1. A single-shot method for measuring fs bunches in linac-based FELs Z. Huang, K. Bane, Y. Ding, P. Emma

2. Growing interests in a few fs and sub-fs x-ray pulses Introduction We (and LCLS users) would like to know the compressed bunch length of the LCLS low charge (20 pC) beam LCLS S-band transverse cavity resolution is limit at 10~20 fs (X-band TCAV resolution ~ 4x smaller) Needs techniques with1-fs resolution (or even lower) Traditional RF zero-phasing is insufficient in measuring very short bunches because of its sensitive to the initial energy spread A longitudinal mapping technique developed by T. Smith’s group overcomes this limitation of RF zero-phasing We propose to use this technique to measure fs bunches in LCLS (taking into account wakefield of a long linac, SLAC-PUB-14104, 2010)

3. Measurement of 60-  m FEL microbunching at Stanford, 2000 Initially proposed by E. Crosson et al., 1995

4. BC2 4.3 GeV add a diagnostic chicane R 56 ’ Run L3 at zero crossing (-90 deg) h 3 L2 (  2 ) To high-resolution energy spectrometer Slightly adjust BC2 R 56 Final energy spread/profile corresponds to short bunch length/profile Wakefield of long linac must be taken into account z zzzz Over-compression  Zero-crossing Apply this method to measure fs bunches Diagnostic chicane can be part of BC2

5. Run LiTrack with 20 pC setup (L2 phase at -31 deg, under-compression) Run L3 at -90 deg (10 GeV over 4.3 GeV leads to ) Run L3 at -90 deg (10 GeV over 4.3 GeV leads to h 3 = 139 m -1 ) Increase BC2 R56 by Increase BC2 R56 by R 56 ’ = -1/ h 3 = -7.18 mm Turn off Linac-3 wake (discussed in next slides) LCLS low charge example After nominal BC2 After adjusted BC2 and L3 Needs to measure ~1e-4 energy spread with a high-resolution spectrometer

6. L3 wake introduces an additional energy spread to the measurement For very short bunches (<10  m), wake-induced energy spread (primarily a linear chirp) is independent of bunch length Linac Wakefieldz zzzz Over-compression Zero-phasing With wakez zzzz More over-compression Zero-crossing with wake Wakefield un-correctedWakefield corrected This simple wake-correction scheme works for almost arbitrary (short) bunch length we want to measure! N: # of e - L: L3 length a: iris radius

7. Linac-3 wake can be corrected by a bit more over-compression Using stronger chirp in Linac-2 Or using stronger R56 in BC2 I 2 is peak current in L2 (same for all BC2 compression settings) I A =17 kA, h 3 is L3 chirp by RF zero-phasing Wakefield compensation Preferred wake-correction method is by shifting R 56 of BC2, which needs to be increased by ~8.08 mm R 56 ’ (= -7.18 mm ) and R 56 ’ (= -7.18 mm = -1/ h 3 ) and  R 56 (≈ -0.9 mm for wake compensation)

8. Wakefield compensation by changing R 56 R 56 ’ = -8.08 mm Real bunch length E-spread/chirp Run LiTrack with 20 pC (L2 phase at -31 deg, under-compression) Run L3 at -90 deg (10 GeV over 553 m leads to ) Run L3 at -90 deg (10 GeV over 553 m leads to h 3 = 139 m -1 ) Turn on Linac-3 wake Increase BC2 R56 by Increase BC2 R56 by R 56 ’=-1/ h 3 = -7.18 mm Wakefield un-corrected +  R 56 Increase BC2 R56 by R 56 ’+  R 56 = -8.08 mm Wakefield corrected

9. A-line as a high-resolution spectrometer Spectrometer screen (PR18)  x = -6.4 m  x = 100 m Energy resolution ~1×10 -5 Spectrometer screen (PR18)  x = -6.4 m  x = 100 m Energy resolution ~1×10 -5

10. Elegant simulation (20 pC, L2 at -31.5 deg) L3ENDBC2 END A-line PR18 ~ 2 mm

11. RMS bunch length (Elegant simulations) Temporal resolution = Energy resolution (~1×10 -5 ) divides by Temporal resolution = Energy resolution (~1×10 -5 ) divides by h 3 ~ 100 m -1 = 0.1 um or 0.3 fs Wakefield/CSR/LSC add a systematic error ~0.5 fs

12. Summary A single-shot method for measuring fs bunches is studied An experimental test at the LCLS using the A-line spectrometer is planned The method requires no extra hardware (besides a high- resolution spectrometer) and may be applicable to other XFEL facilities Thanks R. Iverson, J. Frisch, H. Loos et al. for reviving the A-line spectrometer and for many useful discussions

13. Backup slides

14. Phase shift agrees with theory Wake effect can be corrected empirically by identifying full compression phase through CSR bunch length monitor Real bunch length E-spread/chirp (shift  2 by 1°) Wakefield compensation by shifting L2 phase J. Frisch R 56 ’ = -7.18 mm