1. Christopher Gerth & Christopher Behrens Mini-Workshop on Longitudinal Diagnostics for FELs 11/12 March 2013, PSI, Villigen TDS induced energy spread

2. Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Outline 2 FLASH and longitudinal phase space measurements Time and energy resolution Origin and approximations for TDS induced energy spread Beam preparation for induced energy spread measurements Induced energy spread measurements

3. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Layout of FLASH 3 Two examples of longitudinal phase space measurements TDS streak Dispersion

4. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 4 View screen 1) TDS: Betatron motion of an electron passing a TDS at zero RF crossing: Layout Energy Spectrometer C y : Longitudinal-to-vertical linear Correlation (upstream TDS): for now assume C y = 0 S y : Shear Parameter (‘streak’ strength of TDS): => RMS time resolution: 2) Energy Spectrometer: Betatron motion of an electron: => RMS energy resolution: Basic parameters for design of energy spectrometer, but TDS induces energy spread! y(s) = y 0 (s) + C y (s) z ± S y (s) z

5. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Panofski-Wenzel Theorem 5 General relation for transverse momentum gain of electrons in RF fields: Deflection => Transverse gradient of longitudinal electric field to be present: Constant deflection within aperture (abberation-free) => depends linearly on diameter Longitudinal electric field of LOLA-type (disk-loaded travelling-wave) structure: For zero-crossing operation with deflecting voltage : c => Longitudinal transverse momentum gain: => off-axis electrons experience longitudinal momentum gain

6. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Induced Energy Spread 6 Remember: betatron motion of an electron passing a TDS at zero RF crossing: 1 st term: Express energy spread in rms values (beam size constant in TDS): => => Induced ‘uncorrelated’ energy spread due to finite beam size 3 rd term: Energy chirp along the bunch due to shearing inside the TDS y(s) = y 0 (s) + C y (s) z ± S y (s) z

7. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Elegant simulations for Gaussian bunches 7 => Same time resolution and energy spread but different chirp

8. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 How to measure this? 8 How to measure the energy spread and chirp: 1)Uncompressed bunches (on-crest acceleration): => too long to fit on the screen for larger shear parameters S 2)Compressed bunches: => energy spread increased due to compression ~ C · ΔE 0 => energy spread due to non-linear effects (CSR, space charge) => Produce short bunches by using the collimator in the first bunch compressor to cut away low energy tails at on-crest operation (only ACC1, 3 rd harmonic linearizer off)

9. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Beam preparation 9 On-crest beam Only ACC1 ACC39 off

10. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Beam preparation measured with TDS 10

11. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Data analysis 11 Left: Longitudinal phase space measurements for different deflecting voltages V 0 of the TDS. The achieved longitudinal resolution increases from plot (1) to (4). Linear energy chirp between ±1.5σ. Right: Slice energy spread for 3 slices with slice width equal to the time resolution.

12. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Measured induced energy spread 12

13. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Summary 13 Induced energy spread needs to be taken into account in design of energy spectrometer Results presented at DIPAC 2009 and DIPAC 2011 Latest results (January 2011) still not evaluated  => to be published in a consistent way in refereed journal …

14. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Outlook 14

15. TDS induced energy spread Christopher Gerth Mini-Workshop on Longitudinal Diagnostics for FELs – 11/12 \Mar 2013 Appendix 15