.  The dielectric constant, , used in the dielectric layer model to calculate the synchronous frequencies of our pipes is 1.3, which is comparable with 1.5 in the dielectric layer model.  The preliminary analysis shows that the surface roughness wakefield effects come from both a pure inductive impedance and a resistive part produced by an isolated synchronous mode.

20.  The real surface roughness is completely random. A new beam pipe with completely random distributed bumps is fabricated and will be measured in December.

21.  The individual bump’s size and bumps’ total number are completely the same as the 3rd beam pipe. The only difference is that bumps’ location in the new pipe is completely random. In the 3rd beam pipe, they are partly random.  It is expected to observe the less energy spread and energy loss compared with the 3rd pipe, since the mode will be decayed due to de-coherence.