Flat Beam Photoinjectors for Ultrafast Synchrotron Radiation Sources Steve Lidia

1. Flat Beam Photoinjectors for Ultrafast Synchrotron Radiation Sources Steve Lidia Lawrence Berkeley National Laboratory (and a host of others) WG1, ICFA Workshop, Chia Laguna

2. Femtosource Layout and Operation Deflecting cavities Beam dump 110 MeV linac 10 MeV RF gun Future energy recovery path 600 MeV linac • Generate ~ nC bunch in RF photocathode • Produce small vertical emittance from round beam • Accelerate to ~ 100 MeV • Inject into, followed by four passes through, 600 MeV linac • Produce time / angle correlation within bunch • Radiate in insertion devices and bend magnets • Compress x-ray pulse from ps scale to 50 fs scale Future energy recovery path Baseline beam power 25 kw Use energy recovery for beam power above ~ 100 kW

3. Femtosecond x-ray pulses from picosecond bunches Reduces problems associated with ultra-short electron bunches • Deflecting cavity introduces angle-time correlation into the ~ ps electron bunch • Electrons oscillate along the orbit • Crystal x-ray optics take advantage of the position-time correlation, or angle-time correlation to compress the pulse RF deflecting cavity Voltage U tail trajectory Bunch tilt ~ 140 µ-rad (rms) Radiation opening angle ~ 7 µ-rad @ 1Å >> sr ’ Undulator headtrajectory

4. Flat electron beam productionCritical technique for producing fs-scale x-ray pulses • Flat beam transformation • Generate circular cross-section beam from cathode in solenoidal magnetic field • Follow solenoid with quadrupole channel • Unity transform in x • p/2 phase advance in y • Quadrupole channel transforms beam shear developed on leaving solenoid into linear x,y distribution • Fermilab/NICADD Photoinjector Laboratory (FNPL)

5. Flat beam measurements Round beam image on fluorescent screen Flat beam image on fluorescent screen Beam image through slits for emittance measurement Flat electron beam productionCritical technique for producing fs-scale x-ray pulses • Fermilab/NICADD Photoinjector Laboratory (FNPL) • Demonstrated large emittance ratio (50:1) with small emittance 0.9 mm-mrad @ 1 nC • Limit in vertical emittance will arise from thermal and space charge effects • LBNL collaborating with Fermilab in flat-beam experiments and modeling • Remote operations from Berkeley • Computer modeling to develop understanding of sensitivity, optimize performance • Develop hardware for operations improvements

6. Emittance Compensation in Angular Momentum Dominated Beams • Envelope Equation (generic): R’’ + (g’/gb2)R’ + (g’’/2gb2)R + (eBz/2gbmc)2R = { (p/gbmc)2 + (en/gb)2 }/R3 + K/R pq = gmR2 dq/dt + eBzR2/2 • Cyclotron Phase parameterizes variations in RF gun gradient and solenoid field distribution. dq/dt = eBz/gm

7. Emittance compensation studies at A0 • Studies were performed to investigate the utility of standard emittance compensation in the angular momentum dominated regime, (pq/mc)/ethermal > ~20. • Vertical emittance of the round beam was measured at x3, the insertion point for the skew quad channel. • The Main solenoid current was set to provide different amounts of initial pq, while the Secondary solenoid was scanned over the range of its power supply (0-300A).The bucking coil was turned off. • Gun RF peak gradient ~40MV/m, 9-cell gradient ~10MV/m -> beam energy at exit ~15MeV. Launch phase at 40° from zero-crossing (optimized value from spectrometer measurements).

8. Cyclotron Phase Advance, HOMDYN Model of A0 Overlap of phase with varying cathode solenoid field.

9. Emittance Variations vs. Cyclotron Phase

10. Minimum Emittance Vs. Cyclotron Phase

11. Flat Beam Emittance Scan - A0 Measurements

12. A0 Measurements, cont’d. HOMDYN shows a Minimum at ~1.4p • Simple solenoid model. • Single bunch simulation. • Uniform distribution in r and z. 1.1

13. Flat beam emittance ratio, theory • Theory based on uniform solenoid channel, hard-edged fields, periodic quadrupole channel. • 4D Emittance is conserved: eRn2 = 1/4 { <r2>(<r’2> + <rq’>2) - <rr’>2 - <r2q’>2 }1/2 = {exey}1/2 • Inherited correlations are converted into emittance ratio: eyn/g= bR02/2 ex/ey = 1 + 4k2R02/R0’2 ~ B02R04/pz2eRn,thermal2 • Realistic solenoids and acceleration alter matching condition: bquad = (Rw2/R02) (2pw/eB0)

14. Flat beam modeling • Develop understanding of limitations and sensitivity of the flat-beam transformation • Explore designs • Matching lattice parameters • Effects of RF focusing • Space charge • Analytical model • Characterize circular beam in cylindrical modes • Transform to x – y modes • PARMELA modeling PARMELA model for A0, 1 nC

15. Emittance Ratio, Recent Measurements Measurements courtesy Y.Sun, U. Chicago 10ps laser pulse measurements differ between xL7 and xL8. 34ps laser pulse suffers from gross temporal modulation - spikes + shoulder.

16. Input waveguides Cathode cell Solenoidal magnets Accelerating cells Electric field p-mode RF gun development - key technology that drives pulse repetition rate up to 10-100 kHz • 64 MV/m on cathode • Three independently phased cells • ~ 8 MeV output beam energy for three cells • Limit power dissipation <~ 100 W/cm2

17. RF gun beam dynamics studiesHOMDYN, PARMELA, MAFIA • 64 MV/m on cathode • 43 MV/m cells 2&3, p mode • 10 ps bunch length 60 deg launch phase 1 nC

18. RF gun developmentANSYS model Surface electric and magnetic fields Temperature above cooling water

19. Future Studies • A0 Work • Develop simulation tools to better model pulse structure and multi-bunch averaging. • Identify matching conditions for different Main solenoid fields. • Measure emittance ratio, compare to scaling law. • Femtosource Injector • Complete ANSYS study, finalize gun RF cavity design. • Study solutions from MAFIA, PARMELA, HOMDYN to optimize solenoid fields. • Design skew quadrupole channel. Look for more robust solutions than simple triplet.